OPTIMAL PACKAGING OF HIGH VALUE, TEMPERTURE SENSITIVE, PERISHABLE PRODUCTS DRAFT FINAL REPORT

Transcription

1 OPTIMAL PACKAGING OF HIGH VALUE, TEMPERTURE SENSITIVE, PERISHABLE PRODUCTS DRAFT FINAL REPORT Prepare By: Mohamme Yeasin, Ph.D. Associate Professor, Department of Electrical an Computer Engineering, The University of Memphis, 3815 Central Avenue, Memphis, TN 38152, Sabya Mishra, Ph.D., P.E. Assistant Professor, Dept. of Civil Engineering, University of Memphis, 112D Engr. Sc. Blg., 3815 Central Avenue, Memphis, TN 38152, Tel: , Fax: , Mohsen Maniat Department of Civil Engineering, The University of Memphis, 3815 Central Avenue, Memphis, TN 38152, Phone: (901) , Rakib Al-Faha Department of Electrical an Computer Engineering, The University of Memphis, 3815 Central Avenue, Memphis, TN 38152, Tao Ma, Ph.D., P.E. Post-Doctoral Fellow, Department of Civil Engineering, Intermoal Freight Transportation Institute, The University of Memphis, 3815 Central Avenue, Memphis, TN 38152, Phone: (901) ,

2 This research was fune by the Biologistics cluster of Intermoal Freight Transportation Institute (IFTI) an FeEx Institute of Technology (FIT) at University of Memphis. -ii-

3 Table of Contents 1 Introuction Literature Review Components of supply chain moeling Supply chain rivers Supply chain constraints Supply chain ecision variables Methoology Packaging Moeling quality egraation: Moeling Moel formulation: Notation Inices Variables Sets Constants Unit costs Objective function: Constraints: Numerical Experiment (Vaccine logistic) Results Elimination of packaging cost Reuction in capacity Reuction in eman Future Challenges Environmental issue Big ata Collaboration between packaging an supply chain Conclusions References Appenices iii-

4 List of Tables TABLE 1 Moeling approaches use for planning perishable prouct SCM... 4 TABLE 2 Transportation network information TABLE 3 Deman in each O-D pair TABLE 4 Number of trucks that pass on each path, the remaining quality of the vaccines an amount of coolant neee for each package TABLE 5 Some examples big ata in SCM (65) List of Figures FIGURE 1 FeEx perishable prouct packaging process with ry ice an coolant (68)... 5 FIGURE 2 Illustration of amount of ry ice neee versus ifferent volume for 24 hours (Left) an Illustration of amount of ry ice neee versus time for 1000 (in3) prouct (right) FIGURE 3 The supply chain structure FIGURE 4 The configuration of the 18-line network FIGURE 5 The total cost of logistic an the contribution of each part FIGURE 6 U.S. greenhouse gas emission in 2014 an their main sources (59, 60) FIGURE 7 Volume an Velocity vs. Variety of SCM Data (67) FIGURE 8 Example of a Big Data sources across SCM (Kamaa-Kawai Network)(67) FIGURE Transportation of vaccines in a rural area of Nicaragua by horseback (69) iv-

5 Executive Summary Many of the proucts such as pharmaceuticals, biohazar material, an human organs are frequently shippe across regions, countries, continents, an hemispheres with ifferent environment. During the shipment, these proucts shoul be preserve in a specific conition to prevent severe amage. Consierable amount of perishable proucts spoil before they reach consumers. To avoi spoilage an to maximize revenue of shipping high value, temperature controlle, perishable proucts, precise integration of the prouct, process, package, an istribution is critical. In this stuy, besies conventional inventory an transportation network cost, we incorporate packaging cost in an optimization moel with a single objective function that consists of ifferent components: (i) packaging, (ii) storage, (iii) quality egraation, (iv) network congestion, (v) waste isposal, an (vi) potential supply chain of the perishable proucts; subject to capacity, shelf-life, supply chain, an other pragmatic prouct quality constraints. The propose objective function is non-linear non-convex integer function. We aopte Noma software to solve the optimization problem. Our main goal is to buil a moel that can optimize packaging cost of high value, temperature controlle, perishable proucts supply chain, an maintaining prouct quality. Due to the importance an critical nature of vaccine supply chain, in a numerical case stuy, the propose moel has been simulate a simplifie vaccine supply chain in orer to minimize the logistic cost. The result of the numerical stuy has shown that the cost relate to the packaging of perishable proucts is significantly important. By consiering the amount of packaging as a variable in our moel, it has been shown that the cost of logistic can be reuce consierably. The ifferent scenarios illustrate the capability of the moel in consiering various situations that are likely to occur in real worl cases. -v-

6 1 Introuction Diversity of prouction, transportation, consumers nees an services emans efficiency in supply chain management (SCM) are critical to the success of business operations. While proucts are frequently shippe across regions, countries, continents, an hemispheres with ifferent environment, many of the proucts such as pharmaceuticals, biohazar material, an human organs, are temperature an time sensitive. To ensure that the supply satisfies consumer eman, supply chains of those items, consisting of complex networks of economic activities, shoul be optimize (1). Time is a significantly important factor in SCM of perishable items. Delays in elivering the proucts may impact the quality an quantity of the proucts. For example, raioisotope may have prouction time an must be use within a week in a hospital or meical facility Proper packaging protects perishable proucts from environmental influence. During transportation, perishable items may be expose to harsh environmental conition (i.e. temperature fluctuation, humiity). Insulation an refrigeration are the keys to preserve perishable items uring their shipment (2). Recently, there has been tremenous evelopment in new perishable packaging technologies such as microwave packaging, aseptic processing, moifie or controlle atmosphere packaging, an sous-vie (vacuum cooking) technology worlwie (3). Most perishable packaging evices can be classifie into two categories: (i) Active Col Storage Devices (ACD) an (ii) Passive Col Storage Devices (PCD) (4). ACD use electric power an actively cool the inner prouct. PCD are not epenent on electricity an can maintain specific temperature for certain perio of time using a passive meium of cooling an insulator (4). ACD nee continuous power supply uring transportation an are not convenient ue to limite resource an better prouct generalization. The major avantages of PCD are that (i) they o not nee power supply, (ii) coolant can be change manually for any unwante elay or prouct quality egraation, (iii) they are convenient to hanle an easy to implement tracking or monitoring evice insie or outsie the package, (iv) compatible with any transportation moe, an (v) most importantly the packaging can be optimize base on prouct type. It was reporte that 10% of all perishable prouct spoil before they reach consumers (5). Therefore, precise integration of the prouct, process, package, an istribution is critical to avoi spoilage an private carriers are pruently consiering optimal packaging with emphasis on effective istribution, network optimization, shipment consoliation, cross ocking, supplier management, an supplier integration (6).State-of-the-art practice for profit maximization in SCM is cost optimization in complex transport network, storage, an inventory system (1, 9 12). In this stuy, besies conventional inventory an transportation network cost, we incorporate packaging cost in an optimization moel with a single objective function that consists of ifferent components: (i) packaging, (ii) storage, (iii) quality egraation, (iv) network congestion, (v) waste isposal, an (vi) potential supply chain of the perishable proucts; subject to capacity, shelf-life, supply chain, an other pragmatic prouct quality constraints. The propose objective function is non-linear non-convex integer function. We aopte Noma software(11) to solve the optimization problem. Our main goal is to buil a moel that can optimize packaging cost of high value, time-sensitive, perishable prouct supply chain, an maintaining prouct quality. Due to the importance an critical nature of vaccine supply chain, in a numerical case stuy, the propose moel has been simulate a simplifie vaccine supply chain to minimize the logistic cost.

