Modeling Municipal Solid Waste Management System under Uncertainty
|
|
- Christal Thornton
- 6 years ago
- Views:
Transcription
1 Journal of the Air & Waste Management Association ISSN: (Print) (Online) Journal homepage: Modeling Municipal Solid Waste Management System under Uncertainty Yongping Li & Guohe Huang o cite this article: Yongping Li & Guohe Huang (2010) Modeling Municipal Solid Waste Management System under Uncertainty, Journal of the Air & Waste Management Association, 60:4, 49-45, DOI: / o link to this article: Published online: 22 Feb Submit your article to this journal Article views: 199 View related articles Citing articles: 6 View citing articles Full erms & Conditions of access and use can be found at Download by: [ ] Date: 0 January 2018, At: 16:55
2 ECHNICAL PAPER ISSN: J. Air & Waste Manage. Assoc. 60:49 45 DOI:10.155/ Copyright 2010 Air & Waste Management Association Modeling Municipal Solid Waste Management System under Uncertainty Yongping Li and Guohe Huang Research Academy of Energy and Environmental Studies, North China Electric Power University, Beijing , People s Republic of China Downloaded by [ ] at 16:55 0 January 2018 ABSRAC In this study, a dynamic inexact waste management (DIWM) model is developed for identifying optimal waste-flow-allocation and facility-capacity-expansion strategies under uncertainty and is based on an inexact scenario-based probabilistic programming (ISPP) approach. he DIWM model can handle uncertainties presented as interval values and probability distributions, and it can support assessing the risk of violating system constraints. Several violation levels for facility-capacity and waste-diversion constraints are examined. Solutions associated with different risks of constraint violation were generated. he modeling results are valuable for supporting the planning of the study city s municipal solid waste (MSW) management practices, the long-term capacity expansion for waste management system, and the identification of desired policies regarding waste diversion. Sensitivity analyses are also undertaken to demonstrate that the violations of different constraints have varied effects on the planning of waste-flow allocation, facility expansion, and waste management cost. INRODUCION Many optimization techniques have been developed for supporting decisions of municipal solid waste (MSW) management and evaluating relevant operation and investment policies since the 1960s 1 ; they have involved linear, dynamic, integer, and multiobjective programming methods. For example, Kirca and Erkip 2 formulated IMPLICAIONS In MSW management systems, uncertainties exist in various parameters, impact factors, and waste disposal processes that lead to difficulties in identifying desired alternatives for managing waste under economic objectives and environmental concerns. he developed DIWM model has advantages in uncertainty reflection, dynamic facilitation, policy analysis, and risk assessment. In addition, it can address issues concerning planning for a cost-effective diversion program that targets reducing the MSW amount disposed of by landfills. he results obtained can be used to help MSW managers identify desired policies under various environmental, economic, and system-reliability conditions. a linear programming model for determining transfer station locations in the MSW management system of Istanbul, urkey. Baetz used dynamic programming to determine the optimal sizing and timing for landfills and waste-to-energy facilities. Or and Curi 4 used a mixed integer linear programming (MILP) model for improving solid waste collection and transportation system in the city of Izmir, urkey, to minimize the city s total solid waste collection and transportation costs. Kulcar 5 used a linear programming method for optimizing collection strategies under minimized waste transportation costs in a major urban area. Fiorucci et al. 6 developed a decision support system (DSS) for solid waste management planning in the city of Genova, Italy. Solano et al. 7,8 developed an integrated solid waste management (ISWM) model to assist in identifying desired solid waste management strategies that could satisfy cost, energy, and environmental emission objectives. Chang et al. 9 utilized an integer programming method to support the decisions of location and capacity for a material recovery facility in the city of San Antonio, X. However, in real-world MSW management problems, uncertainties exist in the related costs, impact factors, and objectives that may affect the optimization processes and the decision schemes generated. 10 he complexities could be further amplified by interactions among the uncertain parameters and through additional economic implications. Such complexities have placed many MSW management problems beyond deterministic programming methods. Previously, several efforts were made in developing various methods for dealing with uncertainties in MSW management systems. For example, Koo et al. 11 proposed a framework using a waste resources allocation program and fuzzy set theory to address tradeoffs among the objectives of economic efficiency, environmental quality, and administrative efficiency, such that an optimal site for a new hazardous waste treatment facility in southwestern Korea could be determined. Arey et al. 12 used a mixed optimization and probabilistic analysis approach for determining daily waste management practices in the municipalities of Hamilton and St. Catharines, Ontario, Canada. Chang et al. 1 proposed a fuzzy interval mixed integer multiobjective linear programming model for the evaluation of management strategies for solid waste management in a metropolitan region, demonstrating that uncertainties could be quantified by specific membership functions and interval numbers within a multiobjective analytical framework. Wilson and Baetz 14,15 developed a Volume 60 April 2010 Journal of the Air & Waste Management Association 49
3 Downloaded by [ ] at 16:55 0 January 2018 derived probability model for curbside waste collection activities that allowed for analyzing stochastic information in MSW management systems. Huang et al. 16 advanced an inexact fuzzy-stochastic MILP model for waste management planning in which fuzzy flexible programming was introduced into an interval-parameter chanceconstrained programming framework. Maqsood and Huang 17 explored an inexact two-stage programming model for planning solid waste management under uncertainty in which interval parameters were incorporated within a twostage stochastic optimization framework. Davila et al. 18 proposed a gray integer programming-based game theory for system optimization and cost-benefit analysis at two competing landfills in the Lower Rio Grande Valley, X. Li and Huang 19 developed an interval parameter minimax regret programming method for the planning of MSW management systems in which uncertainties were expressed as interval values and random variables without knowing their probability distributions. Although many previous efforts of MSW management and planning under uncertainty have been conducted, there are few studies focusing on a scenario-based multistage stochastic programming (MSP) method for waste management and planning. In fact, MSP was effective for handling uncertainties expressed as probability distributions and permitting revised decisions in each time stage on the basis of the information of sequentially realized uncertain events In MSP, decision variables are divided into two subsets: those that must be determined before the realizations of random variables are disclosed and those (recourse variables) that can be determined after the random variable values are available. In the past decades, several MSP methods were developed and applied to environmental management and energy systems planning ; unfortunately, few applications of MSP to waste management were reported. he chanceconstrained programming (CCP) method can effectively reflect the reliability of satisfying (or risk of violating) system constraints under uncertainty. It can provide information on the tradeoffs among the objective function value, tolerance values of the constraint, and the prescribed levels of probability that could be valuable to decision-makers for MSW management and planning. Interval-parameter chance-constrained programming (ICCP) is useful for dealing with uncertainties expressed as intervals and probabilities by introducing an interval-parameter programming (IPP) approach into the CCP framework. herefore, one potential approach for better accounting for uncertainties, risks, and policies for planning MSW management systems is to develop an inexact scenariobased probabilistic programming (ISPP) method on the basis of MSP and ICCP techniques. he objective of this study aims to develop a dynamic inexact waste management (DIWM) model for identification of optimal MSW management strategies under multiple uncertainties. he DIWM model is based on ISPP and MILP techniques. he developed DIWM model can (1) handle uncertainties (presented as intervals and probabilities) by constructing a set of scenarios that are representative for the universe of possible outcomes; (2) reflect risk levels of violating system constraints over a multistage context; and () facilitate dynamic analysis for decisions of timing, sizing, and siting in planning capacity expansion for waste management facilities under uncertainty. he modeling results will be useful for generating a range of decision alternatives under various environmental, socioeconomic, and system-reliability conditions. MEHODOLOGY First, a scenario-based MSP model can be formulated as follows 26 : Min f c 1 x 1 E 2 minc 2 x 2 E 2,..., 1 min x c x x 2 subject to A 1 x 1 b 1, 2 x 1 W 2 x 2 b 2, x 1 W x b, x 1, x 2,, x 0. (1a) (1b) where t (b t, c t, t, W t ), t 2,, and are random vectors of appropriate dimension. Assume that the probability associated with each realization of the random vector is known in advance and equal to p i (and i 1, 2,, m), the problem can be equivalently formulated as a linear program by assuming discrete distributions for the uncertain parameters. Convexity properties of the recourse value functions can be effectively used in the decomposition-based solution strategy In model 1, uncertainties can be conceptualized into the scenario tree, with a one-to-one correspondence between the previous random variable and one of the nodes (state of the system) in each stage. 22 However, randomness in other parameters (e.g., waste management facility capacities) also needs to be reflected. he CCP method can be used for dealing with this type of uncertainty and analyzing the risk of violating the uncertain constraints. 29 Consider a general probabilistic linear problem as follows: subject to Min CtX AtX Bt X 0 (2a) (2b) (2c) where X is a vector of decision variables, and A(t), B(t), and C(t) are sets with random elements defined on a probability space, t 29,0. CCP solves the above model by converting it into a deterministic version through (1) fixing a certain level of probability q i (q i [0,1]) for uncertain constraint i, which represents the admissible risk of violating constraint i; and (2) imposing 440 Journal of the Air & Waste Management Association Volume 60 April 2010
