A multi-stage stochastic program for supply chain network redesign problem with price-dependent uncertain demands. (English) Zbl 1458.90086
Summary: In this paper, we address a multi-period supply chain network redesign problem in which customer zones have price-dependent stochastic demand for multiple products. A novel multi-stage stochastic program is proposed to simultaneously make tactical decisions including products’ prices and strategic redesign decisions. Existing uncertainty in potential demands of customer zones is modeled through a finite set of scenarios, described in the form of a scenario tree. The scenarios are generated using a Latin hypercube sampling method and then a forward scenario construction technique is employed to create a suitable scenario tree. The multi-stage stochastic problem is formulated as a mixed-integer linear programming model and then Benders decomposition algorithm is applied for solving it. Numerical results demonstrate the significance of the stochastic model as well as the good performance of Benders algorithm. The scenario tree construction method is also evaluated in terms of out-of-sample and in-sample stability. Finally, several key managerial and practical insights in terms of pricing issues are highlighted.
MSC:
| 90B06 | Transportation, logistics and supply chain management |
| 90B10 | Deterministic network models in operations research |
| 90C15 | Stochastic programming |
Keywords:
supply chain network redesign; pricing and revenue management; multi-stage stochastic programming; non-anticipativity constraints; scenario reduction; Benders decompositionReferences:
| [1] | Aghezzaf, E., Capacity planning and warehouse location in supply chains with uncertain demands, J. Oper. Res. Soc., 453-462, (2005) · Zbl 1104.90004 |
| [2] | Ahmadi-Javid, A.; Ghandali, R., An efficient optimization procedure for designing a capacitated distribution network with price-sensitive demand, Optim. Eng., 15, 3, 801-817, (2014) · Zbl 1364.90036 |
| [3] | Ahmadi-Javid, A.; Hoseinpour, P., Incorporating location, inventory and price decisions into a supply chain distribution network design problem, Comput. Oper. Res., 56, 110-119, (2015) · Zbl 1348.90058 |
| [4] | Albareda-Sambola, M.; Alonso-Ayuso, A.; Escudero, L. F.; Fernández, E.; Pizarro, C., Fix-and-relax-coordination for a multi-period location-allocation problem under uncertainty, Comput. Oper. Res., 40, 12, 2878-2892, (2013) · Zbl 1348.90375 |
| [5] | Alonso-Ayuso, A.; Escudero, L. F.; Garìn, A.; Ortuño, M. T.; Pérez, G., An approach for strategic supply chain planning under uncertainty based on stochastic 0-1 programming, J. Global Optim., 26, 1, 97-124, (2003) · Zbl 1116.90383 |
| [6] | Benders, J. F., Partitioning procedures for solving mixed-variables programming problems, Numerische mathematik., 4, 1, 238-252, (1962) · Zbl 0109.38302 |
| [7] | Birge, J.; Louveaux, F., Introduction to stochastic programming, (2000), Springer New York |
| [8] | Cardona-Valdés, Y.; Álvarez, A.; Pacheco, J., Metaheuristic procedure for a bi-objective supply chain design problem with uncertainty, Transp. Res. Part B, 60, 66-84, (2014) |
| [9] | Conejo, A. J.; Castillo, E.; Minguez, R.; Garcia-Bertrand, R., Decomposition techniques in mathematical programming: engineering and science applications, (2006), Springer Science & Business Media · Zbl 1186.90002 |
| [10] | Defourny B, Ernst D, Wehenkel L. Multistage stochastic programming: a scenario tree based approach. Decision Theory Models for Applications in Artificial Intelligence: Concepts and Solutions: Concepts and Solutions. 2011.; Defourny B, Ernst D, Wehenkel L. Multistage stochastic programming: a scenario tree based approach. Decision Theory Models for Applications in Artificial Intelligence: Concepts and Solutions: Concepts and Solutions. 2011. |
