The solution of bi-criteria flow shop scheduling problem through mathematical modelling and its application in a shoe factory

This paper addresses a problem occurring in a real-life shoe manufacturing factory consisting of 28 machines. Due to a large number of orders, frequent and long delays in the delivery of the products to customers occur, which costs the factory a significant amount. The problem is formulated as a flow shop scheduling (FSS) problem and a 0-1 integer goal programming model is developed. Computational experiments indicate that problems with up to 50 jobs can be solved within a reasonable time by the developed model. A comparison of the results with the actual case in the factory revealed that, on the average, an improvement of 72.0% in total tardiness (TT) was achieved while an improvement of 3.9% was achieved in the maximum completion time. This helped to save the factory significantly. [Received: 30 January 2023; Accepted: 1 June 2023]