Determining Optimal Number of Suppliers in a Multiple Sourcing Model under Stochastic Lead Times

Document Type : Research Paper


Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran


Employing more than one supplier and splitting orders between them is a strategy employed in supply chains to lessen the lead-time risk in unstable environments. In this paper we present a multiple-sourcing inventory system with stochastic lead-times and constant demand controlled by a continuous review, reorder point-order quantity inventory policy. We consider the situation in which the order quantity is equally split between a number of identical suppliers. The aims of this research are to determine the optimal number of suppliers and analyze the percentage savings obtained in a multiple-sourcing system compared to sole-sourcing. The objective function is to minimize the expected total cost per unit time by obtaining the number of suppliers, the reorder point and order quantity as decision variables. Extensive numerical examples are used to examine the effects of different parameters on the percentage savings and the optimal number of suppliers.


Main Subjects

[1] Chiang C. (2001), Order splitting under periodic review inventory system; International Journal of
Production Economics 70; 67–76.
[2] Chiang, C., Benton, W.C. (1994), Sole sourcing versus dual sourcing under stochastic demands and
lead times; Naval Research Logistics 41; 609–624.
[3] Dullaert W., Maes B., Vernimmen B., Witlox F. (2005), An evolutionary algorithm for order splitting
with multiple transport alternatives; Expert Systems with Applications 28; 201–208.
[4] Hill R.M. (1996), Order splitting in continuous review (Q,r) inventory models; European Journal of
Operational Research 95; 53–61.
[5] Hong J.D., Hayya J.C. (1992), Just-in-time purchasing: single or multiple sourcing?; International
Journal of Production Economics 27; 175–181.
[6] Lau H.S., Zhao L.G. (1993), Optimal ordering policies with two suppliers when lead times and
demands are all stochastic; European Journal of Operational Research 68 (1); 120–133
[7] Minner S. (2003), Multiple-supplier inventory models in supply chain management: a review;
International Journal of Production Economics 81–82; 265–279.
[8] Ramasesh R.V., Ord, J.K., Hayya J.C., Pan A. (1991), Sole versus dual sourcing in stochastic leadtimes,
(s,Q) inventory models; Management Science 37 (4); 428–443.
[9] Ramasesh R.V., Ord, J.K., Hayya, J.C. (1993), Note: dual sourcing with non-identical suppliers; Naval
Research Logistics 40; 279–288.
[10] Ryu S.W., Lee K.K. (2003), A stochastic inventory model of dual sourced supply chain with lead-time
reduction; International Journal of Production Economics 81–82; 513–524.
[11] Sculli D., Wu S.Y. (1981), Stock control with two suppliers and normal lead times; Journal of the
Operational Research Society 32 (11); 1003–1009.
[12] Sedarage D., Fujiwara O., Luong H.T. (1999), Determining optimal order splitting and reorder levels
for n-supplier inventory systems; European Journal of Operational Research 116; 389–404.
[13] Thomas D.J., Tyworth J.E. (2006), Pooling lead-time risk by order splitting: A critical review;
Transportation Research Part E 42; 245–257.
[14] Tyworth J.E., Ruiz-Torres A. (2000), Transportation’s role in the sole versus dual-sourcing decisions;
International Journal of Physical Distribution and Logistics Management 30 (2); 128–144
  • Receive Date: 01 March 2006
  • Revise Date: 15 July 2007
  • Accept Date: 12 November 2007
  • First Publish Date: 01 April 2008