4 Downloaded by [ ] at 16:55 0 January 2018 the condition that the constraint should be satisfied with at least a probability level of 1 q i. he feasible solution set is thus subject to the following constraints 10,1 : PrA i tx b i t 1 q i, A i t At, i 1,2,...,m (a) Constraint a is generally nonlinear, and the set of feasible constraints is only convex for some particular cases, one of which is when elements of A i (t) are deterministic and b i (t) are random (for all q i values). Constraint a can be converted into a linear one as follows: A i tx b i t qi, i (b) where b i (t) qi F i 1 (q i ), given the cumulative distribution function (CDF) of b i (i.e., F i (b i )) and the probability of violating constraint i (i.e., q i ). he problem with constraint b is that linear constraints can only reflect the case when the left-hand-side coefficients (A) are deterministic. If both left- and right-hand sides (A and B) are uncertain, the set of feasible constraints may become more complicated; this brings about considerable difficulty to its practical application, particularly for largescale problems. 10,1,2 On the other hand, in many realworld situations, the distribution information may hardly be known, whereas only two bounds of each imprecise parameter can be identified as intervals. herefore, for reflecting uncertainties presented as intervals (in A and C), an extended consideration is the introduction of IPP technique into the CCP framework. his leads to an ICCP model as follows: subject to Min f C X PrA i tx b i t 1 q i, A i t A t, i 1,2,...,m (4a) (4b) x j 0, x j X, j 1,2,...,n (4c) where A {R } m n, C {R } 1 n, X {R } n 1, and R denote a set of interval numbers. An interval value can be defined as a number with known lower and upper bounds but unknown distribution information. 1 hen, model 4 can be converted into an equivalent deterministic version as follows: subject to Min f C X A i tx B t q, A i t A t, i 1,2,...,m (5a) (5b) x j 0, x j X, j 1,2,...,n (5c) where B (t) q {b i (t) qi i 1, 2,, m}. hen, to better reflect (1) uncertainties as presented in probabilities, intervals, and their combinations; (2) dynamics of the uncertainties as well as the relevant decisions; and () reliability of satisfying (or risk of violating) the system constraints under uncertainty, ICCP can be introduced into the above MSP framework. his leads to an ISPP model as follows: subject to Min f C t X t A rt X t B rt, r 1,2,...,m 1 ;,2,..., A it X t A itk Y tk w, itk i 1,2,...,m2 ;,2,...,; k 1,2,..., p tkd tk Y tk (6a) k 1 A st X t A st Y tk B s t qs, s 1,2,...,m ;,2,...,; k 1,2,..., x jt 0, x jt X t, j 1,2,...,n 1 ;,2,..., y jtk 0, y jtk Y tk, j 1,2,...,n 2 ;,2,...,; k 1,2,..., (6b) (6c) (6d) (6e) (6f) where p tk is probability of occurrence for scenario k in period t, with p tk 0 and k p 1 tk 1; is the number of t scenarios in period t, with the total being K t K 1 t ; X t are first-stage variables that must be determined before the realizations of random variables are disclosed; and Y tk are recourse variables that can be determined after the realized random variable values are available. A twostep method is proposed for solving model 6. he submodel for f can be formulated in the first step when the system objective is to be minimized; the other submodel (corresponding to f ) can then be formulated based on the solution of the first submodel. hrough combining solutions of the two submodels, solutions for the ISPP model under a set of q s (s 1, 2,, m ) levels can be obtained. Generally, the ISPP method can deal with uncertainties presented in terms of probabilities and intervals, as well as their combinations, through constructing a multilayer scenario tree. Moreover, the ISSP can reflect dynamics of the uncertainties and the relevant decisions. For all scenarios under consideration, a decision must be made at each stage on the basis of information about the actual realizations of the random variables and the earlier decisions; this allows corrective actions to be taken dynamically for the related policies and can thus help maximize the system benefit. Furthermore, it can be used for Volume 60 April 2010 Journal of the Air & Waste Management Association 441
5 Downloaded by [ ] at 16:55 0 January 2018 examining the reliability of satisfying (or the risk of violating) the system constraints under uncertainty; a range of violations for constraints is allowed that is related to tradeoffs between the system cost and the constraintviolation risk. CASE SUDY Statement of Problems In real-world MSW management problems, many impact factors and their interactions (e.g., uncertainties in economic and technical data, dynamic variation in system components, randomness in waste generation rates, policy analysis in waste-flow allocation, and limited resources and capacities) must be systematically evaluated in planning an integrated MSW system (as shown in Figure 1). he complexities could be further compounded by interactions among the uncertain and dynamic parameters and through additional economic implications caused by improper policies. For example, the MSW generation rates may vary among different consumer behaviors, different communities, and different periods; moreover, waste generation rate from a community could vary temporally, with the detailed level at a given time period being uncertain. Vehicle types, collection efficiencies, oil prices, and collection routes can also affect waste collection; the operation cost may be related to labor fees, equipment prices, energy prices, and management expenses that can result in uncertain waste management cost in the future. Furthermore, the decision for desired waste treatment approach is related to multiple criteria (e.g., environmental, social, and economic objectives) with the detailed practices (e.g., landfill, incineration, composting, and/or recycling) being interrelated and interactive to each other. herefore, incorporation of various uncertain and dynamic complexities within a general mathematical programming framework for improving the regional MSW management is desired. he city of Regina is located in western Canada. Its population is approximately 195,000, and the households generate residential wastes of 71,000 82,000 t/yr.,4 Figure 1. Interrelationships among various system components. Solid waste management in the city covers many areas, ranging from garbage collection to environmental protection. It involves the provision of specific and personal services to most of the residents (through waste collection and recovery) and indirect services to the entire community (through waste disposal and recovery). he generated solid wastes typically include paper, yard waste, food waste, plastics, metals, glass, wood, and other items. Consistent with many communities in western Canada, the city relies mostly on a sanitary landfill for disposal of its MSW. he landfill is located in the northeastern part of the city, occupying 97 ha with an actual landfilling area of 60 ha. Approximately 65,000 t/yr of MSW generated from the residential sector were buried at the landfill (nearly 90% of the total waste generated by households). he existing landfill is expected to be able to accept waste until 2011 or Because of the scarcity of land around the urban center and the growing opposition from the public with regard to landfill operation, the city is making efforts to divert waste with the ISWM approach to change the current practice of relying solely on the landfill for its waste disposal. Nevertheless, various complexities exist in such a diversion effort that can affect the detailed plans for the city s MSW management. On the basis of the city s waste management policy, a projected waste-flow level is preregulated. If this level is not exceeded, a regular (normal) cost to the system will result. However, if it is exceeded, the surplus waste flow will be disposed of at a premium, resulting in an excess cost (penalty) to the system (i.e., excess flow generated waste assigned quota). In addition, from a long-term planning point of view, the waste generation rate in the city will keep increasing because of the population increase and economic development; the waste management facilities will face problems of insufficiency in their capacities to meet the city s overall waste disposal demand in the future. Generally, the challenge for decision-makers is how to address the above uncertainties and dynamic complexities because of a lack of knowledge founded on an incomplete characterization, understanding, or measurement of the study system. 442 Journal of the Air & Waste Management Association Volume 60 April 2010
