A Strategic Level Model for Supply Chain of an Automotive Industry: Formulation and Solution Approach

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Volume-4, Issue-1, February-2014, ISSN No.: 2250-0758 International Journal of Engineering an Management Research Available at: www.ijemr.

1 Volume-4, Issue-1, February-2014, ISSN No.: International Journal of Engineering an Management Research Available at: Page Number: A Strategic Level Moel for Supply Chain of an Automotive Inustry: Formulation an Solution Approach Amit Kumar Gupta 1, Dr. O.P. Singh 2, Dr. R.K. Garg 3 1 Research Scholar of Punjab Technical University, Kapurthala, Punjab, INDIA 2 Professor, Deptartment of Mechanical Engineering, BCET, Guraspur, Punjab, INDIA 3 Professor, Department of Inustrial an Prouction Engineering, NIT Jalanhar, Punjab, INDIA ABSTRACT This paper escribes a strategic level moel of supply chain management (SCM). It explains overall supply chain issues, strategic importance of SCM, an an example of mathematical formulation. A supply chain is a global network of organizations that cooperate to improve the flows of material an information between suppliers an customers at the lowest cost an the highest spee. The objective of a supply chain is customer satisfaction. At the strategic level, a supply chain can be consiere as being compose of five activities: buy, make, move, store an sell. The main aim of this paper is to show a strategic level moel for supply chain of an automobile inustry in mathematical terms, with an example of mathematical formulation. In this paper, a mixe integer linear programming (MILP) moel is formulate first, an then alternative solution proceures are introuce. Keywors: Supply Chain Management, Echelon, MILP Mixe Integer Linear Programming, LINGO I. INTRODUCTION A supply chain is a set of facilities, supplies, customers, proucts an methos of controlling inventory, purchasing, an istribution. The chain links suppliers an customers, beginning with the prouction of raw material by a supplier, an ening with the consumption of a prouct by the customer. Typically, a supply chain is compose of several echelons represente by suppliers, plants, warehouses, istribution centres (DCs), an customers. There are usually ifferent supplier options for purchasing raw materials, ifferent prouction options for the assembly of semi-finishe an/or final proucts, an ifferent istribution options to carry final proucts to market. Generally, the esign an management of a supply chain seek to obtain the best global performances so as to achieve the better performance of single link of the chain [1]. Managers who make ecisions at ifferent levels of the supply chain nee to be supporte by robust tools to evaluate the impact of alternative strategies on a firm s performance, prior to making them in the real environment. Quantitative moeling for strategic supply chain planning continues to be a fruitful research area. These moels can be approache through mathematics or simulation [2]. The purpose of the moeling is usually to provie effective ecision support for strategic resource allocation in the longer term, incluing factors such as: Selection of suppliers, configuration of manufacturers an istributors capacities, as well as allocation of these capacities to proucts an so forth. The main purpose of supply chain moeling lies in minimizing or maximizing an objective function through the ientification of ecisions an trae-off solutions that satisfy conflicting objectives at the same time. Therefore, the use of optimization approaches, which are generally base on mathematical moels, is highly recommene in orer to esign supply chains [3] At present, increase worl competition is forcing supply chain companies to reconsier their capacity allocation strategies, particularly given that ecisions, such as capacity allocation ecisions, have a significant impact on supply chain performance. Given limite raw material supplies an limite capacities for prouction, final prouct transportation an istribution centres, the capacity allocation problem etermines how best to use these resources to meet final prouct eman. In this paper, a strategic capacity allocation problem for an automotive supply chain is consiere with a series of fixe operation costs an supply, prouction, transportation, an istribution capacity constraints. At first a mixe level integer programming (MILP) moel is formulate to solve a multi-prouct capacity allocation problem involving multiple suppliers, 51