7 2 Literature Review Nowaays, the supply chain is complex with broa spectrum. Specific moeling approach cannot capture all the aspects of supply chain processes. Supply chain has to eals with competitive strategic analysis inclue, eman planning, location-allocation ecisions, strategic alliances, istribution channel planning, new prouct evelopment, information technology (IT) selection, outsourcing, supplier selection, pricing, an network restructuring. Though most of the supply chain problems are static in nature, SCM nees to cope up with vehicle routing/scheuling, workforce scheuling, recor keeping, an packaging. Some supply chain problems may involve hierarchical an multi-level planning that overlap ifferent ecision levels. To fill the gap between complexity an reality, moeling of supply chain require ealing with real-worl imension. There is no stanar systematic way to solve firm-specific supply chain problem (7). Stevens, Chopra an Meinl (12, 13) propose guieline to moel supply chain base on three levels of ecision hierarchy consist of (1) operational routines, (2) tactical plans, an (3) competitive strategy. Another popular guieline is propose by Copper et al. (14) consist of three structures of a supply chain network. These structures are: (1) type of supply chain partnership, (2) the structural imensions of a supply chain network an (3) the characteristics of process links among supply chain partners. 2.1 Components of supply chain moeling It is necessary to ientify the key component to moel supply chain. Those components may iffer from one company to another (7), Some examples of those components are: Supply chain rivers The first step of supply chain moeling is goal setting. The major riving forces of the supply chain inclue customer service initiatives, monetary value, information/knowlege transactions, an risk elements Supply chain constraints Constraints represent restrictions or limitations place on a range of ecision alternatives that a company can choose. Examples of constraints are capacity, service compliance, an the extent of eman. Definition of capacity inclues the available space for inventory stocking an manufacturing capability. Supply chain member's prouction, supply, an technical capability etermine its esire outcome regaring the level of inventory, workforce, prouction, outsourcing, IT aoption an capital investment. Service compliance is one of the most important constraints for example elivery time winows, maximum holing time for back orers, prouction ue ates, an riving hours for truck rivers. On the other han, the vertical integration of a supply chain balance the capacity of supply at the preceing stage against the extent of eman of the ownstream supply chain members at the succeeing stage (7) Supply chain ecision variables Decision variables are functionally relate to supply chain performances i.e. the objectives functions of a supply chain are generally expresse as a function of one or more ecision variables. Examples of ecision variable are as (7): The location of prouction plants, warehouses, istribution centers, consoliation points, an sources of supply, -2-

8 Allocation of warehouses, istribution centers, consoliation points an prouction plants that shoul serve customers or suppliers accoringly, Timing of expansion or elimination of manufacturing or istribution facilities, Network structuring, Number of facilities an equipment, Number of stages (echelons), Service sequence, Optimal purchasing volume, prouction, an shipping volume at each noe, Inventory level, Size of workforce. The extent of outsourcing. The moels for supply chain of perishable proucts can be classifie as (i) eterministic an (ii) stochastic (7, 15). For eterministic moel approaches, the researchers have wiely use mathematical techniques such as linear programming (LP), mixe integer programming (MIP), ynamic programming (DP), goal programming (GP). On the other han, popular stochastic moeling approaches inclue simulation (SIM), stochastic ynamic programming (SDP), risk programming (RP) (7). For example, Ferrer et al. (16) moel the optimal scheuling of the harvest of wine grapes using a LP moel with the objective of minimizing operational an grape quality costs. Wioo et al. (17) use DP moeling approach to integrate harvest, prouction, an storage of perishable items with growth an loss functions for maximizing the eman satisfie. Caixeta- Filho (18) eals with LP approach that relates biological, chemical, an logistics constraints to the quality of fruit prouct to harvest, with objective of maximizing revenue. For maximizing revenue, Kazaz et. al. (19) consier two-stage SP moel to etermine the olive trees to contract for an oil proucer in the season with uncertain harvest an eman. TABLE 1 shows summary of some moeling approaches use for planning perishable prouct SCM. Traitional SCM eals with a single objective function to minimize cost or maximize profit. (9, 20 22). There are a large number of publishe stuies that escribe the quality evaluation base pricing moel for perishable prouct supply chains. For example, Xiaojun et. al. (23) propose a moel to reuce foo waste an maximize seller s profit. Their pricing approach was base on ynamically ientifie shelf-life using tracking an monitoring technologies. As prouct price cannot change frequently, they claime that their propose approach has avantage over conventional ynamic prouct pricing. Rong et. al.(24) presente a mixe-integer linear programming moel for foo prouct (bell peppers) SCM where prouct quality is relate to temperature control throughout the supply chain. They formulate quality-base multi-perio prouction an istribution planning problem by minimizing the cost function consisting of prouction costs, cooling costs for transportation equipment, transportation costs, cooling costs for storage facilities, storage costs, an waste isposal costs. Cost optimization was achieve with specific constraints for fresh foo supply chain. Nagurney et. al. (1) emphasize on unifie supply chain network analytics framework to hanle optimization an competitive behavior relevant to perishable prouct market. They moele generalize networks of supply chain problems for a wie variety of prouct an guielines to etermine the arc multipliers that capture perishability. -3-

