A supplement to " A generalized algebraic model for optimizing inventory decisions in a centralized or decentralized multi-stage multi-firm supply chain"

Authors：Francis Leung K N^*

Source：TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW, 2011, 47(5): 778-790.

DOI：10.1016/j.tre.2010.12.007

• Complete backorders
• Inspection
• Lot streaming
• Production-inventory
• The complete/perfect squares method

In this supplement, a number of integrated models under the integer multiplier coordination mechanism is generalized by allowing complete backorders penalized by not only linear but also fixed costs for some/all retailers. The optimal solution to such a three-stage generalized model is algebraically derived, from which optimal expressions for some well-known models are deduced. In addition, an expression for sharing the coordination benefits is modified, and a numerical example for illustrative purposes is presented. A ready future research work involving extension of the generalized model is suggested to conclude the supplement.