2 multiple prouction sites an multiple istribution centres. The moel objective is to maximize the overall profit of the whole supply chain, an to minimize the costs of raw material purchasing an inventory, prouct prouction, transportation an istribution, as well as inventory holing an prouct shortage etc. Seconly, the solution to be MILP moel can be obtaine by using optimization software LINGO. The remainer of this paper is organize as follows. Section 2 presents a review of relate literature an further explains the avances in the approach propose. In Section 3, the propose problem is specifie an the mathematical moel is presente. Sections 4 iscuss the moel solution approach. Finally, conclusions are given in Section 5 II. LITERATURE REVIEW Supply chain management (SCM) is a subject of increasing interest to acaemics, an practitioners. The formulation of strategic level moels for supply chain esign has been a popular research topic in the fiel of Supply Chain Management for two ecaes. Most of these formulations are in the form of mixe integer programming (MIP) moels. SCM can be ivie into two levels: strategic an operational. Moels have been evelope for optimizing supply chain operations at these two levels. The primary objective of strategic optimization moels is to etermine the most cost-effective location of facilities (plants an istribution centers), flow of goos throughout the supply chain (SC), an assignment of customers to istribution centers (DCs). These types of moels o not seek to etermine require inventory levels, an customer service levels. The main purpose of the optimization at the operational level is to etermine the safety stock for each prouct at each location, the size an frequency of the prouct batches that are replenishe or assemble, the replenishment transport an prouction lea times, an the customer service levels. In their pioneering paper, Geoffrion an Graves [4] escribe a multi-commoity singleperio Prouction istribution problem an solve it by Beners Decomposition. This is probably the first paper that presents a comprehensive MIP moel for the strategic esign of supply chains. Cohen an Lee [5] evelope a comprehensive moeling framework for linking material management activities throughout the material prouction istribution supply chain. The framework consists of four sub moels. The optimal solution for each sub-moel is solve iniviually uner some assumptions. However, it woul be extremely ifficult to fin the optimal solutions if all sub moels are integrate. A. Bellabaoui [6] presente a mixe integer programming moel for proucing steel making continuous casting prouction. The mixe integer programming formulation is solve using stanar software packages. Annilie. I. Pettersson[7] analyzes supply chain cost an measurements of supply chain cost in inustry. She prescribes a moel for measuring supply chain cost. The stuy shows that general thorough cost an supply chain analyses in many companies can be improve an further evelope. Kejia Chen an Ping Ji [8] present a MIP moel which gives system integration of the prouction planning an shop floor scheuling problems. The objective of the moel is to seek the minimum cost of both prouction ile time an tariness. The output of the moel is operation scheules with orer starting time an finish time. Jolaymi an Olorunniwo [9] provie a eterministic moel for planning prouction quantities in a multi-plant, multi-warehouse environment with extensible capabilities. When the prouction cannot meet eman the moel allows shortfalls to be met through subcontracting or the use of inventory. Syarif et al.[10] consiere the logistic chain network problem formulate by 0-1 mixe integer linear programming moel. The esign tasks of that moel involve the choice of the plants an istribution centers to be opene an the istribution network esign to satisfy the eman with minimum cost. Chan et al. [11] evelope a hybri genetic algorithm for prouction-istribution problems in a supply chain with multi-plants. Their mathematical moel is propose in linear programming form. III. MODEL STRUCTURE AND FORMULATION 1. Problem Description The supply chain structure of the automobile inustry uner stuy consists of four echelons viz. suppliers, manufacturing plants, istribution centers (DCs) an customers as shown in figure 1. Each supply chain echelon has a set of control parameters that affects the performance of other components. The present work aims for the strategic level moeling of supply chain for a section of automobile inustry having two manufacturing plants locate at ifferent places an manufacturing two types of proucts. Both the proucts are manufacture on the two plants. 52

