Multi-Stage Production Planning

Abstract

The impact of poor production and inventory planning can be significant in any manufacturing firm. On an aggregate level, excessive inventories can lead to poor cash flows necessitating financing to cover operational costs while stock outs can lead to customer service problems and the eventual loss of business. Therefore managers must utilize their aggregate resources effectively while optimizing individual item run quantities on a daily operational level. This paper presents an analytic framework for a hierarchical treatment of a multi-stage linear programming production and inventory problem. The paper is an extension of the single stage case by the author. The problem we address is multi-item, capacitated, and linear. We require certain cost assumptions: monotone costs to determine an optimal aggregate plan and to establish planning horizons, and separability of costs to optimally disaggregate aggregate production. The hierarchical procedure not only makes business and organizational sense, but is also analytically feasible, computationally attractive, and reduces detailed forecasting requirements. The intent of the paper is twofold: first to present an alternative to the classical single monolithic model for the manager and analyst and second, to provide, for the researcher, a basis for a potentially fruitful area of research in hierarchical planning.