Aggregation of Mixed Integer Production Models by Shadow Prices in Supply Chain Management

Abstract

In supply chain management production planning is often separated into several planning levels. These levels have different degrees of detail and are usually connected by aggregation-disaggregation devices. Particularly aggregate parameters, like aggregate holding cost and capacity consumption rates, are to be determined in an optimal way. Following the aggregation levels of the traditional (MIT) hierarchical production planning approach we are analysing different aggregation devices for an aggregate linear capacity adaptation model and an adjoining detailed mixed integer production model. In particular, focusing on the aggregation of demand we are developing two aggregation procedures in using shadow prices of the inventory balance constraints. An extensive numerical investigation is comparing these new aggregation devices for mixed integer models with the more traditional approaches based on an aggregation of work content and on even simpler aggregation procedures in practice.