9 TABLE 1 Moeling approaches use for planning perishable prouct SCM Author Moel Other aspects Main Objective type Ferrer et al.(16) LP, MIP Relaxation heuristic Optimally scheuling of wine grape harvesting Wioo et al. (17) DP Growth an loss functions Flowering harvesting moel Caixeta-Filho(18) LP Orange harvesting scheuling management Kazaz (19) SP Nonlinear optimization Optimization of olive oil prouction Allen an Schuster (25) LP, MIP Nonlinear optimization Optimize crop harvest moel Rantala (26) LP Seeling SCM of multi-unit finish nursery company Fuzzy Itoh et al. (27) LP programming Optimize crop harvest moel Multi-objective Optimization in airy farming, flower bulb an Berge ten et al. (28) SP programming integrate arable farming. Darby-Dowman et al.(29) LP Determining robust planting plans in horticulture Risk Agriculture SCM with multiple criteria ecisionmaking Romero (30) LP programming risk analysis Simulation an Leutscher et al. (31) SDP regression Agricultural SCM optimization Optimal prouction an marketing ecisions for a Stokes et al.(32) SP, MIP nursery proucing ornamental plant Aleotti et al. (33) Miller et al. (34) Hamer (35) Purcell et al. (36) Van Berlo (37) Annevelink (38) Saet et al.(39) LP LP LP LP LP LP LP Fuzzy programming Decision support system Risk programming Goal programming Genetic algorithm Optimize revenue by changing the capacity of foo preservation facilities an consiering the uncertainties in crop markets Planning for prouction an harvesting of packing plant with an LP an fuzzy programs Planting an harvesting plan for fresh crops Decision moel for lanscape lan prouction. Determine sowing, harvesting an prouction plans. Determine plan for the location of pot plants insie a greenhouse. Develop a plan for a pot-plant greenhouse with future plans an transition plans. Packaging protects perishable prouct from environmental influences such as heat, light, irt an ust particles, pressure, enzymes, spurious oors, microorganisms, insect s gaseous emissions, the presence or absence of moisture. The major function of packaging is protection, preservation from external contamination, extension of shelf life, retaration of eterioration, an maintenance of quality an safety of package prouct. Precise integration of the prouct, process, -4-

10 package, an istribution is critical to avoi recontamination. The ieal packaging material shoul be resistant to hazars an shoul not allow molecular transfer from or to packaging materials(5). Other important purposes of packaging are containment, convenience, marketing, an communication. Containment ensures a prouct from intentional ispersion or spill. Communication ensures link between consumer an suppliers. It contains impotent information such as weight, source, ingreients, lifetime, cautions for use require by law, nutritional value. Companies use packaging as a meia for prouct promotion, marketing an braning(40). FIGURE 1 FeEx perishable prouct packaging process with ry ice an coolant (68) Recently, there has been tremenous growth in new perishable packaging technologies such as microwave packaging, aseptic processing, moifie or controlle atmosphere packaging an sous-vie (vacuum cooking) technology worlwie (3). Major perishable packaging evice can be istinguishing in two categories (i) active col storage evices (ACD) an (ii) passive col storage evices (PCD) (4). ACD use electric power an actively cool the inner prouct. Some ACD are esigne have backup system that can provie a specific temperature range up to 24 hours uring power shortfalls or outages. PCD are not epenent on electricity an can maintain specific temperatures for certain perios of time using a passive meium of cooling an insulator. The most common use insulation materials are reflective materials, expane polystyrene foam, an rigi polystyrene foam. Wiely use refrigerants are gel coolant an ry ice (4). ACD nee continuous power supply uring transportation. However, for limite resource an better prouct generalization, this technology is not convenient. The main avantages of temperature controlle express shipping service is that (i). It oes not nee power supply; (ii). Coolant can be change manually for any unwante elay or prouct quality egraation (iii) Convenient to hanle an easy to implement tracking or monitoring evice insie or outsie the package. (iv) Compatible -5-

11 with any transportation e.g. truck, air cargo; most importantly (v) the packet can be optimize for prouct type hence cost effective. Moern packaging technology eals with traceability, tamper inication, an portion control (41). New tracking systems enable tracking of packages through the supply chain from prouction to consumers. Packages are imprinte with a bar coe or universal prouct coe to trace the prouct in the supply chain. Recently, intelligent or smart packaging is esigne to monitor an communicate information about prouct quality ((42, 43). For example, raio frequency ientification, time-temperature inicators (TTIs), ripeness inicators, biosensors, an. These smart evices can be attache to package materials or the insie or outsie of packages. The U.S. Foo an Drug Aministration (FDA) istinguishes TTIs in their Fish an Fisheries Proucts Hazars an Control Guiance (3r eition), so their importance increase in the seafoo inustry. Home Depot, Wal-Mart, an famous retail outlets use raio frequency ientification. This technology ay by ay become very prominent for tracking an tracing for perishable commoities. During transportation, perishable item may expose to harsh environmental conition e.g. temperature fluctuation, humiity. Insulation an refrigeration are the key to preserve perishable item uring shipment. Due to vast improvement in packaging technology, the next generation packaging market revenue is expecte to reach US$ 58 Bn by 2025 ( Next-Generation Packaging Market: Global Inustry Analysis an Opportunity Assessment FMI research report). Recently there has been tremenous growth in new perishable packaging technologies such as microwave packaging, aseptic processing, moifie or controlle atmosphere packaging an sous-vie technology worlwie(3). There are thousans of patent at this area. Shipping giant company, like FaEx o not provie temperature controlle express shipping service. Instea proper use of insulation an refrigerant it is possible to maintain prouct within specific temperature. To monitor prouct quality, they use SenseAware technology(44). The most common use insulation materials are reflective materials, expane polystyrene foam, an rigi polystyrene foam. Wiely use refrigerants are gel coolant an ry ice. Refrigerants keeps the prouct col an frozen (keep consistent temperature) within specific life. Technology like refrigerate cooling packaging nee continuous power supply. However, for limite resource an better prouct generalization this technology is not convenient. It is observe that Total 10% of all perishable prouct spoil before they reach consumers (5). Therefore, precise integration of the prouct, process, package, an istribution is critical to avoi spoilage. Profit maximization of complex multi-billion marke requires effective istribution, network optimization, shipment consoliation, cross ocking, supplier management an supplier integration (6). State of art practice for profit maximization in SCM is cost optimization in complex transport network, storage an inventory system(1, 9 12). Recent improvement of computational efficiency enables us to use genetic algorithms (GA), fuzzy genetic algorithms (FGA) as well as an improve simulate annealing (SA) proceure of multi-objective optimization of SCM. For example, Nakanala et. al. (22) compare performance of those algorithm. They moele fresh foo supply chain in making cost optimize ecisions regaring transportation, with the objective of minimizing the total cost an maintaining the prouct quality. On the other han, moern complex SCM eals with outsourcing of prouction an istribution, prouct ifferentiation as well as quality an price competition, game theory is effectively an wiely use (1, 8). The summary of literature review suggests that the supply chain of time sensitive high-value commoities is emerging, an proven methoologies are yet to be establishe. -6-