3 Fig. 1 Various Echelons of the Supply Chain The strategic level moeling is the long term planning which ecies the basic configuration of the supply chain an etermine the optimum number of the suppliers out of the approve list, plants an istribution centers to keep uner operation an the assignment of customers to istribution centers with an objective of minimizing the total cost of supply chain. All the supply chain activities are controlle by the corporate office using a network of information flow between the corporate office an various echelons. The inustry uner investigation receives the customer orers at its corporate office. The customer orers primarily inclue the three key information i.e. the quantity require, elivery ates an penalty clause for late elivery. All customers emans are aggregate an the annual prouction istribution planning is one by the corporate office. At the strategic level ecision, the corporate office ecies the suppliers an the allocation of the quantities of the raw materials to the selecte suppliers, optimum prouction quantity allocation to various manufacturing plants, the assignment of the istribution centres to the manufacturing plants an also the assignment of the customers to the istribution centres. 2. Assumptions of the Moel Overall, the stuy is base on the following assumptions: It has been assume that prouction of one unit of a prouct requires one unit of plant capacity, regarless of type of prouct. The similar assumption is aopte for istribution centres also. The components/raw materials procurement an finishe prouct inventory at stores follow a continuous-review inventory control policy. The eman for the finishe proucts is eterministic an the eman rate is constant over time horizon uner stuy. The moel consiers the emans generate at each istribution centre inepenently from each other. The processing time, which is the time to perform the operation, is a linear function of the quantity of the proucts prouce. Transportation times of components/raw materials, subassemblies an finishe proucts between the stages of the prouction cycle have been assume to be same in the present moel. A type of prouct can be prouce in more than one plant, an each plant can prouce at least one type of prouct. The transportation time, waiting time, setup time an prouction processing times have been assume to be fixe. The plants usually hol raw material stock to maintain prouction. 3. Limitations of the Moel The moel has not consiere the global consierations like import/export regulations, uty rates an exchange rates etc. The moel will be applicable in supply chains involve in manufacturing an istribution inustry. Moeling is not having the flexibility of supplying the finishe proucts from manufacturing plants to the customers irectly. Moeling is unable to hanle the risk factors at various stages of the supply chains. Preference of various supply chain members have not been consiere in the moeling. 4. Mathematical Moel A mathematical programming moel is formulate in orer to solve the problem. The notations that will be use to escribe the problem an algorithm are as follows: T Z D C S b Inex on prouct, where t = 1.T, T is number of types of proucts prouce Inex on manufacturing plant, where z = 1.Z, Z is the number of manufacturing plants Inex on istribution center, where = 1.D, D is the number of istribution centers Inex on customer, where c = 1.C, C is the number of customers Inex on supplier, where s = 1.S, S is the number of suppliers Binary variable for istribution centre 53

4 b b c z CP D F F tc z z MaxPV MaxTP MinPV MinTP PC Q Q Q ms msz UCT UPC UTC UTC UTC t w 1, w Z tc msz 2 Objective function Binary variable for istribution centre The objective function of the strategic serving customer c moel is to minimize the total cost of entire supply Binary variable for plant z chain. The total cost of the supply chain inclues the Prouction capacity of plant z cost of raw materials, various transportation costs of (number of proucts/year) components/raw materials an finishe proucts Deman of customer c for prouct t between various echelons an various fixe an (number of proucts/year) variable costs associate with the plants an Fixe cost of istribution centre istribution centres. The objective function which is (Rupees/year) the sum of various costs is represente in Fixe cost of plant z (Rupees/year) mathematical form as: Maximum prouction capacity for Min Z prouct t at plant z (number of proucts/year) where all the costs are represente as: Maximum throughput capacity of istribution centre (number of Type Equation proucts per year) Total cost of components/raw Minimum prouction volume require 1 materials supplie by suppliers for prouct t at plant z to keep the plant operational (number of proucts/year) Minimum throughput require at istribution centre to keep the istribution centre operational (number of proucts/year) Unit cost of component/raw material m of supplier s (Rupees per component or Rupees per Kg) Quantity of prouct t prouce at plant z (number of proucts per year) 5 Quantity of prouct t shippe from plant z to istribution centre (number of proucts/year) 6 Quantity of component/raw material m shippe from supplier s to plant z (number of proucts/year) 7 Unit throughput cost (hanling an inventory)of prouct t at istribution centre (Rupees/prouct) 8 Unit prouction cost for prouct t at plant z (Rupees/prouct) Unit transportation cost of prouct t from istribution centre to customer c (Rupees per prouct) Unit transportation cost of prouct t from plant z to istribution centre (Rupees per prouct) Unit transportation cost of component/raw material m from supplier s to plant z (Rupees per unit of component/raw material) 2 Weight factors for plant an istribution centre volume flexibility Total cost of entire supply chain (Rupees/year) 3 4 Transportation cost of components/raw materials from suppliers to the manufacturing plants. Fixe cost associate with plant operations Variable costs associate with plant operations Fixe cost associate with istribution centre operations Variable cost associate with istribution centre operations Transportation cost of proucts from plants to the istribution centres Transportation cost of proucts from istribution centres to customers Finally the expression for objective function to minimize the total cost of entire supply chain is given by Eq. 1.1 Min Z = (1.1) 54

