Optimizing location, routing and inventory decisions in an integrated supply chain network under uncertainty

Document Type: Research Paper


School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran


This study extends a mathematical model that integrates the location, allocation, inventory replenishment and routing decisions simultaneously. To cope with inherent uncertainty of parameters, we implement a continuous-time Markov process and derive the performance measures of the system. Using the obtained results, the problem is formulated as a mixed integer nonlinear programing model (MINLP), where the total costs of location, transportation and inventory are minimized. In addition,we develop a simulated annealing(SA)-based meta-heuristic algorithm to tackle the computational complexity of the problem. Finally, severalcomputational experimentsare provided to assess effectiveness of the proposed algorithm and the model.


Main Subjects

Ahmadi-Javid, A., and Seddighi, A. H. (2012). A location-routing-inventory model for designing multisource distribution networks. Engineering Optimization44, 637-656.
Ahmed, M. A. (2007). A modification of the simulated annealing algorithm for discrete stochastic optimization. Engineering Optimization39, 701-714.
Baek, J. W., and Moon, S. K. (2014). The M/M/1 queue with a production-inventory system and lost sales. Applied Mathematics and Computation233, 534-544.
Berman, O., and Kim, E. (2001). Dynamic order replenishment policy in internet-based supply chains. Mathematical Methods of Operations Research53, 371-390.
Chew, E. P., Lee, L. H., and Rajaratnam, K. (2007). Evolutionary algorithm for an inventory location problem. In "Evolutionary Scheduling", pp. 613-628. Springer.
Cochran, W. G., and Cox, G. M. (1957). Experimental designs.
Daskin, M. S., Coullard, C. R., and Shen, Z.-J. M. (2002). An inventory-location model: Formulation, solution algorithm and computational results. Annals of operations research110, 83-106.
Diabat, A. (2015a). A capacitated facility location and inventory management problem with single sourcing. Optimization Letters, 1-16.
Diabat, A., and Theodorou, E. (2015). A location–inventory supply chain problem: Reformulation and piecewise linearization. Computers & Industrial Engineering90, 381-389.
Diabat, D. (2015b). A hybrid genetic algorithm based heuristic for an integrated supply chain problem. Journal of Manufacturing Systems.
Farahani, R. Z., Rashidi Bajgan, H., Fahimnia, B., and Kaviani, M. (2015). Location-inventory problem in supply chains: a modelling review. International Journal of Production Research53, 3769-3788.
Javid, A. A., and Azad, N. (2010). Incorporating location, routing and inventory decisions in supply chain network design. Transportation Research Part E: Logistics and Transportation Review46, 582-597.
Kalpakam, S., and Shanthi, S. (2001). A perishable inventory system with modified (S− 1, S) policy and arbitrary processing times. Computers & Operations Research28, 453-471.
Kirkpatrick, S., and Vecchi, M. P. (1983). Optimization by simmulated annealing. science220, 671-680.
Liao, S.-H., Hsieh, C.-L., and Lai, P.-J. (2011). An evolutionary approach for multi-objective optimization of the integrated location–inventory distribution network problem in vendor-managed inventory. Expert Systems with Applications38, 6768-6776.
Liu, K., Zhou, Y., and Zhang, Z. (2010). Capacitated location model with online demand pooling in a multi-channel supply chain. European Journal of Operational Research207, 218-231.
Melo, M. T., Nickel, S., and Saldanha-Da-Gama, F. (2009). Facility location and supply chain management–A review. European journal of operational research196, 401-412.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. The journal of chemical physics21, 1087-1092.
Miranda, P. A., and Garrido, R. A. (2008). Valid inequalities for Lagrangian relaxation in an inventory location problem with stochastic capacity. Transportation Research Part E: Logistics and Transportation Review44, 47-65.
Ozsen, L., Daskin, M. S., and Coullard, C. R. (2009). Facility location modeling and inventory management with multisourcing. Transportation Science43, 455-472.
Qi, L., Shen, Z. J. M., and Snyder, L. V. (2009). A continuous‐review inventory model with disruptions at both supplier and retailer. Production and Operations Management18, 516-532.
Ramezanian, R., and Saidi-Mehrabad, M. (2013). Hybrid simulated annealing and MIP-based heuristics for stochastic lot-sizing and scheduling problem in capacitated multi-stage production system. Applied Mathematical Modelling37, 5134-5147.
Ross, S. M. (2014). "Introduction to probability models," Academic press.
Sadjadi, S. J., Makui, A., Dehghani, E., and Pourmohammad, M. (2015). Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations. Applied Mathematical Modelling.
Saffari, M., Asmussen, S., and Haji, R. (2013). The M/M/1 queue with inventory, lost sale, and general lead times. Queueing Systems75, 65-77.
Schultz, C. R. (1990). On the optimality of the (S—1, S) policy. Naval Research Logistics (NRL)37, 715-723.
Schwarz, M., Sauer, C., Daduna, H., Kulik, R., and Szekli, R. (2006). M/M/1 queueing systems with inventory. Queueing Systems54, 55-78.
Shen, Z. (2007). Integrated supply chain design models: a survey and future research directions. Journal of Industrial and Management Optimization3, 1.
Shu, J., Teo, C.-P., and Shen, Z.-J. M. (2005). Stochastic transportation-inventory network design problem. Operations Research53, 48-60.
Sigman, K., and Simchi-Levi, D. (1992). Light traffic heuristic for anM/G/1 queue with limited inventory. Annals of Operations Research40, 371-380.
Tawarmalani, M., and Sahinidis, N. V. (2005). A polyhedral branch-and-cut approach to global optimization. Mathematical Programming103, 225-249.
Teimoury, E., Modarres, M., Ghasemzadeh, F., and Fathi, M. (2010). A queueing approach to production-inventory planning for supply chain with uncertain demands: Case study of PAKSHOO Chemicals Company. Journal of Manufacturing Systems29, 55-62.