Multiple-stage multiple-machine capacitated lot-sizing and scheduling with sequence-dependent setup: A case study in the wheel industry

Abstract

This paper studies a real-world problem of simultaneous lot-sizing and scheduling in a capacitated flow shop. The problem combines two significant characteristics in production which are multiple-stage production with heterogeneous multiple machines and sequence-dependent setup time. Setup time does not hold the triangle inequality, thus there may be a setup for a product without actual production. Consequently, a novel mixed integer programming (MIP) formulation is proposed and tested on real data sets of wheel production. Exact approaches cannot find a feasible solution for the model in a reasonable time, so MIP-based heuristics are developed to solve the model more quickly. Test results show that the formulation is able to contain the problem requirements and the heuristics are computationally effective. Moreover, the obtained solution can improve on a real practice at the plant.

A Matheuristic Approach for Solving a Simultaneous Lot Sizing and Scheduling Problem with Client Prioritization in Tire Industry

“…As mentioned before, the underlying constraints to consider vary significantly from one industry to another. Recent papers dealing with simultaneous lot sizing and scheduling (LSS) problems put more focus on particular features of these industries [7]: the beverage industry [10], [11] and [12], steel manufacturing [13], [14] and [15], the automotive industry [16] and [17], glass-container manufacturing [18], the tile industry [19], the chemical industry [20], and the paper industry [21]. Additionally some research has been conducted in the tire industry [22] and [23] and more specifically in the off-the-road tire industry [24] and [25].…”

“…They analysed the impact of time window length, effect of overlapping time windows and capacity constraints and showed that even for simple instances with time-invariant parameters, the worst-case ratio may be unbounded. R&F procedures are often coupled with F&O heuristics as in [16] where a multi-level multi-machine CLSP with setup times was dealt with. The R&F heuristic proposed was a two-level partition of the problem.…”