A Mixed Integer Programming Model for Multi-Period Dyeing and Batching Problem in a Yarn Plant

Abstract

In a so-called multi-period yarn dyeing and batching problem, we try to determine the optimal batching of customer orders to be dyed in dye machines in each shift to minimize total lateness and earliness costs. In addition to weight, production quantity and volume capacity of the machines, there is a set of technical dyeing interaction constraints such as flotte, colour types, colour percentages and chemical recipe of customer orders when yarns are immersed in a large vat of coloured water known as the dye-liquor that includes dyestuffs, plus a range of chemicals to assist the dyeing process in the same shift. Furthermore, because of multi-period multi-shift nature of the problem, there is a setup carryover restriction which enforces that from shift to shift the colours must be processed in the increasing degree of darkness, i.e., in technical terms, the colour percentage of the batch increases. To the best of our knowledge, there is no study in the literature to solve this combinatorial optimization problem. Hence, in this paper, we first develop a novel mixed integer programming (MIP) formulation and then, we present a case study in a worldwide known yarn manufacturing company.