6 Downloaded by [ ] at 16:55 0 January 2018 able 1. echnical data. Waste generation levels and the associated probabilities (t/wk) Waste generation rate in period 1 Waste generation rate in period 2 Waste generation rate in period 17, 14 (0.125), 144, 1494 (0.280), 1495, 1577 (0.404), 1578, 1648 (0.191) 1418, 1510 (0.19), 1511, 1605 (0.575), 1606, 1702 (0.22) 1465, 1555 (0.185), 1556, 1648 (0.605), 1649, 1759 (0.210) Lower and upper bounds of regular waste flow (t/wk) o landfill 700, 950 (), 600, 850 (t 2), 500, 750 (t ) o composting facility 100, 200 (), 250, 00 (t 2), 00, 400 (t ) o recycling facility 200, 00 (), 00, 400 (t 2), 50, 450 (t ) Waste-diversion rate 75% (), 6% (t 2), 50% (t ) In detail, the main problems include the following questions: (1) What collection techniques should be used to enhance waste diversion activities? (2) What facilities should be adopted to meet the overall demand for waste disposal? () What is the cost-effective means for satisfying waste disposal and diversion requirements? and (4) What capacity for waste diversion should be expanded and/or developed? able 1 presents the waste generation rates and the associated probabilities, the relevant waste diversion able 2. Costs and revenues for waste management ($/t). goals, and the regular waste levels. he study time horizon is 15 yr, consisting of three 5-yr periods. As required by the authorities, 50% diversion of residential waste landfilled would be achievable within the planning horizon. able 2 provides collection and transportation costs for allowable and excess waste flows from the city to the three facilities, operating costs of the three facilities, penalties for surplus flows, and revenues from the composting and recycling facilities. Costs for waste collection and transportation are estimated based on the existing conditions in the collection areas, the average container size, collection frequency, collection mode (automatic and manual), and collection time (per load). he economic penalties are associated with (1) operating cost for excess waste flows (i.e., disposed locally to alternative and more expensive facilities), (2) transportation cost for excess flows to more remote facilities, and () extra expenses and/or fines caused by the improper policies. Consequently, the penalties are significantly higher than the regular costs. able presents the fixed and variable costs for capacity expansions of the three facilities. he cost and revenue data listed in ables 2 and are expressed in present values. he modeling parameters are mainly identified or assumed based on representative data from governmental reports and literatures. 9 Modeling Formulation In the study system, many factors and related processes are complex with multiperiod, multilayer, and multiuncertainty features. he developed ISPP method is capable Cost/Revenue t 2 t Normal cost for shipping regular waste o landfill 2.0, , , 2.98 o composting facility 68.0, , , o recycling facility 9.0, , , 70.1 Normal cost for treating regular waste Landfill 9.0, , , Composting facility 21.0, , , Recycling facility 61.0, , , 4.95 Normal cost for shipping regular residue Composting facility 1.68, , , 1.6 Recycling facility 1.47, , , 1.09 Normal revenue generated by regular waste Composting facility 5.0, , , 6.48 Recycling facility 45.0, , , 5.65 Penalty cost for shipping excess waste o landfill 48.0, , , 5.98 o composting facility 102.5, , , o recycling facility 141.0, , , 105. Penalty cost for treating excess waste Landfill 18.0, , , Composting facility 4.0, , , 27.2 Recycling facility 104.0, , , Penalty cost for shipping excess residue Composting facility 2.52, , , 2.04 Recycling facility 2.21, , , 1.6 Excess revenue generated by excess waste Composting facility 5.0, , , 6.48 Recycling facility 45.0, , , 5.65 Volume 60 April 2010 Journal of the Air & Waste Management Association 44
7 able. Capital parameters for facility expansion. Planning Period Parameter t 2 t Cost for landfill expansion Fixed cost ($10 6 ) 4.04, ,4.9.09,.72 Variable cost ($/t) 2.47, , ,2.45 Cost for composting facility development/expansion Fixed cost ($10 6 ) 2.10, , ,1.9 Variable cost ($/t) 2.00, ,2. 1.5,1.98 Cost for recycling facility expansion Fixed cost ($10 6 ) 2.78, , ,2.6 Variable cost ($/t) 6.5, , ,5.89 Downloaded by [ ] at 16:55 0 January 2018 of dealing with this type of problem. Moreover, MILP technique will be introduced into the ISPP framework to facilitate dynamic analysis for decisions of timing, sizing, and siting in planning capacity expansions for waste management facilities through constructing a multilayer scenario tree. Decisions for capacity expansion can then be made based on the progressively acquired information about the actual realizations of the random variables and the decisions in the previous stages; this allows corrective actions to be undertaken dynamically such that the relevant expansion costs can be minimized. hus, based on techniques of ISPP and MILP, a DIWM model can be formulated as follows: General Objective Function. (1) Cost for regular waste transportation and operation i 1 L t it R it OP it ] (7a) (2) Cost for excess waste transportation and operation i 1 L t p tkm itk DR it DP it (7b) k 1 () Cost for regular residue transportation and operation i 2 p tkflc 1t Y 1tk VLC 1t X 1tk k 1 p tkfc it Y itk VC it X itk k 1 (7e) (6) Revenue from composting and recycling facilities i 2 L t it RE it i 2 L t p tkm itk RM it (7f) k 1 Constraints. (1) Constraints of waste management facility capacity Pr t L t 1t M 1tk FE i it M itk i 2 t LC X 1tk, t 1,2,...,; k 1,2,..., 1q (7g) t it M itk Pr C i X itk, (7h) t 1,2,...,; i 2, ; k 1,2,...,1q (2) Constraints of waste flow to the landfill i 2 L t it FE i F it OP 1t (7c) Pr 1t M 1tk DG 1t WG, tk t; k 1,2,..., 1 q (7i) (4) Cost for excess residue transportation and operation i 2 L t p tkm itk FE i D it DP 1t (7d) k 1 (5) Capital cost for facility expansion () Constraints of waste disposal demand it M itk WG, tk t; i 1 k 1,2,..., (4) Constraints of regular waste flow (7j) 444 Journal of the Air & Waste Management Association Volume 60 April 2010
8 Downloaded by [ ] at 16:55 0 January 2018 Y itk it l it it u, i, t (7k) (5) Constraints of excess waste flow 0 M itk it, i, t; k 1,2,..., (7l) (6) Constraints of waste management facility expansion 1, 0, if capacity expansion is undertaken if otherwise, i, t; k 1,2,..., t Y 1tk 1, t 1,2,...,; k 1,2,..., (7m) (7n) X itk N itk Y itk, i, t; k 1,2,..., (7o) X itk 0, i, t; k 1,2,..., (7p) In the DIWM model, the objective function covers (1) expense for handling regular and probabilistic excess flows, (2) revenue from composting and recycling facilities, and () probabilistic expansion cost for the three facilities. he model includes continuous and binary decision variables. he binary variables represent the development or expansion options for waste management facilities in different periods (i.e., Y itk ); their solutions can be used for answering the questions related to timing, sizing, and siting for waste management facility development and/or expansion under uncertainty. he continuous variables represent the optimized waste flows from the city to the waste management facilities. Furthermore, the continuous variables include two subsets: those (the first-stage variables, it ) that must be determined before the random variables (i.e., waste generation rates) are known, and those (the recourse variables, M itk and X itk ) that will be determined after the random variables are disclosed. A set of chance constraints on waste management capacities and waste-diversion rates are considered that can help investigate the risks of violating the capacity and diversion constraints. In the DIWM model, fixed-charge cost functions (i.e., eq 7e) are used to reflect economies-of-scale (EOS) effects on the capacity-expansion costs. 25,28 he fixed cost is linked to the capacity expansion activity, whereas the variable cost is linked to the capacity expansion size. he total cost for facility expansion would increase with the capacity expanded; however, because of the fixed-charged cost function, the unit cost for facility expansion would be decreased with the amount of capacity expanded, which reflects the EOS effect on the expansion cost. For example, the unit cost for the landfill expansion in period 1 would be $[6.51, 8.05]/t when the landfill capacity expanded is 1 million t; in comparison, the unit cost for the landfill expansion in period 1 would be $[4.49, 5.6]/t when the capacity expanded is 2 million t. Several assumptions are made when formulating and solving the DIWM model, including (1) on the basis of the local waste management policies, an allowable waste-flow level from the city to each facility is preregulated (violation of this limit will lead to penalties in terms of raised transportation and operation costs); (2) all solid waste flows have to be shipped to a disposal site within a certain period after their generation and no mass loss is incurred in the transportation process; () construction or expansion of any facility should be completed within the time period during which it was initiated; (4) in this study, waste collection and disposal serve only the city s residential sector; (5) uncertainties associated with waste management facility capacity and waste-diversion rate are characterized as random variables with normal probability distributions; and (6) the models are converted into a linear programming model by assuming discrete distributions for the random variables. hen, the DIWM model can be transformed into two deterministic submodels that correspond to the lower and upper bounds of the desired objective. Interval solutions can then be obtained by sequentially solving the two submodels, which can be further interpreted for generating multiple decision alternatives for MSW management under uncertainty. Submodel 1: Min f L t it R it OP it i 1 subject to t i 1 L t p tkm itk DR it DP it k 1 L t it FE i F it OP 1t i 2 i 2 L t p tkm itk FE i D it DP 1t k 1 p tkflc 1t Y 1tk VLC 1t X 1tk k 1 i 2 i 2 p tkfc it Y itk VC it X itk k 1 L t it RE it i 2 (8a) L t p tkm itk RM it k 1 t L 1t M 1tk FE i it M itk LC q i 2 (8b) t X 1tk, t 1,2,...,; k 1,2,..., Volume 60 April 2010 Journal of the Air & Waste Management Association 445