5 Constraints For an MIP supply chain esign moel, there are many generic constraints to be consiere. In the present supply chain esign moel, constraints are put on the volume flexibility, the balance constraints of components/raw materials an finishe proucts, the capacity limit an throughput limit. These constraints are given by Eqs explaine in brief below: (i) Volume Flexibility: The total volume flexibility is the weighte sum of plants volume flexibility an istribution centres volume flexibility. This shoul satisfy the minimum volume flexibility requirement. The total volume flexibility is expresse as given by Eq. 1.2 whereas the constraint on volume flexibility is represente by Eq Total weighte volume flexibility, W = Plant volume flexibility Distribution volume flexibility W (1.2) W (1.3) (ii) Supplier s Capacity Limits: This constraint ensures that the quantities of raw materials supplie by a supplier to all the allocate plants are within the supply capacity. m,s (1.4) (iii) Materials Requirements of Plants: This constraint ensures that the raw materials quantities arriving from various suppliers fulfill the materials requirements of the plant for prouction of both types of proucts. r,z (1.5) (iv) Prouction Capacity Limits of the Plants: This constraint specifies that the total prouction quantities of both types of proucts o not excee plant capacity. z (1.6) (v) Lower an Upper Bouns on Capacities of Plants: This constraint enforces the minimum an maximum prouction capacities for plants. Min Max t,z (1.7) (vi) Lower an Upper Bouns on Throughput Capacities of Distribution Centres: This constraint enforces the minimum an maximum throughput capacities for istribution centres an ensures that customer assignments can be mae only to istribution centres satisfying the above Min Max (1.8) (vii) Distribution Centre Customer Assignment: This constraint specifies that any particular customer must be assigne to only single istribution centre. 1 c (1.9) (viii) Plant s Output Balance: This constraint ensures that the quantity shippe from a plant to the various allocate istribution centres is equal to what is available at that plant. t,z (1.10) (ix) Deman Requirements at Customers: This constraint ensures that, for both types of proucts, the total shipments from the plants to the istribution centres are exactly equal to the total eman requirements of all the customers. t (1.11) (x) Deman Balance at the Distribution Centres: This constraint ensures that all the incoming quantities of the proucts at the istribution centre from the allocate plants matches with all the outgoing quantities of the proucts from the istribution centres to all allocate customers. t, (1.12) (xi) Non-negativity: This constraint ensures that all the variables are non-negative. m,t,s,z, (1.13) (xii) Binary variables: This constraint ensures the variables to be binary 0 or 1 z,,c (1.14) IV. SOLUTION TO MILP MODEL The use of conventional tools for solving the MIP problem is limite ue to the complexity of the problem an the large number of variables an constraints, particularly for realistically size problems. LINGO an Operations Research software tool is use to solve the strategic MILP moel for supply chain of the sai automobile inustry. LINGO solves the problems by using branch an boun methoology. The main purpose of LINGO is to allow a user to quickly input a moel formulation, solve it, assess the correctness or appropriateness of the formulation base on the solution, quickly make minor moifications to the formulation, an repeat the process. LINGO features a wie range of commans, any of which may be invoke at any time. LINGO optimization moel has two attributes: objective function of problem an constraints of problem. 55

