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Scheduling multiple products with limited resources and varying demandsremain a critical challenge for many industries. This work presents mixedinteger programs (MIPs) that solve the Economic Lot Sizing Problem (ELSP) andother Dynamic Lot-Sizing (DLS) models with multiple items. DLS systems areclassified, extended and formulated as MIPs. Especially, logical constraintsare a key ingredient in succeeding in this endeavour. They were used toformulate the setup/changeover of items in the production line. Minimising theholding, shortage and setup costs is the primary objective for ELSPs. This isachieved by finding an optimal production schedule taking into account thelimited manufacturing capacity. Case studies for a production plants are usedto demonstrate the functionality of the MIPs. Optimal DLS and ELSP solutionsare given for a set of test-instances. Insights into the runtime and solutionquality are given.

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