Iterated Local Search for Foundry Lotsizing and Scheduling Problem with Setup Costs

Abstract

The paper presents a novel Iterated Local Search (ILS) algorithm to solve multi-item multi-family capacitated lot-sizing problem with setup costs independent of the family sequence. The model has a direct application to real production planning in foundry industry, where the goal is to create the batches of manufactured castings and the sequence of the melted metal loads to prevent delays in delivery of goods to clients. We extended existing models by introducing minimal utilization of furnace capacity during preparing melted alloy. We developed simple and fast ILS algorithm with problem-specific operators that are responsible for the local search procedure. The computational experiments on ten instances of the problem showed that the presence of minimum furnace utilization constraint has great impact on economic and technological conditions of castings production. For all test instances the proposed heuristic is able to provide the results that are comparable to state-of-the art commercial solver.

Archives of Foundry Engineering

“…Moreover, if the bottleneck level increases, the differences also increase: it's because RH is not very sensitive to the bottleneck level. However, it is worth noticing that the difference varied depending on the problem size and for (10,2) problem the CPLEX alone is the best approach. The gap between the solutions achieved by CPLEX and the solutions provided by the two other proposed approaches increases with the number of castings, the number of alloys and the bottleneck level.…”

“…In this research we used the same approaches that has been described in [2]. Our goal was to find whether a simple heuristic can be efficient, when compared to the results achieved by CPLEX Solver.…”

“…The ILS algorithm is similar to the one proposed in [2]; in particular, we used the same evolutionary based algorithm as a local search and the same move in the perturbation phase. The modified representation (Table 1) consists of two parts (segments): table y representing alloy types that are produced in furnaces no.…”

“…In order to examine the influence of the bottleneck level on system performance, each instance was computed for five variants of the furnace capacity tightness C max -from very tight 1.0*C to very loose 1.4*C (this parameter simultaneously determines an increasing level of line bottleneck). To ensure comparability of the results for problems of different sizes, three values of setup penalty for alloy type change between two subperiods were set to (1000, 200, 100), inversely proportional to the numbers of alloys in examined instances (2,10,20). Also, the minimal utilization of furnaces capacity during alloy melting process was set to 60% in each subperiod.…”

“…In our previous papers we investigated the production systems consisting of one furnace-one moulding line [1] and one furnacetwo moulding lines [2], where the furnace was a bottleneck. This time we study a planning process in the foundry equipped with two furnaces and one moulding line, which is a bottleneck.…”