6 1. Inputs to the MILP Moel For obtaining solution by LINGO solver, following ata from automobile inustry has to be collecte an given as input: Unit prouction cost at plants Unit throughput cost (inventory an hanling) per prouct at istribution Unit transportation cost of proucts from plants to istribution centers Fixe cost of plants Fixe costs of istribution centers Prouction capacities of the plants Minimum throughput cost (inventory an hanling) capacity to keep the istribution centers operational Maximum throughput (inventory an hanling) capacity of istribution centers Minimum prouction volume to keep the plants operational Maximum prouction capacity of plants for each prouct Annual eman of the proucts Number of components/raw materials per prouct note from Bill of Materials Utilization rate of components/raw materials per prouct Ientifie suppliers, their capacities an per unit cost of components/raw materials Unit transportation cost of components/raw materials from the suppliers to the plants Unit transportation cost of finishe proucts from istribution centers to the customers Minimum require volume flexibility (weighte sum of volume flexibility at plants an istribution centers) has been restricte to be greater than or equal to zero. 2. Output of MILP Moel After giving the above as input, the strategic moel, given by Eq. 1.1 is able to give the following outputs: Quantities of proucts prouce at the plants. Quantities of raw materials shippe from the suppliers to the plants. Quantities of proucts shippe from plants to the istribution centers. Quantities of proucts shippe from the istribution centers to the customers. Total volume flexibility. Total cost of the entire supply chain. V. CONCLUSION The major aim of the work presente in this paper is to provie a cost effective approach that woul enable manufacturing organizations to gain competitive ege in the global market by coorinating between supplier an buyer to create a win win situation for a ecentralize moel. This work formulates the strategic MILP moel of an automotive supply chain. The main objective of the moel is to minimize the total cost of the entire supply chain. The solution to the MILP moel can be obtaine by using optimization software LINGO. The present moel mainly tackles material flow across the supply chain; the information flow may also be incorporate in the esign. VI. ACKNOWLEDGEMENT The authors wish to thank Punjab Technical University, Kapurthala (Inia) an the case automotive inustry for proviing continuous support an cooperation in carrying out this research work. REFERENCES [1] Aslam T., Ng A.H.C., Multi-objective Optimization for Supply Chain Management: a Literature Review an New Development. SCMIS 8 th International Conference on Supply Chain Management an Information Systems, 6-9 October 2010, 1-8. [2] Aguilar-Savén, R.S., Business Process Moelling: Review an Framework. Int. J. Prouction Economics, 90, [3] Hammami, R., Frein, Y., Haj-Alouane, A.B., Supply Chain Design in the Delocalization Context: Relevant Features an New Moeling Tenencies. Int. J. Prouction Economics, 113, [4] Geoffrion AM, Graves GW. Multicommoity istribution system esign by Beners ecomposition. Management Science 1974;20: [5] Cohen MA, Lee HL. Resource eployment analysis of global manufacturing an istribution networks. Journal of Manufacturing an Operations Management 1989;2: [6] A. Bellabaoui, J. Teghem A Mixe Integer linear programming moel for the continuous casting planning International Journal of Prouction Economics, 104(2006), [7] Kejia Chen, Ping Ji A mixe integer programming moel for avance planning an scheuling European Journal of Operations Research, 181(2007), [8] Kejia Chen, Ping Ji A mixe integer programming moel for avance planning an 56

7 scheuling European Journal of Operations Research, 181(2007), [9] Jolayemi, J. K., Olorunniwo, F. O., 2004, A eterministic moel for planning prouction quantities in a multi-plant, multi-warehouse environment with extensible capacities. International Journal of Prouction Economics, 87, [10] Syarif, A., Yun, Y. an Gen, M., 2002, Stuy on multi-stage logistic chain network: a spanning tree-base genetic algorithm approach. Computers & Inustrial Engineering, 43, [11] Chan, F. T. S an Chung, S. H., 2005, A hybri genetic algorithm for prouction an istribution. OMEGA, 33, Copyright Vanana Publications. All Rights Reserve.

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