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

First of all, a number of integrated models with/without lot streaming under the integer multiplier coordination mechanism is generalized by allowing lot streaming and three types of inspection for some/all upstream firms. Secondly, the optimal solutions to the three- and four-stage models are individually derived, both using the perfect squares method, which is a simple algebraic approach so that ordinary readers unfamiliar with differential calculus can easily understand how to obtain the optimal solution procedures. Thirdly, optimal expressions for some well-known models are deduced. Fourthly, expressions for sharing the coordination benefits based on Goyal’s (1976) scheme are derived, and a further sharing scheme is introduced. Fifthly, two numerical examples for illustrative purposes are presented. Finally, some future research works involving extension or modification of the generalized model are suggested.     

Uncertainty propagation in a supply chain or supply network

A supply chain is characterized by uncertain demands (demand-side uncertainty) and uncertainties associated with the performances of the production facilities (supply-side uncertainty). In this paper, a method is proposed to plan production in a supply chain with a multi-echelon supply process with unreliable production facilities working in markets with uncertain demand. In such a system it is necessary to consider the global and cumulative effects on the performance of the entire supply chain. We introduce the salient features of uncertainty propagation in supply chains and demonstrate their impact quantitatively using a test problem from the automotive industry.