9 t it M itk C i q X itk, i 2, ; k 1,2,..., t 1,2,...,; (8c) 1t M 1tk DG 1t q WG, tk t; k 1,2,...,Kt (8d) it M itk WG, tk t; k 1,2,...,Kt (8e) i 1 it l it it u, i, t (8f) 0 M itk it, i, t; k 1,2,..., (8g) subject to t L t 1topt M 1tk FE i itopt M itk i 2 t LC q X 1tk, t 1,2,...,; k 1,2,..., t itopt M itk C i q X itk, t 1,2,...,; i 2, ; k 1,2,..., (9b) (9c) Downloaded by [ ] at 16:55 0 January 2018 Y itk 1, 0, if capacity expansion is undertaken if otherwise, (8h) i, t; k 1,2,..., t Y 1tk 1, t 1,2,...,; k 1,2,..., (8i) Submodel 2: 0 X itk N itk Y itk, i, t; k 1,2,..., (8j) Min f L t itopt R it OP it i 1 i 1 L t p tkm itk DR it DP it k 1 L t itopt FE i F it OP 1t i 2 i 2 L t p tkm itk FE i D it DP 1t k 1 p tkflc 1t Y 1tk VLC 1t X 1tk k 1 i 2 p tkfc it Y itk VC it X itk k 1 L t itopt RE it i 2 i 2 L t p tkm itk RM it k 1 (9a) itopt M 1tk DG 1t q WG, tk t; k 1,2,...,Kt (9d) itopt M itk WG, tk t; k 1,2,...,Kt (9e) i 1 M itkopt M itk itopt, i, t; k 1,2,..., (9f) 1, if capacity expansion is undertaken Y itk 0, if otherwise, (9g) Y itk Y itkopt i, t; k 1,2,..., t Y 1tk 1, t 1,2,...,; k 1,2,..., (9h) X itkopt X itk N itk Y itk, i, t; k 1,2,..., (9i) where it opt, M itk opt, X itk opt, and Y itk opt are the solutions of submodel 1; M itk opt, X itk opt, and Y itk opt are the solutions of submodel 1. Solutions of DIWM model can then be obtained through integration of the solutions of submodels 1 and 2. he modeling results can be used for supporting decisions of the city s long-term MSW management, such as (1) identification of desired capacity expansion schemes for waste management facilities, (2) allocation of waste flows to suitable facilities, and () analysis of the tradeoff between the cost of waste management and the risk of system disruption. RESULS AND DISCUSSION Figure 2 presents the solutions for waste-flow-allocation patterns to the landfill (including the allowable and excess waste flows) under different waste-generation scenarios and constraint-violation levels (i.e., q levels). Scenario 1 (denoted as symbol LLL) means that the waste generation rates are low in all of the three periods; scenario 6 (denoted as symbol HHH) corresponds to high waste generation rates in the three periods. Moreover, excess flows would be generated if the allowable waste-flow levels as 446 Journal of the Air & Waste Management Association Volume 60 April 2010
10 Downloaded by [ ] at 16:55 0 January 2018 Figure 2. Waste flows to the landfill under different q levels for the (a) lower and (b) upper bounds. preregulated by the authority are exceeded; under such a condition, the total waste flows are the sum of allowable waste and probabilistic excess waste. he results indicate that the waste-flow-allocation patterns would vary with waste generation scenarios and constraint-violation levels (Figure 2). For example, under waste generation scenario MMM (i.e., when the city s waste generation rates are medium in all of the three periods with a joint probability of 14.05%), the total waste disposed of by the landfill would be [516.1, 5622.] 10 t when q 0.01, [5229.9, ] 10 t when q 0.05, and [514.4, 5800] 10 t when q 0.1. In comparison, under waste generation scenario HHH (i.e., when the city s waste generation rates are high in all of the three periods, with a joint probability of 0.9%), the waste allocated to the landfill would be [5625.8, 598.9] 10 t when q 0.01, [5724.6, ] 10 t when q 0.05, and [5809, ] 10 t when q 0.1. he solutions under the other waste-generation scenarios can be similarly interpreted based on the results as presented in Figure 2. In summary, waste flow disposed of by the landfill would increase as the q level raises; this is because an increased q level leads to a softened landfill capacity and a relaxed diversion requirement, whereas the landfill possesses the relatively low costs (regular and penalty costs) for disposing of waste compared with the other two facilities. he total waste flows (obtained from the DIWM model) diverted to the composting and recycling facilities are summarized in Figure. he waste-flow-allocation patterns would vary under different scenarios and q levels because of the temporal and spatial variations of waste generation scenarios and management conditions. For example, under scenario HHH, the optimized waste flows (including allowable and excess flows) treated by the composting facility would be [164.2, 182.9] 10, [1460.7, 1582.] 10, and [1460, ] 10 t under q 0.01, 0.05, and 0.1, respectively; the optimized flows diverted to the recycling facility would be [1551., ] 10, , and t under q 0.01, 0.05, and 0.1, respectively. Correspondingly, the total flows diverted would be [194.5, 85] 10 t under q 0.01, [095.6, 217.2] 10 t under q 0.05, and [02.7, 124] 10 t under q 0.1. In general, waste flows to the composting and recycling facilities should increase as the q level is raised because of the relaxed capacities of the two facilities; however, the results indicate that the waste flows to the two facilities would decrease with the q level. his is because an increased q level can also lead to a relaxed waste-diversion requirement, such that less waste flows would be treated by the two facilities because of their high collection and operation costs. In this study, the increased q level means a raised risk of violating the constraints of waste-management-facility capacities and waste-diversion rates (i.e., relaxed constraints), leading to different waste-management-facility expansion plans in the city. he results indicate that, under all q levels, the landfill would be expanded in period 2, whereas no expansion would be undertaken in periods 1 and. However, different waste generation rates and q levels would lead to varied expansion schemes for the landfill, as shown in Figure 4. For example, when the city s waste generation rates are low in all three periods, its landfill would be expanded with increments of [11.2, 40.7] 10 t under q 0.01, [06.7, 429.6] 10 t under q 0.05, and [08, 4.1] 10 t under q 0.1. In comparison, when the city s waste generation rates are high in all three periods, this facility would be expanded with increments of [41, 511.1] 10, [409.2, 519.7] 10, and [411.2, 524.4] 10 t under q 0.01, 0.05, and 0.1, respectively. Figure 5 presents the solutions for composting facility expansion schemes obtained from the DIWM model. he expansion plans for this facility would also be changed under different q levels. he results indicate that when q 0.01 this facility would be expanded under most of the scenarios over the planning horizon; in comparison, when q 0.05 and 0.1, this facility would only be expanded in period 1 under advantageous conditions, whereas no expansion would be undertaken in periods 2 and. Figure 6 provides the optimal expansion schemes for the recycling facility under q 0.01, 0.05, and 0.1. he results indicate that the recycling facility would be expanded with different Figure. otal waste flows diverted to the composting and recycling facilities for the (a) lower and (b) upper bounds. Volume 60 April 2010 Journal of the Air & Waste Management Association 447
11 Downloaded by [ ] at 16:55 0 January 2018 Figure 4. Expansion schemes for the landfill for the (a) lower and (b) upper bounds. increments in period 1 under the three q levels, whereas no expansion would be needed in periods 2 and. Figure 7 presents the total expanded diversion capacities (for composting and recycling facilities) under different q levels. he total expanded capacities for waste diversion would decrease as the q level is increased. In fact, an increased q level leads Figure 6. Expansion schemes for the recycling facility for the (a) lower and (b) upper bounds. to a decreased strictness for capacity constraint and a relaxed requirement for waste diversion synchronously, such that a lower diversion capacity-expansion level could be generated. Variations in q level also correspond to the decisionmakers preferences regarding the tradeoff between the total cost and the constraint-violation risk. Figure 8, a and b, shows the results for total cost from the DIWM model Figure 5. Expansion schemes for the composting facility for q (a) 0.01, (b) 0.05, and (c) 0.1. Figure 7. Expansion schemes for total diversion capacities for the (a) lower and (b) upper bounds. 448 Journal of the Air & Waste Management Association Volume 60 April 2010
12 Downloaded by [ ] at 16:55 0 January 2018 Figure 8. Costs for waste management activities under different q levels: (a) lower- and (b) upper-bound total cost, (c) lower and (d) upper cost for waste disposal, and (e) lower and (f) upper expansion cost. under a range of q levels (including the lower- and upperbound values, f ). he total costs for the city s waste management would be $[70.25, 96.97] 10 6 under q 0 (i.e., no violation on any constraint), $[69.80, 95.5] 10 6 under q 0.01, $[68.04, 9.49] 10 6 under q 0.05, and $[67.67, 9.0] 10 6 under q heir midvalues (i.e., f mid [f f ]/2) would be $ , $ , $ , and $ when q 0, 0.10, 0.05, and 0.10, respectively. Figure 8, c and d, shows the results for waste disposal cost under different q levels. he costs for directly disposing of waste would be $[57.92, 80.84] 10 6 under q 0, $[57.55, 80.29] 10 6 under q 0.01, $[57.58, 80.40] 10 6 under q 0.05, and $[57.2, 79.99] 10 6 under q Moreover, the expanses for waste-management-facility expansion would be $[12.2, 15.1] 10 6 (q 0), $[12.25, 15.06] 10 6 (q 0.01), $[10.46, 1.09] 10 6 (q 0.05) and $[10.4, 1.04] 10 6 (q 0.10), as shown in Figure 8, e and f. he results indicate that the total cost would decrease as q level is raised. his is because (1) an increased q level leads to a decreased strictness for the facility-capacity constraints and thus results in a lower capacity-expansion amount and a lower capital cost; and (2) an increased q level corresponds to a lower waste-diversion requirement, so that more waste flows would be allocated to the landfill and bring about a lower disposal of cost. In this study, two sensitivity analyses were undertaken to identify the effects of variations among different constraints on the objective value. Figure 9, a and b, show the results of the first sensitivity analysis (denoted as SA1) for examining the effects of facility-capacity constraint variation on the system cost under a range of q levels. In SA1, the waste-diversion rates were considered as a set of deterministic values (i.e., no violation on the wastediversion constraint). he total cost obtained would be $[70.14, 95.86] 10 6, $[68.98, 95.19] 10 6 and $[68.95, 95.10] 10 6 under q 0.01, 0.05, and 0.1, respectively. he corresponding mid-values of the total costs would be $8 10 6, $ and $ when q 0.10, 0.05, and 0.10, respectively. he mid-value of total cost would be $ when q 0. Consequently, the mid-cost variations would be $ (q 0.01), $ (q 0.05), and $ (q 0.1) when a set of chance constraints on waste-management-facility capacities were enforced. Figure 9, c and d, presents the results of the second sensitivity analysis (denoted as SA2) for the effects of waste-diversion variation on the objective value, through considering the facility-capacity constraints as a set of interval values (i.e., no violation on the waste-managementfacility constraint). he total cost obtained from SA2 would be $[69.89, 95.47] 10 6 (q 0.01), $[69.62, 95.17] 10 6 (q 0.05), and $[69.51, 95.10] 10 6 (q 0.1); correspondingly, their mid-values would be $ , $ , and $ when q 0.01, 0.05, and 0.10, respectively. he variations would be $ (q 0.01), $ (q 0.05), and $ (q 0.10), compared with the result under q 0. However, because of the potential for groundwater contamination, the scarcity of land near the urban center, and the growing opposition from the public with regard to landfill disposal, solid waste management is becoming an increasingly complex issue for Volume 60 April 2010 Journal of the Air & Waste Management Association 449