12 3 Methoology This section provies a escription of methoology for moeling an simulation of optimal packaging of high value, time sensitive, perishable proucts. 3.1 Packaging Since perishable proucts on the way from their origins to estinations may be subject to harsh environmental conitions (such as excessive temperature), the careful packaging nees to be one to ensure the safe elivery of the proucts. The cost of the packaging neee for a certain perishable prouct mainly epens on the range of temperature control, the size of the package, the environmental conition, an the time length of the shipment. Base on the type of perishable prouct, the range of temperature control may change. For instance, in case of bloo-relate proucts the temperature control is between +2 C to +8 C to prevent freezing (freezing will amage the prouct). Size of the package is usually preefine, an it epens on the size of the prouct an the amount of protective material neee to keep the prouct safe. The size of the boxes, the shape of the proucts, the algorithm that use to pack the prouct insie of boxes, an the metho for loaing the container can consierably reuce the costs. Numerous stuies can be foun in the litrature in this area (46, 46 48); however, it is not the concern of this stuy. Time length of the shipment irectly affects the cost of packaging. Using an efficient system of col storage, which minimizes the processing time, an optimizes the istribution of the shipments on the transportation network, woul significantly reuce the time length of the shipment an consequently the cost of packaging. There are ifferent types of passive col storage systems an the benefits of using them is explaine in the introuction. Here we consier two of these systems which have been utilize by FeEx in packaging of perishable shipments. Some of the benefits of these systems inclue (but not limite to) (i) eliminating the nee for refrigerate vehicles, (ii) easier an safer to switch moes of transportation, an (iii) improve storage capacity for a short time since there is no nee for a refrigerate warehouse. Dry ice is usually consiere for freezing conition, an coolant gel is consiere for keeping the proucts col (between +2 C to +8 C). The amount of coolant gel or ry ice neee to keep the prouct at a certain temperature control etermines a great portion of the packaging cost. These amounts can be estimate base on the following formulation uner ieal (1)environmental conitions (73 o F an 50% relative humiity) (49). Coolant = V m Tn Kc CT (1) Where V m is the volume of the prouct; Tn is the time that the prouct nees to be in a temperature control; Kc is the constant for ifferent methos of cooling system (for coolant gel it is 4147 an for ry ice it is 5184); to reuce the heat transfer through packaging container walls, commonly, expane polystyrene foam has been use. The thickness of the foam (CT) epens on the environmental conition an usually it is between 0.5 to 2 inches. In orer to protect the proucts from humiity an isturbance, seale plastic bag, absorbent pas, proper outer box an other protective parts may be use, hence, the cost of them nees to be consiere in the moel. -7-

13 Amount of refrigerant (lb) Amount of refrigerant (lb) Amounts of ry ice neee for ifferent volume an time are illustrate in the FIGURE 2. For instance, 1 poun of ry ice woul be enough to keep a 1000 (in3) prouct at the freezing conition for 10 hours while 2-inch foam is use Volume (in 3 ) Time (hrs) FIGURE 2 Illustration of amount of ry ice neee versus ifferent volume for 24 hours (Left) an Illustration of amount of ry ice neee versus time for 1000 (in3) prouct (right). 3.2 Moeling quality egraation: Due to various storage conitions, quality factors, prouct (2)features, preicting the quality of a prouct remains challenging. Most moels for preicting the prouct quality are base on the assumption that there is normally one leaing quality characteristic for a given prouct (23). For instance, for the perishable foo, the freshness of the proucts coul be consiere as the leaing quality factor (23), while in perishable pharmaceutical proucts the effectiveness (potency) of the prouct may be consiere as the main quality attribute of interest. Most perishable proucts are at the highest level of their quality right after the prouction an over time the quality woul ecrease. For estimating the quality egraation, many moels have been propose for ifferent proucts. The summary of these stuies coul be foun in the eteriorating inventory literature (50 53). In the present stuy, we have use the first-orer reactions with exponential time ecay which frequently has use in perishable foo an pharmaceutical proucts (23, 24, 54). The kinetic formulation can be expresse as: q t = kqn (2) Where q is the measure value of the chosen leaing quality factor, n is the orer of the reaction, etermining whether the reaction rate is epenent on the amount of quality left (23). Most often, power factor, n, will have a value of either 0 or 1 for linear to exponential egraation, respectively. k is the rate of egraation epening on environmental conitions like temperature an can be estimate by Arrhenius Equation as follows: k = k 0 e [E a/rt] (3) -8-

