Managing a Non-Cooperative Supply Chain with Limited Capacity

Operations Research, Vol. 59, No. 4 (2011) 866-881

16 Pages Posted: 27 Jul 2012 Last revised: 6 Dec 2015

See all articles by Rodney P. Parker

Rodney P. Parker

Indiana University Bloomington

Roman Kapuscinski

University of Michigan, Stephen M. Ross School of Business

Date Written: August 1, 2011

Abstract

We consider a two-stage serial supply chain with capacity limits, where each installation is operated by managers attempting to minimize their own costs. A multiple-period model is necessitated by the multiple stages, capacity limits, stochastic demand, and the explicit consideration of inventories. With appropriate salvage value functions, a Markov equilibrium policy is found. Intuitive profit dominance allows for existence of a unique equilibrium solution, which is shown to be a modified echelon base-stock policy. This equilibrium policy structure is sustained in the infinite horizon. A numerical study compares the behavior of the decentralized system with the first-best integrated capacitated system. The performance of this decentralized system relative to the integrated system across other parameters can be very good over a broad range of values. This implies that an acceptable system performance may be attained without the imposition of a contract or other coordinating mechanism, which themselves may encounter difficulties in implementation in the form of negotiation, execution, or enforcement of these agreements. We find instances where tighter capacities may actually enhance channel efficiency. We also examine the effect of capacity utilization on the system suboptimality.

Keywords: inventory, capacity, supply chain, competition, Markov games

JEL Classification: C60, C61, C62, C69, C70, C72, C73, C79, D24, L10, L11, L22, L60, L68, L62, M10, M11

Suggested Citation

Parker, Rodney P. and Kapuscinski, Roman, Managing a Non-Cooperative Supply Chain with Limited Capacity (August 1, 2011). Operations Research, Vol. 59, No. 4 (2011) 866-881, Available at SSRN: https://ssrn.com/abstract=2118192

Rodney P. Parker (Contact Author)

Indiana University Bloomington ( email )

1309 E 10th Street, HH4129
Bloomington, IN 47405
United States

Roman Kapuscinski

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
48
Abstract Views
610
PlumX Metrics