13 Figure 9. Effects of violating different constraints on total cost: (a) lower- and (b) upper-bound under SA1, and (c) lower- and (d) upper-bound under SA2. Downloaded by [ ] at 16:55 0 January 2018 the city. he traditional aim of the local waste managers (i.e., to provide a reliable and low-cost waste removal service for residents through operating solely a landfill) is being required to alter. herefore, from a long-term planning point view, the city should develop an ISWM approach that highlights waste diversion through various reduction, reuse, recycling, and composting programs. Figure 10 presents the relative difference of total costs (denoted as R [(f 0 f*) 100/f 0 ]%) among DIWM, SA1, SA2 and under q 0, where f* are mid-costs obtained from the DIWM, SA1, and SA2 under several q levels, and f 0 is the mid-cost obtained when q 0. he maximum relative difference (of f* and f 0 ) would be.2% obtained through DIWM under q 0.1 (i.e., [( )/ 8.11] 100%); this implies that the system would achieve the lowest cost when approximately 10% of the violations against capacity and diversion constraints are allowed. However, this would be linked to a potentially high system-failure risk. Summarily, the results illustrate that (1) the system cost (obtained from DIWM, SA1, and SA2) are all lower than that under q 0, (2) the cost obtained from DIWM under a range of q levels are lower than those obtained from SA1 and SA2 because more relaxation on system constraints is allowed in the DIWM model, and () violation of different constraints has different effects on the system cost. Figure 10. conditions. Relative difference of system costs under different Figure 11 presents the plans for the city s landfill expansion under SA1 and SA2. Although the landfill would be expanded in period 2 under SA1 and SA2, their expansion plans would be different from each other. For example, when waste generation rates are low over the planning horizon, under SA1, the landfill would be expanded with increments of [00.8, 419.2] 10 t when q 0.01, [281.4, 404.9] 10 t when q 0.05, and [270.5, 95.7] 10 t when q 0.1; in comparison, under SA2, this facility would be expanded with increments of [28.7, 444.8] 10, [4.7, 459.7] 10, and [52.9, 468.7] 10 t under q 0.01, 0.05, and 0.1, respectively. Generally, under all of waste-generation scenarios, the amount of landfill expansion under SA1 would be lower than that under SA2. his is because, in SA1, a set of chance constraints on waste-management-facility capacities were considered; this could lead to a decreased strictness for the landfill-capacity constraints and thus result in a lower capacity-expansion amount. On the other hand, in SA2, chance constraints on waste-diversion rates were undertaken; this allowed more waste flows being allocated to the landfill, leading to a higher expansion requirement for this facility. Figure 12 shows the results for the expansion schemes of total diversion capacities (including recycling and composting facilities) under SA1 and SA2, which are also different from each other. For example, under scenario MMM, the total diversion capacities expanded under SA1 would be [505.5, 55.4], [402., 450], and [99.6, 450] t/wk when q 0.01, 0.05, and 0.1, respectively; in comparison, the total diversion capacities expanded under SA2 would be [519, 548.], [456.9, 481.9], and [419.1, 444] t/wk under q 0.01, 0.05, and 0.1, respectively. However, when chance constraints on waste management capacities and waste-diversion rates were considered simultaneously (i.e., in DIWM model), the expanded amount of diversion capacity would be lower than those under SA1 and SA2 (see Figure 8). his is because the DIWM model is associated with a relaxed capacity constraint (i.e., leading to a reduced capacity expansion) and a decreased requirement for waste diversion (i.e., allowing more waste disposed of at the landfill); the two facts could 450 Journal of the Air & Waste Management Association Volume 60 April 2010
14 Downloaded by [ ] at 16:55 0 January 2018 Figure 11. Expansion schemes for the landfill under SA1 and SA2: (a) lower- and (b) upper-bound under q 0.01, (c) lower- and (d) upper-bound under q 0.05, and (e) lower- and (f) upper-bound under q 0.1. lead to a lower diversion capacity-expansion level obtained from the DIWM model. CONCLUSIONS In this study, a DIWM model has been developed for planning a MSW management system under uncertainty that is based on an ISPP method. ISPP integrates MSP and ICCP into a general framework such that ISPP can handle uncertainties presented as interval values and probability distributions and support assessing the risk of violating various constraints. Moreover, the developed DIWM model can reflect the dynamics of system uncertainties and decision processes under a representative set of waste generation scenarios. he DIWM model has been applied to a real case of planning a long-term MSW management system. he results demonstrate that the DIWM model can help tackle the dynamic, interactive, and uncertain characteristics of MSW management systems. he results indicate that optimized solutions have been generated for binary and continuous decision variables under various conditions. hey can be used for answering several questions such as (1) how to plan capacity expansion/development for MSW management facilities under multiple uncertainties, (2) how to allocate waste flows to meet a projected diversion goal within a multistage context, and () how to achieve a compromise between a minimized system cost and a maximized system reliability? Generally, decisions at a lower risk level would lead to an increased reliability in fulfilling system requirements but with a higher cost; conversely, a desire for reducing the cost could result in an increased risk of violating system constraints. In the DIWM model, only the EOS effect on the expansion cost was reflected by fixed-charge cost functions; however, the EOS effects on waste transportation and treatment costs (for regulated and excess waste flows) were both neglected, such that the DIWM model can be solved through linear programming method. If the EOS effects on waste transportation and treatment costs are considered, uncertainties and nonlinearities may exist in many system components. A direct nonlinear algorithm is ineffective in dealing with such complexities. In addition, multiple local optima may exist in a nonlinear program, leading to difficulties in identifying the global optimum. Such difficulties could be further intensified because of the existence of interval and stochastic uncertainties. herefore, one of the main challenges with the nonlinear DIWM model is the identification of uncertain relationships between the objective function and the related decision variables. Further research for nonlinear DIWM will be desired for more robustly reflecting the complexities in the MSW management systems. On the other hand, because of the complex nature of the waste management system, the data required for defining different scenarios were extensive. Although most of the obtained data are relatively accurate, others are less so. herefore, increasing the certainty of the datasets through further investigation and verification would help increase the certainty of the generated solutions. Moreover, in practical applications, the solutions from the proposed model are suitable for a preliminary evaluation of various alternatives and for identifying the important data requirement. he model results would be more applicable Volume 60 April 2010 Journal of the Air & Waste Management Association 451
15 Downloaded by [ ] at 16:55 0 January 2018 Figure 12. Expansion schemes for total diversion capacities under SA1 and SA2 for q (a) 0.01, (b) 0.05, and (c) 0.1. for practical situations, if postoptimality analysis methods (e.g., multicriteria decision analysis, group decisionmaking, and public survey) can be performed. NOMENCLAURE i type of waste management facility, with i 1 for landfill, i 2 for composting facility, and i for recycling facility t time period,, 2,, L t length of time period t (wk) DP it operating cost of facility i for excess waste flow during period t ($/t) DG 1t waste diversion rate (%), which represents waste to the landfill (in each period) that should not exceed the level regulated by the authority DR it collection and transportation cost for excess waste flow to facility i during period t ($/t) D it transportation cost for excess residue from facility i to the landfill during period t ($/t) FE i residue flow rate from facility i to the landfill (% of incoming mass to facility i) F it transportation cost for residue flow from facility i to the landfill during period t ($/t) FLC 1t fixed-charge cost for landfill expansion in period t ($10 6 ) FC it fixed-charge cost for the development and/or expansion of composting and recycling facilities in period t ($10 6 ) LC existing landfill capacity (t) M itk amount by which the preregulated waste-flow level is exceeded when the waste generation rate is WG tk with probability p tk under scenario k (t/wk) N itk variable upper bound for the expanded capacity in period t under scenario k (t or t/wk) OP it operating cost of facility i for preregulated waste flow during period t ($/t) p tk probability of occurrence for waste generation in period t under scenario k number of waste generation scenarios in period t q admissible risk of violating capacity and diversion constraints, and q [0, 1] RE it revenue generated from composting and recycling facilities during period t ($/t) RM it revenue from composting and recycling facilities because of excess flow during period t ($/t) C i existing capacity of composting and recycling facilities (t/wk) R it collection and transportation cost for preregulated waste to facility i during period t ($/t) 452 Journal of the Air & Waste Management Association Volume 60 April 2010
An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina
Journal of Environmental Management 81 (2006) 188 209 www.elsevier.com/locate/jenvman An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina Y.P.