14 Where k 0 is the rate constant, E a is the energy of activation for the reaction that controls quality loss, R is the gas constant, an T is the absolute temperature. Depening on n, Equation 3 can represent moels for quality changes that follow a linear to exponential ecay (55). This means that we can estimate the quality level of a prouct at a certain location in the foo supply chain base on an initial quality (q 0 ). For a time perio with length τ, this leas to the Equation 4 an 5 for zero-orer an first-orer reactions, respectively. q = q 0 τ k 0 e [E a/rt] q = q 0 e τ(k 0e [E a/rt] ) (4) (5) In practice, k is etermine at a number of temperatures an the ata set (k, T) are then analyze by least-squares fitting proceure to form a linearize Arrhenius Equation. Taking the natural logarithm of both sies of Equation 3 yiels: ln(k) = ln(k 0 ) E a R 1 (6) T Thus, E a R an ln(k 0 ) can be obtaine by calculating the slope an intercept of the fitte line. 3.3 Moeling Various management ecisions nee to be mae for a supply chain. With toay s computing power, no moel can consier all aspects of a real supply chain. For the sake of simplicity (without loos of generality) each moel tries to approximate the reality an focuses on critical constraints. Time an environmental conitions are the main issues for perishable proucts since the quality of the proucts may egrae rastically by ignoring these two factors. For a large number perishable proucts, the major cost of controlling environmental conitions can be associate with the temperature control, an in many moels, temperature is the main factor in quality egraation moel (24). Thus, in this stuy, prouct temperature an time are consiere to be the main factors in estimating the quality egraation. Each Prouct has a specific prouction process. In orer to have a general moel, prouction process is not consiere in our moel. However, this element can reaily be consiere for a specific prouct. The general representation of the supply chain moel consiere for this stuy is epicte in FIGURE 3 which primarily moels the istribution an elivery services. Here, we consier a thir-party logistics company that provies the logistic services between iniviual, enterprise suppliers, an consumers. At the logistic service provier (LSP) centers at the origin, the goos are collecte from the suppliers, an they will be evaluate, labele, packe, store an prepare to be shippe to the consumers of the goos. Since the focus of this stuy is on high value, temperature controlle, perishable proucts, long-term storage shoul be avoie. On the way from the prouct origins to estinations, we might have several istribution centers (hubs) which form a transportation network. Each LSP at the origin may irectly be connecte to another LSP at the estination. In aition, each hub center may connect to another hub center that efines ifferent paths between an LSP an a consumer. -9-

15 FIGURE 3 The supply chain structure 3.4 Moel formulation: Notation The following notation is utilize to escribe the moel formulation Inices t Time step Inex a Link number Inex O-D pair number Inex n Path number Inex i The number of LSP at the origin j The number of hub at the network k The number of LSP at the estination a i An inex to show the number of links that pass ith LSP at the origin a j An inex to show the number of links that pass jth hub at the network a k An inex to show the number of links that pass kth LSP at the estination m An inex to show the type of package c An inex to show the type of cooling metho Variables t f n Flow at the nth path of th O-D pair at tth time step. 0 t a Free flow time of the ath link in the network. n t P c m Unit cost of type-m package with cooling metho c for nth path of th O-D pair an v The th time amount step. of waste prouct Sets A Set of links T Set of time steps D Set of O-D pairs N Set of paths G Set of cooling methos I Set of LSPs at the origin J Set of hubs at the network K Set of LSPs at the estination -10-

16 3.4.5 Constants δ a n Binary variable that shows if the link a is a part of path n connecting th O-D pair α a The constant that will be set base on the characteristics of the link a t C a The capacity of the link a at tth time step β a The constant that will be set base on the characteristics of the link a n N c m Number of type-m packages with cooling metho c V m The volume of type-m packages limit D k Capacity of the kth LSP at the estination limit H j Capacity of the jth hub center limit O i t Capacity of the ith LSP at the origin at time step t c k 0 The rate constant for the quality egraation q limit Allowable quality limit E a The energy of activation for the reaction R The gas constant Temp c The absolute temperature for the cth cooling type t limit The maximum allowable time travel for th O-D pair I t The initial time at tth time step Supply The quantity of the supply for th O-D pair CT The thickness of the foam Unit costs T S a Unit cost of travel for the link a O S i t Unit cost of processing packages at ith LSP at the origin at time step t H S j Unit cost of processing packages at jth hub center D S k Unit cost of processing packages at kth LSP at the estination W Unit cost of waste isposal P S m c The fixe price for type-m package with cooling metho c Unit price of coolant material for cooling metho S C 3.5 Objective function: The objective function is presente in Equation 7. The goal is to fin the flow in each path that minimizes the costs of logistic of high value, temperature controlle, perishable proucts between two LSPs or between one LSP an consumers. The costs consist of six parts: (i) transportation cost, (ii) processing an inventory cost at the LSP centers at the origin, (iii) processing cost at the hub centers, (iv) processing cost at the LSP centers at estination, (v) packaging cost, an (vi) waste cost. Base on the common transportation moels, time of the travel epens on the usage of each link (56). Thus, the travel cost of each unit at a link in supply chain network is not fixe but rather epens partly on the usage of the link. In the propose moel, the unit cost of transportation for each link at a time interval epens on the congestion, moe of transportation, an characteristics of the link (such as free flow time an capacity of the link). The total cost of travels between ifferent centers is consiere as transportation cost. -11-

17 min [( f t n δ a n t a n ) (t 0 a (1 + α a ( 1 t C f n t δ a n a n )β a )) (7) S T a ] + f t n δ ai n i t a i n O S i t Subject to + f t n δ ak n k t a k + f t n δ aj n j t a j n + P t n c m N c m t n m n n c S k D S j H + W v f t n δ a n (t 0 a (1 + α a ( 1 t C f n t δ a n a a n n D, n N t C a a )β ) δ a n ) a A, t + I t t limit t T, (8) (9) (10) q 0 exp ( [ (t 0 a (1 + α a ( 1 t C f n t δ a n a a n a )β ) δ a n ) + I t ] (k 0 e [E a RT ] )) q limit t T, D, n N, c G f t n δ ai n a i n f t n δ ak n a k n limit O i limit D k i I, t T k K, t T (11) (12) f t n δ aj n a j n limit H j j J, t T t f n = Supply W D t n (13) (14) -12-

