Hybrid flowshops: an LP based heuristic for the planning level problems

In this paper we present an LP based heuristic to a class of planning level problems in hybrid flowshops. The shopfloor under consideration has a certain number of centers arranged in a serial way, each composed of a group of machines working in parallel. We first present the general planning problem modeled as multi-level, parallel processors, multi-item, capacitated, lot-sizing problem with set up times. We suggest an hierarchical approach where parallel processors, multi-item, capacitated, lot-sizing problems with set up times are to be solved. We show how the later problems, in case of identical processors, may be reformulated and solved as trans-shipment problems when the amount of capacity lost in setups are fixed for each period and each processor