| [11] | Dupačová, J.; Consigli, G.; Wallace, S. W., Scenarios for multistage stochastic programs, Ann. Oper. Res., 100, 1-4, 25-53, (2000) · Zbl 1017.90068 |
| [12] | Dupačová, J.; Gröwe-Kuska, N.; Römisch, W., Scenario reduction in stochastic programming, Math. Programm., 95, 3, 493-511, (2003) · Zbl 1023.90043 |
| [13] | Dupačová, J., Multistage stochastic programs: the state-of-the-art and selected bibliography, Kybernetika, 31, 2, 151-174, (1995) · Zbl 0860.90093 |
| [14] | Fattahi, M.; Govindan, K., Integrated forward/reverse logistics network design under uncertainty with pricing for collection of used products, Ann. Oper. Res., 253, 1, 193-225, (2017) · Zbl 1369.90028 |
| [15] | Fattahi, M.; Govindan, K.; Keyvanshokooh, E., Responsive and resilient supply chain network design under operational and disruption risks with delivery lead-time sensitive customers, Transp. Res. Part E, 101, 176-200, (2017) |
| [16] | Fattahi, M.; Mahootchi, M.; Govindan, K.; Moattar Husseini, S. M., Dynamic supply chain network design with capacity planning and multi-period pricing, Transp. Res. Part E, 81, 169-202, (2015) |
| [17] | Fattahi, M.; Mahootchi, M.; Husseini, S. M., Integrated strategic and tactical supply chain planning with price-sensitive demands, Ann. Oper. Res., 242, 2, 423-456, (2016) · Zbl 1350.90008 |
| [18] | Fattahi, M.; Mahootchi, M.; Moattar Husseini, S.; Keyvanshokooh, E.; Alborzi, F., Investigating replenishment policies for centralised and decentralised supply chains using stochastic programming approach, Int. J. Prod. Res., 53, 1, 41-69, (2015) |
| [19] | Georgiadis, M. C.; Tsiakis, P.; Longinidis, P.; Sofioglou, M. K., Optimal design of supply chain networks under uncertain transient demand variations, Omega, 39, 3, 254-272, (2011) |
| [20] | Goh, M.; Lim, J. Y.; Meng, F., A stochastic model for risk management in global supply chain networks, Eur. J. Oper. Res., 182, 1, 164-173, (2007) · Zbl 1127.90038 |
| [21] | Govindan, K.; Fattahi, M., Investigating risk and robustness measures for supply chain network design under demand uncertainty: A case study of Glass supply chain, Int. J. Prod. Econ., 183, Part C, 680-699, (2017) |
| [22] | Govindan, K.; Fattahi, M.; Keyvanshokooh, E., Supply chain network design under uncertainty: A comprehensive review and future research directions, Eur. J. Oper. Res, 263, 1, 108-141, (2017) · Zbl 1380.90041 |
| [23] | Govindan, K.; Jafarian, A.; Nourbakhsh, V., Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic, Comput. Oper. Res., 62, 112-130, (2015) · Zbl 1348.90091 |
| [24] | Guillén, G.; Mele, F.; Bagajewicz, M.; Espuna, A.; Puigjaner, L., Multiobjective supply chain design under uncertainty, Chem. Eng. Sci., 60, 6, 1535-1553, (2005) |
| [25] | Hanjoul, P.; Hansen, P.; Peeters, D.; Thisse, J.-F., Uncapacitated plant location under alternative spatial price policies, Manag. Sci., 36, 1, 41-57, (1990) · Zbl 0694.90045 |
| [26] | Heitsch, H.; Römisch, W., Generation of multivariate scenario trees to model stochasticity in power management, (Power Tech, 2005 IEEE Russia, (2005), IEEE), 1-7 |
| [27] | Huang, E.; Goetschalckx, M., Strategic robust supply chain design based on the Pareto-optimal tradeoff between efficiency and risk, Eur. J. Oper. Res., 237, 2, 508-518, (2014) · Zbl 1304.90034 |
| [28] | Huang, K.; Ahmed, S., The value of multistage stochastic programming in capacity planning under uncertainty, Oper. Res., 57, 4, 893-904, (2009) · Zbl 1226.90055 |
| [29] | Kall, P.; Wallace, S. W., Stochastic programming, (1994), Wiley · Zbl 0812.90122 |
| [30] | Keyvanshokooh, E.; Fattahi, M.; Seyed-Hosseini, S.; Tavakkoli-Moghaddam, R., A dynamic pricing approach for returned products in integrated forward/reverse logistics network design, Appl. Math. Modell., 37, 24, 10182-10202, (2013) · Zbl 1427.90048 |