18 f n t Z + D, t T, n N (15) V m [( t 0 a (1 + α a ( 1 a) a t C n f n t δ a n )β δa n ) + I t ] n P t a c m = S K c CT C P + S m c (16) At each logistic service centers at the origin, the proucts will be receive, labele an store for an appropriate time for shipment to their estination. The cost of storage, labor cost an other expenses in these centers simplifie in the secon term of the objective function. Similarly, the thir part of the cost function account for the cost of LSP centers at the estination. Between each LSP center, there coul be several hub centers. In each hub base on the moe of travel, some routine tasks nee to be one for each package. The cost relate to these activities can be expresse in the fourth part of the cost function. It is worth mentioning that the cost for each center coul be ifferent from the other centers, an these values nee to be efine for each center. The fifth term in the Equation 7 estimates the cost of the cooling package. Base on the Equation n 1, the unit cost of packaging (P t c m ) epens on the type of package, cooling metho, an the time of the travel which can be estimate by Equation 16. At the first part of this equation, the amount of refrigerant material neee for the package is estimate (base on Equation 1) an multiplie by the unit cost of the material. A fixe cost is ae to account for the cost of seale plastic bag, absorbent pas, Expane polystyrene foam, an outer corrugate box. Depening on the value of the prouct, there shoul be a penalty for the waste prouct (prouct that i not meet the quality limitations). In estimating the value of a prouct, not only the prouction cost an isposal cost shoul be consiere, but also the negative social impacts of losing the prouct shoul be estimate. For instance, in the case of shipping human organs, the waste of the shipment may jeoparize the life of a patient, or in the case of foo inustry the loss of the prouct may lea to costumer s issatisfaction. The last term in the objective function aresses the waste cost. 3.6 Constraints: The constraints consiere in our moel can be ivie into eight general categories as represente in Equations The first set of constraints, Equation 8, ensures that the flow on each link is less than the capacity of the link at all of the time steps. The flow in a link can be calculate base on the flow on the paths that contain the link. The secon set of constraints limits the time travel between each O-D pair. The time of the shipment for a perishable prouct shoul be less than the shelf-life of the prouct as inicate in Equation 9. The quality egraation of the prouct can be controlle by the set of inequalities at the Equation 10. These set of constraints are formulate base on the first-orer egraation moel escribe in Equation 6. If all of these two sets of constraints satisfie (time an quality constraints), there woul be no waste in the shipment. The amount of proucts that fail to satisfy these constraints woul be consiere as waste costs in the cost function. The sets of constraints at the Equations 11 an 12 prevent the LSP center at the origin an estination from being overloa. Similarly, Equation 13 assures that the flow that passes through each hub is less than the capacity of the hub. Flow conservation constraints at the Equation 14 check that the summation of the flow on all paths connecting each O-D pair to be equal to the quantity of the proucts that nee to ship between that O-D pair. The last constraint, Equation 15, -13-

19 represents integer an non-negativity nature of variables to limit the search space to an to obtain physically meaningful solutions. 4 Numerical Experiment (Vaccine logistic) Despite many efforts, immunization programs are struggling to meet the emans of routine immunization an supplemental campaigns, an the existing systems cannot keep pace with the changing lanscape of immunization programs (15, 57). For instance, base on WHO (15, 57) 2.8 million vaccine oses lost in five countries ue to col chain failures in Thus, the propose moel has been simulate as a simplifie vaccine logistic system to minimize the logistic cost while keeping the quality of the prouct in a certain range by consiering the proper amount of packaging. The leaing quality factor for most vaccines is the potency of the vaccines. The simplest plausible moel for vaccine potency egraation is first-orer kinetics (58). In this case stuy, we are assuming a hypothetical vaccine base on (58). In orer to control the quality of the prouct, we limit the potency to 80% of the initial potency which here we assume it as 100% for all vaccine. Many vaccines consist of proteins that may rapily break own an become ineffective when expose to temperatures above 10 C an therefore must remain in environment with strictly controlle temperatures (4). To ensure that the vaccines are kept in the proper conition, we use insulate boxes escribe in section 2. Enough coolant gel for keeping the temperature of the prouct between 2-8 o C for the entire time of storage an travel is consiere for each package. Thus, in calculating the rate of egraation (k) the average temperature of 5 o C (278 Kelvin) is use. The transportation network consiere here is between the three LSP centers at the origin which transport the vaccines to the LSP centers at the estination through two or three hub centers. The configuration of the network is epicte in FIGURE 4.The LSP centers that receive the proucts from the suppliers are at the top tier which transports the prouct to the specifie LSP centers at the last tier of the network. The secon an thir tiers of the network consist of hub centers that help to istribute the flow in the network. These ifferent centers are connecte with 18 links of transportation. These links coul be associate with the various moes of transportation, but, for the sake of simplicity, all the links are assume to be roas, an the proucts are shippe by trucks. Base on the transportation network, we have consiere six O-D pairs an ten paths between them. The information of each path along with the set of links that forms each path are shown in FIGURE 4. The free flow, the capacity of each link, an the parameter relate to characteristic of the link are presente in TABLE 2 Transportation network information Moreover, the time elay in each center is a ranom number between 1 to 2 hours an the elay in each path can fin in the appenix. -14-

20 Path number Path an link connections O-D pairs Origin Destin Set of Links 1 1 C 1 o C 1 1, 7, C 1 o C 1 2, 8, C 1 o C 2 2,8, C 2 o C 2 3,8, C 2 o C 2 4,9, C 2 o C 3 4,9, C 3 o C 2 5,9, C 3 o C 3 5,9, C 3 o C 3 6,10, C 3 o C 3 6,10,17,18 FIGURE 4 The configuration of the 18-line network. As explaine before we are consiering passive cooling system with coolant gel. Consiering ieal environmental conitions (73 o F an 50% relative humiity) Equation 1 is use for calculating the amount of coolant assuming the thickness of the insulating foam is 0.5 an inch. We have consiere three sizes of boxes to pack the appropriate amount of vaccine for the consumers as shown in TABLE 3 Deman in each O-D pair. The volume of the vaccine is expresse by number of boxes with ifferent sizes. In aition, for the practical issues, we assume that only 70% of the volume of the container of a truck (150x80x80 inch) coul be fille. The supply an eman for each O-D pairs in term of number of boxes an number of trucks are tabulate in TABLE 3 Deman in each O-D pair. Base on the amount of eman we are consiering two-time steps, an the whole time horizon is two ays. By increasing the eman, the travel time an elay at the LSP an hub centers woul increase, an consequently, the quality of the prouct woul ecrease. In this situation, the time step interval nees to be shorter which irectly epens on the LSP equipment an machinery to avoi the rastic quality loss. Developing an LSP is not always possible, in result, in some cases having waste of prouct is inevitable. In this case stuy, the eman is selecte base on the capacity of the LSP an supply chain network; therefore, by istributing appropriate flow in each path the wastage of the vaccine is prevente. Although we trie to estimate realistic values of the unit costs for ifferent part, many factors may change these values, an they shoul be set at the beginning for a specific situation. Here we assume that the unit cost of travel for each truck for one hour (S a T ) is equal to $150 for all links; the unit cost of inventory an processing for all centers is a number between $500 to $1000 for each truck an the overall cost for each path is tabulate in the appenix. The unit cost of coolant gel is $0.5 for each poun; the fixe cost for the small, meium, an large boxes are equal to $0.4, $0.5, an $0.6, respectively; To avoi any waste in our proucts, we set a large number for the unit cost of waste. Thus all of the proucts have their minimum quality requirement an no vaccine woul be waste. -15-

