An Integrated Model for a Two-supplier Supply Chain with Uncertainty in the Supply

Document Type : Research Paper


Department of Industrial Engineering, University of Science and Culture, Tehran, Iran


The objective of this paper is to study an integrated two-supplier supply chain whose suppliers are unreliable. An unreliable supplier is alternative between available (ON) and unavailable (OFF) states which are considered to be independent exponential variables. The suppliers apply a continuous review policy and the retailer uses an adapted continuous review base on an(R,Q) policy. Transportation times are constant and lead times are non-zero random variables. The retailer faces independent Poisson demands. Using the idea of the one-for-one ordering policy, we implicitly incorporate the distribution function of the random delay for obtaining the value of the expected costs of system. Finally, resorting to a dozen of sample problems, we show that the average cost reduction in our inventory system is at least 3.69% and at most 36.95% comparing to the one with only one supplier.


Main Subjects

[1] Arreola-Risa A., DeCroix G.A. (1998), Inventory management under random supply
disruptions and partial backorders; Naval Research Logistics 46; 687–703.
[2] Axsäter S. (1990), Simple solution procedures for a class of two-echelon inventory problems;
Operations Research 38(1); 64-69.
[3] Axsäter S. (1993), Exact and approximation evaluation of batch-ordering policies for twolevel
inventory systems;Operations Research 41(4); 777-785.
[4] Balcıog̃lu B., and Gürler Ü. (2011), On the use of phase-type distributions for inventory
management with supply disruptions; Applied Stochastic Models in Business and
Industry27: n/a. doi: 10.1002/asmb.879.
[5] Gupta D. (1996), The (Q,r) inventory system with an unreliable supplier;INFOR 34; 59–76.
[6] Gürler Ü., Parlar M. (1997), An inventory problem with two randomly available suppliers;
Operations Research; 45(6); 904-918.
[7] Hadley G., Whitin T.M. (1963), Analysis of inventory systems;Prentice-Hall: Englewood
Cliffs N.J.
[8] Haji R., Sajadifar S.M. (2008), Deriving the exact cost function for a two-level inventory
system with information sharing;Journal of Industrial and System Engineering, 2(1); 41-50.
[9] Hill R.M. (1996), Order splitting in continuous review (Q, r) inventory models;European
Journal of Operational Research 95; 53–61.
[10] Minner S. (2003), Multiple supplier inventory models in supply chain management: a review.
International Journal of Production Economic 81:82; 265-279.
[11] Mohebbi E. (2003), Supply interruptions in a lost-sales inventory system with random lead
time;Computers & Operations Research 30; 411–426.
[12] Mohebbi E. (2004), A replenishment model for the supply-uncertainty problem. International
Journal of Production Economics 87; 25–37.
[13] Mohebbi E., Hao D. (2006), When supplier’s availability affects the replenishment lead time
- an extension of the supply interruption problem; European Journal of Operational Research
175; 992–1008.
[14] Ozekici S., Parlar M. (1999), Inventory models with unreliable suppliers in a random
environment;Annals of Operations Research 91; 123–136.
[15] Parlar M., Berkin D. (1991), Future supply uncertainty in EOQ models; Naval Research
Logistics 38; 107–121.
[16] Parlar M., Perry D. (1995), Optimal (Q; r; T) policies in deterministic and random yield
models with uncertain future supply; European Journal of Operational Research 84; 431–
[17] Parlar M., Wang Y., Gerchak Y. (1995), A periodic review inventory model with Markovian
supply availability;International Journal of Production Economics 42; 131–136.
[18] Parlar M., Perry D. (1996), Inventory models of future supply uncertainty with single and
multiple suppliers;Naval Research Logistics 43; 192–210.
[19] Parlar M. (1997), Continuous-review inventory problem with random supply
interruptions;European Journal of Operational Research 99; 366–385.
[20] Parlar M. (2000), Probabilistic analysis of renewal cycles: An application to a non-Markovian
inventory problem with multiple objectives;Operations Research 48; 243–255.
[21] Sajadifar S.M., Hendi A.M., Haji R. (2008), Exact evaluation of a two sourcing supply chain
with order splitting and information sharing; IEEE conference 2008.
[22] Sajadifar S.M., Pourghannad B. (2010), An integrated supply chain model for the supply
uncertainty problem; International Conference on Industrial Engineering and Operations
Management, Dhaka, Bangladesh.
[23] Tajbakhsh M.M., Zolfaghari S., Lee C.G. (2007), Supply uncertainty and diversification: A
review. in: Jung H., Chen F.F., Jeong B. (Eds), Trends in supply chain design and
management: Technologies and Methodologies. Springer.
[24] Weiss H.J., Rosenthal E.C. (1992), Optimal ordering policies when anticipating a disruption
in supply demand; European Journal of Operational Research 59; 370–382.