Dynamic lot size MIPs for multiple products and ELSPs with shortages, capacity and changeover limits

Abstract: Scheduling multiple products with limited resources and varying demands remain a critical challenge for many industries. This work presents mixed integer programs (MIPs) that solve the Economic Lot Sizing Problem (ELSP) and other Dynamic Lot-Sizing (DLS) models with multiple items. DLS systems are classified, extended and formulated as MIPs. Especially, logical constraints are a key ingredient in succeeding in this endeavour. They were used to formulate the setup/changeover of items in the production line. Minimising the holding, shortage and setup costs is the primary objective for ELSPs. This is achieved by finding an optimal production schedule taking into account the limited manufacturing capacity. Case studies for a production plants are used to demonstrate the functionality of the MIPs. Optimal DLS and ELSP solutions are given for a set of test-instances. Insights into the runtime and solution quality are given.