21 TABLE 2 Transportation network information Link Number Capacity (Trucks) Free Flow Time (hr.) α β Number of O-D pair Small Box (216 x 119 x 41 mm) TABLE 3 Deman in each O-D pair. Meium Box (216 x 119 x 76 mm) Large Box (241x221x114 mm) Number of trucks The propose objective function is nonlinear, an the search space is nonconvex an is limite to integer values. In such cases the objective function is very expensive to evaluate as optimization process requires multiple feeback between ecision variable selection an constraints in the feasible region search process uring step size an irection fining evaluation. Often, it is ifficult to accurately obtain the erivate of the objective function. Solving large problem instances requires heuristics to approximate an relax the feasible region search process for faster convergence to obtain an optimal value without any guarantee of global optimality. To solve the propose optimization problem we have use an non-linear integer constraine off the shelf solve calle NOMAD available in opti-toolbox as an a-on to MATLAB (11). -16-

22 5 Results Given the scenario presente in the previous section, the optimization problem is solve, an the result is shown in TABLE 4 Number of trucks that pass on each path, the remaining quality of the vaccines an amount of coolant neee for each package.. In some cases, although all of the flow coul pass through one path, because of the congestion in the links an centers, the optimum solution happens when the flow is istribute between ifferent paths. The amount of coolant for various size of boxes in each path are shown in TABLE 4 Number of trucks that pass on each path, the remaining quality of the vaccines an amount of coolant neee for each package.. Because of the characteristic of the transportation network (the travel time in each path is about the same range), there are small changes in the amount of neee coolant in one type of package. Nevertheless, the ifference from a time step to the other one is significant. For instance, there is 4.3 lb. ifferent between the coolant neee for ay 1 an ay 2 for each large box. Multiplying this number by the number of large boxes, one can realize that there is an enormous saving of coolant comparing to the case that the amount of coolant is selecte regarless of the step time an the flow in each path. This shows the importance of the optimum col packaging in the logistic of high value, temperature controlle, perishable proucts. TABLE 4 Number of trucks that pass on each path, the remaining quality of the vaccines an amount of coolant neee for each package. Flow in Remaining Path Day 1 Day 2 each path Quality (%) number Day Day Day Day Small Meium Large Small Meium Large box box box box box box Note: NA represents Not applicable The optimum cost an the contribution of ifferent parts of the logistic cost are shown in FIGURE 4. It is observe that consierable portion of logistic cost is the packaging cost. Although in ifferent situations, the percentages are shown in the iagram may change, the packaging cost for high value, temperature controlle, perishable proucts seems to be a consierable cost. Consiering this cost as a separate cost in our moel helps to fin the optimum flow that leas to the minimum total logistic cost of the supply chain. As an instance of avantages of optimizing the logistic cost base on the propose moel, the cost of logistic is calculate when the flow is istribute to the shortest paths without consiering congestion. Comparing the result shows that the cost is 13% larger than the cost base on the propose moel. In the case where the flow is istribute evenly between ifferent paths the cost is 43% larger than the cost base on the propose moel. Flow in each link an the flow that passes through each center are tabulate an are ae to the appenix. -17-

23 25% Total Cost $271,266,267 43% Packaging Transportation Inventory & Processing 32% FIGURE 5 The total cost of logistic an the contribution of each part. 5.1 Elimination of packaging cost To investigate the effect packaging cost on the flow pattern, we have solve the optimization problem without consiering the cost of col packaging. The cost associate with the optimum flows erive at this conition is 28% larger ($76,289,771 more) than the optimum cost consiering the col packaging cost in the moel. This example clearly shows the importance of the col packaging cost in etermining the optimum flow on the transportation network. The numerical result of this experiment is in the appenix. 5.2 Reuction in capacity The capacity of each link an centers may vary at ifferent hours of a ay. Moreover, because of averse climatic conitions, the capacity of one or more links of the network will most likely be partially or completely isrupte for a specific time interval. The avantage of the propose moel is that it can account for such isruptions. To realize the effect of capacity change, we assume the capacity of the of link 8, 16, an 17 on the first ay woul reuce by 5000, 1500, an 2000, respectively. These reuctions happen just on the first ay, an on the secon ay the capacity woul be restore to original state. Comparing the cost for the new conition with the original cost, there is a 2% ($4,995,778) increase in total cost. That happens because a significant portion of the flow has been shifte to the secon ay an, in turn, the cost of inventory an packaging has been increase. -18-

24 Normalize Cost TABLE 6 The flow in each path Path number Day 1 Day Reuction in eman In orer to investigate the effect of eman on the optimum solution series of experiments have been one. In these experiment the eman of all O-D pairs is graually reuce to 50% an the optimization problem is solve for the reuce emans. To compare the cost, each part is ivie by eman an is normalize with respect to 1. The result has been shown at the FIGURE 6. It can be seen from the graphs that the total cost is ecreasing with the reuction of eman. This reuction is more significant for the packaging cost. By reucing eman, the time of travel woul ecrease an consequently the amount of coolant woul ecrease an the cost of packaging an transportation woul ecrease as well. The inventory cost is not sensitive to the eman since this cost is not affecte by the time of the travel. The etaile numerical result is ae to the appenix Transportation Packaging Inventory Total % 50% 60% 70% 80% 90% 100% Percentage of Deman FIGURE 6 Variation of normalize cost for ifferent parts. -19-