| [31] | Keyvanshokooh, E.; Ryan, S. M.; Kabir, E., Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated benders decomposition, Eur. J. Oper. Res., 249, 1, 76-92, (2016) · Zbl 1346.90136 |
| [32] | Kiya, F.; Davoudpour, H., Stochastic programming approach to re-designing a warehouse network under uncertainty, Transp. Res. Part E, 48, 5, 919-936, (2012) |
| [33] | Klibi, W.; Martel, A., Modeling approaches for the design of resilient supply networks under disruptions, Int. J. Prod. Econ., 135, 2, 882-898, (2012) |
| [34] | Lin, C.-C.; Wu, Y.-C., Optimal pricing for build-to-order supply chain design under price-dependent stochastic demand, Transp. Res. Part B, 56, 31-49, (2013) |
| [35] | McKay, M. D.; Beckman, R. J.; Conover, W. J., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 2, 239-245, (1979) · Zbl 0415.62011 |
| [36] | Melo, M. T.; Nickel, S.; Da Gama, F. S., Dynamic multi-commodity capacitated facility location: a mathematical modeling framework for strategic supply chain planning, Comput. Oper. Res., 33, 1, 181-208, (2006) · Zbl 1077.90006 |
| [37] | Melo, M. T.; Nickel, S.; Saldanha-da-Gama, F., Facility location and supply chain management - A review, Eur. J. Oper. Res., 196, 2, 401-412, (2009) · Zbl 1163.90341 |
| [38] | Nickel, S.; Saldanha-da-Gama, F.; Ziegler, H.-P., A multi-stage stochastic supply network design problem with financial decisions and risk management, Omega, 40, 5, 511-524, (2012) |
| [39] | Pan, F.; Nagi, R., Robust supply chain design under uncertain demand in agile manufacturing, Comput. Oper. Res., 37, 4, 668-683, (2010) · Zbl 1175.90049 |
| [40] | Phillips, R. L., Pricing and revenue optimization, (2005), Stanford University Press |
| [41] | Pimentel, B. S.; Mateus, G. R.; Almeida, F. A., Stochastic capacity planning and dynamic network design, Int. J. Prod. Econ., 145, 1, 139-149, (2013) |
| [42] | Poojari, C. A.; Lucas, C.; Mitra, G., Robust solutions and risk measures for a supply chain planning problem under uncertainty, J. Oper. Res. Soc., 59, 1, 2-12, (2008) · Zbl 1167.90596 |
| [43] | Rexhausen, D.; Pibernik, R.; Kaiser, G., Customer-facing supply chain practices—the impact of demand and distribution management on supply chain success, J. Oper. Manag., 30, 4, 269-281, (2012) |
| [44] | Santoso, T.; Ahmed, S.; Goetschalckx, M.; Shapiro, A., A stochastic programming approach for supply chain network design under uncertainty, Eur. J. Oper. Res., 167, 1, 96-115, (2005) · Zbl 1075.90010 |
| [45] | Schütz, P.; Tomasgard, A.; Ahmed, S., Supply chain design under uncertainty using sample average approximation and dual decomposition, Eur. J. Oper. Res., 199, 2, 409-419, (2009) · Zbl 1176.90447 |
| [46] | Shen, Z.-J. M., A profit-maximizing supply chain network design model with demand choice flexibility, Oper. Res. Lett., 34, 6, 673-682, (2006) · Zbl 1112.90013 |
| [47] | Snyder, L. V.; Daskin, M. S.; Teo, C.-P., The stochastic location model with risk pooling, Eur. J. Oper. Res., 179, 3, 1221-1238, (2007) · Zbl 1127.90039 |
| [48] | Snyder, L. V., Facility location under uncertainty: a review, IIE Trans., 38, 7, 547-564, (2006) |
| [49] | Sodhi, M. S., Managing demand risk in tactical supply chain planning for a global consumer electronics company, Prod. Oper. Manag., 14, 1, 69-79, (2005) |
| [50] | Talluri, K. T.; Van Ryzin, G. J., The theory and practice of revenue management, (2006), Springer Science & Business Media · Zbl 1083.90024 |
| [51] | Wagner, J.; Falkson, L., The optimal nodal location of public facilities with price sensitive demand, Geogr. Anal., 7, 1, 69-83, (1975) |
| [52] | Zhang, S., On a profit maximizing location model, Ann. Oper. Res., 103, 1-4, 251-260, (2001) · Zbl 1009.90063 |
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