Modelling Set-up Times Overlapping Two Periods in the Proportional Lot-Sizing Problem with Identical Parallel Machines

This paper presents a new mixed integer programming model for the Proportional Lot-Sizing Problem (PLSP) with identical parallel machines and set-up times overlapping two periods. The proposed model assumes constant period length and explicitly calculates the distribution of set-up operations among periods. The presented results of computational experiments with standard mip methods prove that the untying set-ups from period borders enables the reduction of the total costs in optimal solutions.