25 6 Future Challenges 6.1 Environmental issue Dry ice or carbon ioxie soli (UN 1845) is angerous an hazarous material for air transport. Dry ice changes to carbon ioxie (CO2) gas an accumulate in enclose spaces like aircraft cargo hols. It isplaces oxygen, therefore, requires special hanling an care (regulate by Feeral Regulations Coe: 49CFR). The esign an construction of packaging use for ry ice shipments must prevent the builup of pressure an cracks. Dry ice must never be place in an airtight container. Overall, in ifferent stages of perishable prouct packaging, we emit Carbon Dioxie irect to the environment. Carbon ioxie is the major greenhouse gas, emitte by human activities. In 2014, about 80.9% of U.S. greenhouse gas was CO2(59). Carbon ioxie is naturally present in the atmosphere as part of the Earth's carbon cycle. Inustrialization is changing the carbon cycle by aing more CO2. While CO2 emissions come from a variety of natural sources, human-relate emissions are responsible for the increase that has occurre in the atmosphere since the inustrial revolution. Total Emissions of CO2 in 2014 was 6,870 Million Metric Tons of CO2 equivalent. U.S. FIGURE 6 U.S. greenhouse gas emission in 2014 an their main sources (59, 60). Excessive emission of CO2 has a great impact on the greenhouse effect an global warming. There are two major effects of global warming: Increase of temperature on the earth by about 3 to 5 C (5.4 to 9 Fahrenheit) an sea levels will rise by at least 25 meters (82 feet) by the en of this century. Globally ry ice is use in Healthcare, Foo Processing, Inustrial Cleaning, Packaging an Transport sectors(61). The Global Dry Ice Inustry Report 2015 shows the alarming increasing eman for ry ice. Flourishing of this inustry may bring a isaster in natural carbon circle. In our research, we foun a significant gap between the use of prouction, use, refurbish an reuse an optimization of ry ice. There is no such market analysis an guieline for: 1. Market size of ry ice an coolant for packaging inustry, 2. Safe an secure ry ice prouction process to reuce environment impact, -20-

26 3. Proper instruction to use/reuse an refurbish ry ice, 4. Optimize the amount of coolant use to minimize climate effect, 5. The treatment plants for waste isposal. 6.2 Big ata Amazon uses big ata to monitor, secure, an track 1.5 billion items in its inventory that are place aroun 200 fulfillment centers aroun the ifferent geographical location. Amazon relies on preictive analytics for its anticipatory shipping to preict when an where a customer will purchase a prouct, an pre-ship it to a istribution center close to the final estination or customer(62). On the other han, Wal-Mart hanles more than a million customer transactions each hour. Their RFID tracking system generates more than 2.5 petabytes of ata which is 100 to 1000 times the ata of conventional bar coe systems (63). UPS use telematics technology in their freight segment to reesign logistical networks (64). Sipping giant company like FaEx o not provie temperature controlle express shipping service. To monitor prouct quality, they use SenseAware technology (44). SenseAware measures environmental conitions on the unit level, such as: (1) Current location, (2) Relative humiity, (3) Temperature, (4) Light exposure, (5) Barometric pressure, (6) Shock etection, (7) Route alert, (8) Time base location alert. For auit, customer complaint or process improvement initiative, SenseAware preserves this enormous amount of ata for a certain amount of time. TABLE 5 Some examples big ata in SCM (65). TABLE 5 Some examples big ata in SCM (65) SCM lever Functional problem Type of ata Marketing Sentiment analysis of eman an new trens Procurement Informing supplier negotiations Warehouse Warranty Analytics Operations Transportation Real-time route optimization Blogs an news, fees, ratings an reputation from 3 r parties, weblogs, loyalty programs, call centers recors, customer surveys SRM Transaction ata, Supplier current capacity & top customers, supplier financial performance information Internet of things sensing, user emographics, historical asset usage ata Traffic ensity, weather conitions, transport systems constraints, intelligent transportation systems, GPSenable Big Data telematics -21-

27 Figure 7 Volume an Velocity vs. Variety of SCM Data (67) Figure 8 Example of a Big Data sources across SCM (Kamaa-Kawai Network)(67) Figure 7 Volume an Velocity vs. Variety of SCM Data (67) shows Volume an Velocity vs. Variety of ifferent SCM Data (65) an a Kamaa-Kawai network example consist of istance forces between the 52 ata sources an each of the four SCM levers (Marketing, Procurement, Warehouse Management an Transportation) respectively. Eventually, SCM organizations are flooe with huge an complex big ata. To notice such size an complexity, McAfee et al. (64) escribe that business collect more ata than they know what to o with. Big ata analysis is practical problem for moern enterprises. Now a ay s profit an success of a company epen on those big ata analyses. In this stuy, we attempt to investigate the optimal packaging of high value, temperature controlle, an perishable proucts by consiering the effects of the supply chain, quality -22-

28 egraation, network congestion, an storage. This moel can be useful for firm-specific supply chain problem but a practical optimization approach shoul consier realistic constraints that come from these big ata mining (for example mining on ata, come from traffic ensity, weather conitions, transport systems constraints, intelligent transportation systems, GPS-enable big ata telematics) for better generalization. Most of the moel implementation approach avoi incorporating SCM big ata because those ata are not publically available an trae secrets. 6.3 Collaboration between packaging an supply chain Intelligent packaging contains components that enable the monitoring the conition of package prouct an the environment (insie an surrouning the prouct) uring transport an storage(66). This technology is an extension of the communication function of traitional packaging system. Intelligent packaging system provies customer reliable an correct information on the conitions of the prouct, packaging integrity, an the environment. It improves the overall performance of supply chains an wastage reuction (66). Conventional package manufacturing systems are base on a one-way flow of materials, from crale-to-grave (C2G). As it is a one-way flow out of the factory, the manufacturer loses the value of reusing the material. The C2G esign approach is base on taking, making an wasting an a major contributor to environment pollution an greenhouse effect (66). Hence, ecoefficiency strategies come forwar to promote consumption reuction, prevention of waste an emissions, lifespan extension of proucts, an reuction of the effects, without suggesting a real alternative to the C2G material flows(67, 68). Eco-efficiency strategies thus only focus on the reuction of environmental impacts mae by human activity. Rather than seeking to eliminate waste afterwar, Braungart et al.(68) propose crale-to-crale (C2C) framework which irectly eals with maintaining resource quality an prouctivity through many cycles of use. Packaging materials shoul be as cheap as possible. However, this inustrial eman for cost optimization leas packaging esign to multilayer composites or laminates that are ifficult to reuse or recycle. The lack of foresight in the esign of packaging an the extensive use of many ifferent materials inevitably results in (1) reuce performance an attractiveness of recycle packaging, (2) complicate an expensive recycle processes, an (3) own-cycling of packaging materials (68). Prouction cost of intelligent evices can be kept low by mass prouction. Therefore, those evices are often consiere as relatively cheap an isposable. Figure 9 Transportation of vaccines in a rural area of Nicaragua by horseback (69) -23-