More informationApplied Mathematical Modelling
Applied Mathematical Modelling 36 (2012) 2658 2673 Contents lists available at SciVerse ScienceDirect Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm A mathematical model for
More informationApplied Energy 87 (2010) Contents lists available at ScienceDirect. Applied Energy. journal homepage:
Applied Energy 7 () 7 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy A two-stage inexact-stochastic programming model for planning carbon dioxide
More informationINTERVAL ANALYSIS TO ADDRESS UNCERTAINTY IN MULTICRITERIA ENERGY MARKET CLEARANCE
1 INTERVAL ANALYSIS TO ADDRESS UNCERTAINTY IN MULTICRITERIA ENERGY MARKET CLEARANCE P. Kontogiorgos 1, M. N. Vrahatis 2, G. P. Papavassilopoulos 3 1 National Technical University of Athens, Greece, panko09@hotmail.com
More informationCapacity Dilemma: Economic Scale Size versus. Demand Fulfillment
Capacity Dilemma: Economic Scale Size versus Demand Fulfillment Chia-Yen Lee (cylee@mail.ncku.edu.tw) Institute of Manufacturing Information and Systems, National Cheng Kung University Abstract A firm
More informationThis is a refereed journal and all articles are professionally screened and reviewed
Advances in Environmental Biology, 6(4): 1400-1411, 2012 ISSN 1995-0756 1400 This is a refereed journal and all articles are professionally screened and reviewed ORIGINAL ARTICLE Joint Production and Economic
More informationWater 2015, 7, ; doi: /w Article. Eleni Bekri 1,2, *, Markus Disse 1 and Panayotis Yannopoulos 2
Water 2015, 7, 6427-6466; doi:10.3390/w7116427 Article OPEN ACCESS water ISSN 2073-4441 www.mdpi.com/journal/water Optimizing Water Allocation under Uncertain System Conditions for Water and Agriculture
More informationHow to Cite or Link Using DOI
Computers & Operations Research Volume 39, Issue 9, September 2012, Pages 1977 1987 A stochastic production planning problem with nonlinear cost Lixin Tang a,,, Ping Che a, b,, a, c, Jiyin Liu a Liaoning
More informationtool applied for forecasting in waste management
tool applied for forecasting in waste management Dr. Martin PAVLAS Version 1.0, 1.9.2016 Justine represents a sophisticated tool for simultaneous forecasting of waste amounts and waste parameters at different
More informationVehicle Routing Tank Sizing Optimization under Uncertainty: MINLP Model and Branch-and-Refine Algorithm
Vehicle Routing Tank Sizing Optimization under Uncertainty: MINLP Model and Branch-and-Refine Algorithm Fengqi You Ignacio E. Grossmann Jose M. Pinto EWO Meeting, Sep. 2009 Vehicle Routing Tank Sizing
More informationChance Constrained Multi-objective Programming for Supplier Selection and Order Allocation under Uncertainty
Chance Constrained Multi-objective Programming for Supplier Selection and Order Allocation under Uncertainty Xi Li 1, Tomohiro Murata 2 Abstract This paper proposes a chance-constrained multi-objective
More informationGREY FUZZY MULTIOBJECTIVE OPTIMIZATION MODEL FOR RIVER WATER QUALITY MANAGEMENT
GREY FUZZY MULTIOBJECTIVE OPTIMIZATION MODEL FOR RIVER WATER QUALITY MANAGEMENT Subhankar Karmakar and P. P. Mujumdar Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India.
More information1.1 A Farming Example and the News Vendor Problem
4 1. Introduction and Examples The third section considers power system capacity expansion. Here, decisions are taken dynamically about additional capacity and about the allocation of capacity to meet
More informationCapacitated Facility Location Problems, With Partial Assignment and Multiple Time Periods for Effective Management of Municipal Solid Waste
Volume 117 No. 11 2017, 145-154 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Capacitated Facility Location Problems, With Partial Assignment and
More informationDecision Support and Business Intelligence Systems
Decision Support and Business Intelligence Systems (9 th Ed., Prentice Hall) Chapter 4: Modeling and Analysis Learning Objectives Understand the basic concepts of management support system (MSS) modeling
More informationGlobal Supply Chain Planning under Demand and Freight Rate Uncertainty
Global Supply Chain Planning under Demand and Freight Rate Uncertainty Fengqi You Ignacio E. Grossmann Nov. 13, 2007 Sponsored by The Dow Chemical Company (John Wassick) Page 1 Introduction Motivation
More informationA New Fuzzy Modeling Approach for Joint Manufacturing Scheduling and Shipping Decisions
A New Fuzzy Modeling Approach for Joint Manufacturing Scheduling and Shipping Decisions Can Celikbilek* (cc340609@ohio.edu), Sadegh Mirshekarian and Gursel A. Suer, PhD Department of Industrial & Systems
More informationStrategic Design of Robust Global Supply Chains: Two Case Studies from the Paper Industry
Strategic Design of Robust Global Supply Chains: Two Case Studies from the Paper Industry T. Santoso, M. Goetschalckx, S. Ahmed, A. Shapiro Abstract To remain competitive in today's competitive global
More informationCHAPTER 5 SUPPLIER SELECTION BY LEXICOGRAPHIC METHOD USING INTEGER LINEAR PROGRAMMING
93 CHAPTER 5 SUPPLIER SELECTION BY LEXICOGRAPHIC METHOD USING INTEGER LINEAR PROGRAMMING 5.1 INTRODUCTION The SCMS model is solved using Lexicographic method by using LINGO software. Here the objectives
More informationProduction Planning under Uncertainty with Multiple Customer Classes
Proceedings of the 211 International Conference on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia, January 22 24, 211 Production Planning under Uncertainty with Multiple Customer
More informationStackelberg Game Model of Wind Farm and Electric Vehicle Battery Switch Station
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Stackelberg Game Model of Wind Farm and Electric Vehicle Battery Switch Station To cite this article: Zhe Jiang et al 2017 IOP
More informationCLUSTERING EFFICIENCY OF SCENARIOS IN THE VSS CAPTURE FOR THE TRANSPORTATION PROBLEM WITH STOCHASTIC DEMAND. José Ernesto Agüero Gutiérrez
CLUSTERING EFFICIENCY OF SCENARIOS IN THE VSS CAPTURE FOR THE TRANSPORTATION PROBLEM WITH STOCHASTIC DEMAND José Ernesto Agüero Gutiérrez Universidad Católica de la Santísima Concepción Caupolicán 491,
More informationThis document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore. Title Inexact management modeling for urban water supply systems Author(s) Xu, Y.; Huang, G. H.; Xu, T. Y.
More informationModels in Engineering Glossary
Models in Engineering Glossary Anchoring bias is the tendency to use an initial piece of information to make subsequent judgments. Once an anchor is set, there is a bias toward interpreting other information
More informationOil Export Tanker Problem- Demurrage and the Flaw of Averages
ENERGY EXPLORATION & EXPLOITATION Volume 26 Number 3 2008 pp. 143 156 143 Oil Export Tanker Problem- Demurrage and the Flaw of Averages Mansoor Hamood Al-Harthy 1 1 Petroleum and Chemical Engineering Department,
More informationMetaheuristics for scheduling production in large-scale open-pit mines accounting for metal uncertainty - Tabu search as an example.
Metaheuristics for scheduling production in large-scale open-pit mines accounting for metal uncertainty - Tabu search as an example Amina Lamghari COSMO Stochastic Mine Planning Laboratory! Department
More informationA Case Study of Capacitated Scheduling
A Case Study of Capacitated Scheduling Rosana Beatriz Baptista Haddad rosana.haddad@cenpra.gov.br; Marcius Fabius Henriques de Carvalho marcius.carvalho@cenpra.gov.br Department of Production Management
More informationMetaheuristics. Approximate. Metaheuristics used for. Math programming LP, IP, NLP, DP. Heuristics
Metaheuristics Meta Greek word for upper level methods Heuristics Greek word heuriskein art of discovering new strategies to solve problems. Exact and Approximate methods Exact Math programming LP, IP,
More informationInternational Journal of Supply and Operations Management
International Journal of Supply and Operations Management IJSOM November 2017, Volume 4, Issue 4, pp. xxx-xxx ISSN-Print: 2383-1359 ISSN-Online: 2383-2525 www.ijsom.com Supplier and Carrier Selection and
More informationGenerational and steady state genetic algorithms for generator maintenance scheduling problems
Generational and steady state genetic algorithms for generator maintenance scheduling problems Item Type Conference paper Authors Dahal, Keshav P.; McDonald, J.R. Citation Dahal, K. P. and McDonald, J.
More information^ Springer. The Logic of Logistics. Theory, Algorithms, and Applications. for Logistics Management. David Simchi-Levi Xin Chen Julien Bramel
David Simchi-Levi Xin Chen Julien Bramel The Logic of Logistics Theory, Algorithms, and Applications for Logistics Management Third Edition ^ Springer Contents 1 Introduction 1 1.1 What Is Logistics Management?
