Note--Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem

This paper concerns a multilocation newsboy problem with normal demand at each location and identical linear holding and penalty cost functions at each location. Consolidation of demand from several facilities is considered, and an expression is derived for the resulting expected holding and penalty costs as a function of the demand parameters for each location (means, variances, and correlation coefficients). The expression is used to demonstrate that (i) the expected holding and penalty costs in a decentralized system exceed those in a centralized system; (ii) the magnitude of the saving depends on the correlation of demands; and (iii) if demands are identical and uncorrelated, the costs increase as the square root of the number of consolidated demands.