A Queuing Model for Stochastic Location‌-inventory Problem with Waiting Cost Considerations

Authors

1 Department of Industrial Engineering, Faculty of Engineering, Payame Noor University, Yazd, Iran

2 Department of Industrial Engineering, Payame Noor University, Tehran, Iran

Abstract

This paper presents a three-level supply chain model which includes single supplier, several distribution centers and sets of retailers. For this purpose, by adopting the queuing approach, a mixed nonlinear integer programming model is formulated. The proposed model follows minimizing the total cost of the system by determining: 1) the number and location of distribution centers between candidated ones; 2) the possibility of allocating each of the retailers to the distribution centers; 3) the amount of retailers demand; and 4) the policy of distribution centers. In the proposed model, the cost of waiting in queue is also considered. In order to make the problem more realistic, we consider uncertain demand and lead-time, which follow Poisson and Exponential distributions, respectively. Hence, we apply continuous-time Markov process approach to obtain the amount of annual ordering, purchase and inventory. Then, the results are used to formulate the location-inventory problem. Finally, the proposed model is solved using GAMS software version 24.1.3.

Keywords


1.     Fox, M.S., Barbuceanu, M. and Teigen, R., Agent-oriented supply-chain management, in Information-based manufacturing. 2001, Springer.81-104.

2.     Diabat, A., Abdallah, T. and Le, T., "A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods", Annals of Operations Research, Vol. 242, No. 2, (2016), 373-398.

3.     Friesz, T.L., Lee, I. and Lin, C.-C., "Competition and disruption in a dynamic urban supply chain", Transportation Research Part B: Methodological, Vol. 45, No. 8, (2011), 1212-1231.

4.     Nekooghadirli, N., Tavakkoli-Moghaddam, R., Ghezavati, V.R. and Javanmard, S., "Solving a new bi-objective location-routing-inventory problem in a distribution network by meta-heuristics", Computers & Industrial Engineering, Vol. 76, (2014), 204-221.

5.     Le, T., Diabat, A., Richard, J.-P. and Yih, Y., "A column generation-based heuristic algorithm for an inventory routing problem with perishable goods", Optimization Letters,  Vol. 7, No. 7, (2013), 1481-1502.

6.     Miranda, P.A. and Garrido, R.A., "Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand", Transportation Research Part E: Logistics and Transportation Review, Vol. 40, No. 3, (2004), 183-207.

7.     Kalpakam, S. and Shanthi, S., "A perishable inventory system with modified (s− 1, s) policy and arbitrary processing times", Computers & Operations Research, Vol. 28, No. 5, (2001), 453-471.

8.     Baumol, W.J. and Wolfe, P., "A warehouse-location problem", Operations Research, Vol. 6, No. 2, (1958), 252-263.

9.     Shu, J., Ma, Q. and Li, S., "Integrated location and two-echelon inventory network design under uncertainty", Annals of Operations Research, Vol. 181, No. 1, (2010), 233-247.

10.   Kaya, O. and Urek, B., "A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain", Computers & Operations Research, Vol. 65, (2016), 93-103.

 

11.   Ameli, M.S.J., Azad, N. and Rastpour, A., "Designing a supply chain network model with uncertain demands and lead times", Journal of Uncertain Systems, Vol. 3, No. 2, (2009), 123-130.

12.   Mak, H.Y. and Shen, Z.J.M., "A two‐echelon inventory‐location problem with service considerations", Naval Research Logistics (NRL), Vol. 56, No. 8, (2009), 730-744.

13.   Schwarz, M., Sauer, C., Daduna, H., Kulik, R. and Szekli, R., "M/m/1 queueing systems with inventory", Queueing Systems,  Vol. 54, No. 1, (2006), 55-78.

14.   Krishnamoorthy, A., Nair, S.S. and Narayanan, V.C., "An inventory model with server interruptions", in Proceedings of the 5th International Conference on Queueing Theory and Network Applications, ACM, (2010), 132-139.

15.   Saffari, M., Haji, R. and Hassanzadeh, F., "A queueing system with inventory and mixed exponentially distributed lead times", The International Journal of Advanced Manufacturing Technology, Vol. 53, No. 9-12, (2011), 1231-1237.

16.   Krishnamoorthy, A. and Viswanath, N.C., "Stochastic decomposition in production inventory with service time", European Journal of Operational Research, Vol. 228, No. 2, (2013), 358-366.

17.   Berman, O., Krass, D. and Tajbakhsh, M.M., "A coordinated location-inventory model", European Journal of Operational Research, Vol. 217, No. 3, (2012), 500-508.

18.   Maleki, L., Pasandideh, S.H.R., Niaki, S.T.A. and Cárdenas-Barrón, L.E., "Determining the prices of remanufactured products, capacity of internal workstations and the contracting strategy within queuing framework", Applied Soft Computing, Vol. 54, (2017), 313-321.

19.   Ghomi-Avili, M., Tavakkoli-Moghaddam, R., Jalali, G. and Jabbarzadeh, A., "A network design model for a resilient closed-loop supply chain with lateral transshipment", International Journal of Engineering-Transactions C: Aspects, Vol. 30, No. 3, (2017), 374-383.

20.   Cárdenas-Barrón, L.E., González-Velarde, J.L. and Treviño-Garza, G., "A new approach to solve the multi-product multi-period inventory lot sizing with supplier selection problem", Computers & Operations Research, Vol. 64, (2015), 225-232.

21.   Cárdenas-Barrón, L.E. and Treviño-Garza, G., "Corrigendum to “an optimal solution to a three echelon supply chain network with multi-product and multi-period”[applied mathematical modelling, 38 (5–6), 1911–1918]", Applied Mathematical Modelling, Vol. 5, No. 40, (2016), 4268-4269.

22.   Chen, Q., Li, X. and Ouyang, Y., "Joint inventory-location problem under the risk of probabilistic facility disruptions", Transportation Research Part B: Methodological, Vol. 45, No. 7, (2011), 991-1003.

23.   Luo, K., Bollapragada, R. and Kerbache, L., "Inventory allocation models for a two-stage, two-product, capacitated supplier and retailer problem with random demand", International Journal of Production Economics, Vol. 187, (2017), 168-181.

24.   Srivathsan, S. and Viswanathan, S., "A queueing-based optimization model for planning inventory of repaired components in a service center", Computers & Industrial Engineering, Vol. 106, (2017), 373-385.

25.   Diabat, A., Dehghani, E. and Jabbarzadeh, A., "Incorporating location and inventory decisions into a supply chain design problem with uncertain demands and lead times", Journal of Manufacturing Systems, Vol. 43, (2017), 139-149.