More informationOptimizing the supply chain configuration with supply disruptions
Lecture Notes in Management Science (2014) Vol. 6: 176 184 6 th International Conference on Applied Operational Research, Proceedings Tadbir Operational Research Group Ltd. All rights reserved. www.tadbir.ca
More informationSimultaneous Perspective-Based Mixed-Model Assembly Line Balancing Problem
Tamkang Journal of Science and Engineering, Vol. 13, No. 3, pp. 327 336 (2010) 327 Simultaneous Perspective-Based Mixed-Model Assembly Line Balancing Problem Horng-Jinh Chang 1 and Tung-Meng Chang 1,2
More informationOPTIMAL DESIGN OF DISTRIBUTED ENERGY RESOURCE SYSTEMS UNDER LARGE-SCALE UNCERTAINTIES IN ENERGY DEMANDS BASED ON DECISION-MAKING THEORY
OPTIMAL DESIGN OF DISTRIBUTED ENERGY RESOURCE SYSTEMS UNDER LARGE-SCALE UNCERTAINTIES IN ENERGY DEMANDS BASED ON DECISION-MAKING THEORY Yun YANG 1,2,3, Da LI 1,2,3, Shi-Jie ZHANG 1,2,3 *, Yun-Han XIAO
More informationIntroduction to Management Science 8th Edition by Bernard W. Taylor III. Chapter 1 Management Science
Introduction to Management Science 8th Edition by Bernard W. Taylor III Chapter 1 Management Science Chapter 1- Management Science 1 Chapter Topics The Management Science Approach to Problem Solving Model
More informationCh.01 Introduction to Modeling. Management Science / Instructor: Bonghyun Ahn
Ch.01 Introduction to Modeling Management Science / Instructor: Bonghyun Ahn Chapter Topics The Management Science Approach to Problem Solving Model Building: Break-Even Analysis Computer Solution Management
More informationA simulation-based two-stage interval-stochastic programming model for water resources management in Kaidu-Konqi watershed, China
Science Press Journal of Arid Land 2012, 4(4): 390 398 doi: 10.3724/SP.J.1227.2012.00390 jal.xjegi.com; www.chinasciencejournal.com A simulation-based two-stage interval-stochastic programming model for
More informationOptimizing capital investments under technological change and deterioration: A case study on MRI machine replacement
The Engineering Economist A Journal Devoted to the Problems of Capital Investment ISSN: 0013-791X (Print) 1547-2701 (Online) Journal homepage: http://www.tandfonline.com/loi/utee20 Optimizing capital investments
More informationMathematical Model to Optimize the Energy Consumed by a Semiconductors Manufacturing Industry An Application
Journal of Mathematical Modelling and Application 2013, Vol. 1, No. 8, 78-83 ISSN: 2178-2423 Mathematical Model to Optimize the Energy Consumed by a Semiconductors Manufacturing Industry An Application
More informationModeling of competition in revenue management Petr Fiala 1
Modeling of competition in revenue management Petr Fiala 1 Abstract. Revenue management (RM) is the art and science of predicting consumer behavior and optimizing price and product availability to maximize
More informationIntegrated planning of operations and spare parts logistics under uncertainty in the supply chain of maintenance service providers
Integrated planning of operations and spare parts logistics under uncertainty in the supply chain of maintenance service providers Masoumeh Kazemi Zanjani, JEng, PhD Concordia University, Montreal, Canada
More informationScheduling and Coordination of Distributed Design Projects
Scheduling and Coordination of Distributed Design Projects F. Liu, P.B. Luh University of Connecticut, Storrs, CT 06269-2157, USA B. Moser United Technologies Research Center, E. Hartford, CT 06108, USA
More informationThe Research of the Project Proprietor s Management Control of Engineering Change
SHS Web of Conferences 17, 02011 (2015 ) DOI: 10.1051/ shsconf/20151702011 C Owned by the authors, published by EDP Sciences, 2015 The Research of the Project Proprietor s Management Control of Engineering
More informationPAPER No. : 02 MANAGERIAL ECONOMICS MODULE No. : 03 PRINCIPLES: INDIVIDUAL AND MARKET
Subject Paper No and Title Module No and Title Module Tag 02: Managerial Economics 03: Principles: Individual and Market COM_P2_M3 TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Principles-
More informationLogistic and production Models
i) Supply chain optimization Logistic and production Models In a broad sense, a supply chain may be defined as a network of connected and interdependent organizational units that operate in a coordinated
More informationRECYCLING TECHNICAL ASSISTANCE Project #562 FINAL REPORT
RECYCLING TECHNICAL ASSISTANCE Project #562 FINAL REPORT BOROUGH OF LEWISTOWN MIFFLIN COUNTY, PENNSYLVANIA PRELIMINARY RATE EVALUATION CURBSIDE REFUSE AND RECYCLABLES COLLECTION AND DISPOSAL PROGRAM FEBRUARY
More informationA Fuzzy Optimization Model for Single-Period Inventory Problem
, July 6-8, 2011, London, U.K. A Fuzzy Optimization Model for Single-Period Inventory Problem H. Behret and C. Kahraman Abstract In this paper, the optimization of single-period inventory problem under
More informationManaging risks in a multi-tier supply chain
Managing risks in a multi-tier supply chain Yash Daultani (yash.daultani@gmail.com), Sushil Kumar, and Omkarprasad S. Vaidya Operations Management Group, Indian Institute of Management, Lucknow-226013,
More informationMODULE 1 LECTURE NOTES 2 MODELING OF WATER RESOURCES SYSTEMS
1 MODULE 1 LECTURE NOTES 2 MODELING OF WATER RESOURCES SYSTEMS INTRODUCTION In this lecture we will discuss about the concept of a system, classification of systems and modeling of water resources systems.
More informationA Comparative Analysis of Ontario s Recycling Programs
CONTACT A Comparative Analysis of Ontario s Recycling Programs Bruce G. Wilson, Dept. of Civil Engineering, University of New Brunswick Dr. Bruce G. Wilson, P.Eng. Department of Civil Engineering, University
More informationBusiness case studies. (Logistic and production models)
Business case studies (Logistic and production models) 1. Logistics planning in the food industry The logistic system of the food manufacturing company consists of a network whose nodes represent suppliers
More informationA multiobjective optimization model for optimal supplier selection in multiple sourcing environment
RATIO MATHEMATICA 26 (2014), 95 112 ISSN:1592-7415 A multiobjective optimization model for optimal supplier selection in multiple sourcing environment M. K. Mehlawat, S. Kumar Department of Operational
More informationOptimization under Uncertainty. with Applications
with Applications Professor Alexei A. Gaivoronski Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Alexei.Gaivoronski@iot.ntnu.no 1 Lecture 3
More informationApplying Anticipatory Networks to Scenario Planning and Backcasting in Technological Foresight
Applying Anticipatory Networks to Scenario Planning and Backcasting in Technological Foresight Andrzej M.J. Skulimowski Decision Sciences Department, AGH University of Science & Technology, Kraków, Poland
More informationSWOLF Overview and Illustrative Analyses. Jim Levis, PhD Research Assistant Professor Department of Civil, Construction, and Environmental Engineering
SWOLF Overview and Illustrative Analyses Jim Levis, PhD Research Assistant Professor Department of Civil, Construction, and Environmental Engineering S WOLF http://go.ncsu.edu/swm-lca 1 Research background
More informationStochastic Lot-Sizing: Maximising Probability of Meeting Target Profit
F1 Proceedings of the 2012 International Conference on Industrial Engineering and Operations Management Istanbul, Turkey, July 3 6, 2012 Stochastic Lot-Sizing: Maximising Probability of Meeting Target
More informationLogistic and production models (contd..)
g) Multiple plants Logistic and production models (contd..) In this section it is assumed that a manufacturing company has a network of M production plants, located in geographically distinct sites that
More informationMaterials Management: Changes and Challenges in the Recycling Stream. Susan Robinson ASTSWMO, August 2017
Materials Management: Changes and Challenges in the Recycling Stream Susan Robinson ASTSWMO, August 2017 Market update: China, paper, plastic & more Market volatility and uncertainty are key works for
More informationFigure -1 Functional Elements of the Life Cycle Analysis of Municipal Solid Waste Management Alternatives.
System Description for a Life-Cycle Inventory of Municipal Solid Waste Management Alternatives Morton A. Barlaz and Ranji Ranjithan North Carolina State University (7/22/95) Executive Summary The objective
More informationWaste Management & Research
http://wmr.sagepub.com/ An optimisation model for regional integrated solid waste management I. Model formulation M. Abou Najm, M. El-Fadel, G. Ayoub, M. El-Taha and F. Al-Awar Waste Manag Res 2002 20:
More informationIntroduction to Management Science
Test Item File Introduction to Management Science Bernard W. Taylor III Martha Wilson California State University, Sacramento Upper Saddle River, New Jersey 07458 Contents Chapter 1 Management Science
More informationA Concurrent Newsvendor Problem with Rationing
A Concurrent Newsvendor Problem with Rationing Pinto Roberto CELS Research Center on Logistics and After-Sales Services University of Bergamo Viale Marconi, 5-24044 Dalmine, Italy roberto.pinto@unibg.it
More informationPower Grid Simulation Model for Long Term Operation Planning
A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 35, 2013 Guest Editors: Petar Varbanov, Jiří Klemeš, Panos Seferlis, Athanasios I. Papadopoulos, Spyros Voutetakis Copyright 2013, AIDIC Servizi
More informationWebShipCost - Quantifying Risk in Intermodal Transportation
WebShipCost - Quantifying Risk in Intermodal Transportation Zhe Li, Heather Nachtmann, and Manuel D. Rossetti Department of Industrial Engineering University of Arkansas Fayetteville, AR 72701, USA Abstract
More informationAdvanced skills in CPLEX-based network optimization in anylogistix
Advanced skills in CPLEX-based network optimization in anylogistix Prof. Dr. Dmitry Ivanov Professor of Supply Chain Management Berlin School of Economics and Law Additional teaching note to the e-book
More informationStochastic optimization based approach for designing cost optimal water networks
European Symposium on Computer Arded Aided Process Engineering 15 L. Puigjaner and A. Espuña (Editors) 2005 Elsevier Science B.V. All rights reserved. Stochastic optimization based approach for designing
More information1 / Consultant s Perspective & Role
Solid Waste Management Strategy for City / Borough of Juneau (CBJ) Executive Summary Presentation November 27 29, 2007 Richard Hertzberg & Chris Bell 1 / Consultant s Perspective & Role Objective Technical
More informationUniversity Question Paper Two Marks
University Question Paper Two Marks 1. List the application of Operations Research in functional areas of management. Answer: Finance, Budgeting and Investment Marketing Physical distribution Purchasing,
More informationUNWRAPPING AMBITIOUS PACKAGING COMMITMENTS IN THE U.S.
UNWRAPPING AMBITIOUS PACKAGING COMMITMENTS IN THE U.S. Insights from a Cross-Sector Salon Conversation Sponsored by the U.S. Chamber of Commerce Foundation and AMERIPEN. 1 INTRODUCTION This report summarizes
More informationUNWRAPPING AMBITIOUS PACKAGING COMMITMENTS IN THE U.S.
