A Stationary Analysis of a Multicommodity Inventory System with Interacting Set-Up Costs

Abstract

The stationary characteristics of a periodic review multicommodity inventory problem are investigated. The analysis is carried first for a two-commodity system and is then extended to an n-commodity system $(n\geqq 1)$. The stochastic model assumes a dyadic replenishment policy (either nothing is ordered or all commodities are ordered simultaneously) with proportional costs plus a single set-up cost. For $n = 2$ and when the demands for the commodities are independently and exponentially distributed, the cost structure of the problem is analyzed, and in one numerical example the optimal operating costs for individual and joint ordering policies are compared.

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