UNWRAPPING AMBITIOUS PACKAGING COMMITMENTS IN THE U.S. Insights from a Cross-Sector Salon Conversation Sponsored by the U.S. Chamber of Commerce Foundation and AMERIPEN. 1 INTRODUCTION This report summarizes
More informationOPERATIONS RESEARCH Code: MB0048. Section-A
Time: 2 hours OPERATIONS RESEARCH Code: MB0048 Max.Marks:140 Section-A Answer the following 1. Which of the following is an example of a mathematical model? a. Iconic model b. Replacement model c. Analogue
More information1.0 Summary of Recommendations
1.0 Summary of Recommendations Recommendations for Portugal can be summarised as follows: 1. Changes to charging systems and incentives a. Undertake a review of charges currently paid by householders with
More informationIncorporating behavioral model into transport optimization
Incorporating behavioral model into transport optimization Michel Bierlaire Transport and Mobility Laboratory School of Architecture, Civil and Environmental Engineering Ecole Polytechnique Fédérale de
More informationA Multi-Objective Optimization Model For Operations Planning Of Multi-Reservoir Systems
City University of New York (CUNY) CUNY Academic Works International Conference on Hydroinformatics 8-1-2014 A Multi-Objective Optimization Model For Operations Planning Of Multi-Reservoir Systems Daniel
More informationIntegrated Design, Planning, and Scheduling of Renewables-based Fuels and Power Production Networks
Antonio Espuña, Moisès Graells and Luis Puigjaner (Editors), Proceedings of the 27 th European Symposium on Computer Aided Process Engineering ESCAPE 27 October 1 st - 5 th, 217, Barcelona, Spain 217 Elsevier
More informationComments by Eureka Recycling January 2014
Beverage Container Model within Zero-Waste Context: Thank you for the opportunity to comment on the beverage container recovery model. We recognize beverage container deposit legislation is an effective
More informationBasic Linear Programming Concepts. Lecture 2 (3/29/2017)
Basic Linear Programming Concepts Lecture 2 (3/29/2017) Definition Linear Programming (LP) is a mathematical method to allocate scarce resources to competing activities in an optimal manner when the problem
More informationDavid Simchi-Levi M.I.T. November 2000
Dynamic Pricing to improve Supply Chain Performance David Simchi-Levi M.I.T. November 2000 Presentation Outline The Direct-to-Consumer Model Motivation Opportunities suggested by DTC Flexible Pricing Strategies
More informationsustainable communities
Waste partnerships in sustainable communities Presented by: Mirka Januszkiewicz Director, Waste Management Services Regional Municipality of Durham November 2009 What is sustainability Sustainability is
More informationIntroduction. Challenges Related to Waste Reduction and Reuse AGENDA ITEM 6
AGENDA ITEM 6 To: Russ Smith, Senior Manager, Environmental Resource Management From: Maura Walker Date: August 7, 2012 Re: Stage 1 Integrated Solid Waste and Resource Management Plan Issues for Consideration
More informationMANDATORY COMMERCIAL RECYCLING DIVISION 7. CALIFORNIA INTEGRATED WASTE MANAGEMENT BOARD
1 MANDATORY COMMERCIAL RECYCLING 2 3 TITLE 14. NATURAL RESOURCES 4 5 DIVISION 7. CALIFORNIA INTEGRATED WASTE MANAGEMENT BOARD CHAPTER 9.1. MANDATORY COMMERCIAL RECYCLING 6 7 8 9 10 11 12 13 14 18835. Purpose.
More informationApplying Robust Optimization to MISO Look- Ahead Commitment
Applying Robust Optimization to MISO Look- Ahead Commitment Yonghong Chen, Qianfan Wang, Xing Wang, and Yongpei Guan Abstract Managing uncertainty has been a challenging task for market operations. This
More informationAPPLICATION OF MATHEMATICAL MODELING IN MANAGEMENT ACCOUNTING
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS N. 38 2017 (573 580) 573 APPLICATION OF MATHEMATICAL MODELING IN MANAGEMENT ACCOUNTING Jiaxin Wang Donglin Wang Department of Basic Education Beijing Polytechnic
More informationOptimization under Uncertainty. with Applications
with Applications Professor Alexei A. Gaivoronski Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Alexei.Gaivoronski@iot.ntnu.no 1 Lecture 2
More information1 Introduction 1. 2 Forecasting and Demand Modeling 5. 3 Deterministic Inventory Models Stochastic Inventory Models 63
CONTENTS IN BRIEF 1 Introduction 1 2 Forecasting and Demand Modeling 5 3 Deterministic Inventory Models 29 4 Stochastic Inventory Models 63 5 Multi Echelon Inventory Models 117 6 Dealing with Uncertainty
More informationCharacterization of environmental impact indices of solid wastes in Surulere Local Government Area, Nigeria with GaBi 5 LCA modeling technique
International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) Characterization of environmental impact indices of solid wastes in Surulere Local Government Area, Nigeria with GaBi 5 LCA modeling
More informationARTICLE IN PRESS. Int. J. Production Economics
Int. J. Production Economics ] (]]]]) ]]] ]]] Contents lists available at ScienceDirect Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe Incorporating uncertainty into a supplier
More informationNegotiation Decision Analysis on Pricing of Mobile Application Development with the Trading Platform under the B2B Market
Negotiation Decision Analysis on Pricing of Mobile Application Development with the Trading Platform under the B2B Market Jei-Zheng Wu Department of Business Administration Soochow University, Taipei,
More informationUsing the Analytic Hierarchy Process in Long-Term Load Growth Forecast
Journal of Electrical Engineering 5 (2017) 151-156 doi: 10.17265/2328-2223/2017.03.005 D DAVID PUBLISHING Using the Analytic Hierarchy Process in Long-Term Load Growth Forecast Blagoja Stevanoski and Natasa
More informationThe Multi criterion Decision-Making (MCDM) are gaining importance as potential tools
5 MCDM Methods 5.1 INTRODUCTION The Multi criterion Decision-Making (MCDM) are gaining importance as potential tools for analyzing complex real problems due to their inherent ability to judge different
More informationQute: Quality-of-Monitoring Aware Sensing and Routing Strategy in Wireless Sensor Networks S H A O J I E T A N G T E M P L E U N I V E R S I T Y
Qute: Quality-of-Monitoring Aware Sensing and Routing Strategy in Wireless Sensor Networks S H A O J I E T A N G J I E WU T E M P L E U N I V E R S I T Y Examples of WSNs Wireless Sensor Networks (WSNs)
More informationISyE 3133B Sample Final Tests
ISyE 3133B Sample Final Tests Time: 160 minutes, 100 Points Set A Problem 1 (20 pts). Head & Boulders (H&B) produces two different types of shampoos A and B by mixing 3 raw materials (R1, R2, and R3).
More informationAquifer Thermal Energy Storage (ATES) Smart Grids
Aquifer Thermal Energy Storage (ATES) Smart Grids Tamás Keviczky t.keviczky@tudelft.nl http://www.dcsc.tudelft.nl/~tkeviczky/ Delft Center for Systems and Control Delft University of Technology The Netherlands
More informationNovember 20, His Worship Rob Ford Mayor, City of Toronto 100 Queen St. W. City Hall, Second floor, West Toronto, ON M5H 2N2.
November 20, 2012 His Worship Rob Ford Mayor, City of Toronto 100 Queen St. W. City Hall, Second floor, West Toronto, ON M5H 2N2 Dear Sir: Re: Solid Waste Management Services Waste Diversion The Canadian
More informationResearch Article Integrated Production-Distribution Scheduling Problem with Multiple Independent Manufacturers
Mathematical Problems in Engineering Volume 2015, Article ID 579893, 5 pages http://dx.doi.org/10.1155/2015/579893 Research Article Integrated Production-Distribution Scheduling Problem with Multiple Independent
More informationPRODUCT ASSORTMENT UNDER CUSTOMER-DRIVEN DEMAND SUBSTITUTION IN RETAIL OPERATIONS
PRODUCT ASSORTMENT UNDER CUSTOMER-DRIVEN DEMAND SUBSTITUTION IN RETAIL OPERATIONS Eda Yücel 1, Fikri Karaesmen 2, F. Sibel Salman 3, Metin Türkay 4 1,2,3,4 Department of Industrial Engineering, Koç University,
More informationNetwork Flows. 7. Multicommodity Flows Problems. Fall 2010 Instructor: Dr. Masoud Yaghini
In the name of God Network Flows 7. Multicommodity Flows Problems 7.1 Introduction Fall 2010 Instructor: Dr. Masoud Yaghini Introduction Introduction In many application contexts, several physical commodities,
More informationSupply Chain Network Design under Uncertainty
Proceedings of the 11th Annual Conference of Asia Pacific Decision Sciences Institute Hong Kong, June 14-18, 2006, pp. 526-529. Supply Chain Network Design under Uncertainty Xiaoyu Ji 1 Xiande Zhao 2 1
More informationALPHA MOTORS, LTD.: Integrating Life-Cycle Environmental Concerns into Product Design
World Resources Institute Sustainable Enterprise Program A program of the World Resources Institute ALPHA MOTORS, LTD.: Integrating Life-Cycle Environmental Concerns into Product Design For. more than
More informationInternational Journal of Industrial Engineering Computations
International Journal of Industrial Engineering Computations 2 (2011) 319 328 Contents lists available at GrowingScience International Journal of Industrial Engineering Computations homepage: www.growingscience.com/ijiec
More information