Scenario-based Modeling Approach and Scatter Search Algorithm for the Stochastic Slab Allocation Problem in Steel Industry

A common problem encountered in steel companies is that of allocating the surplus slabs to customer orders so as to minimize the total cost of production and inventory. Due to many unpredictable events arising in practical manufacture environment, slab yields and customer demands are full of uncertainties. This paper focuses on such uncertainties and studies the stochastic version of the slab allocation problem that has received little attention in the literature. Using a scenario-based approach, we formulate the problem as a mixed integer linear programming (MILP) model. To make the MILP model more concision, we reformulate it with less variables and constraints by using a scenarios aggregation approach. The commercial optimization software such as IBM ILOG CPLEX can solve the model to optimality for small and medium scale instances, but fail to solve large scale instances to optimality. Thus, a scatter search algorithm with directed local search based on follow-up technique is proposed to solve the problem approximately. Moreover, we introduce a random perturbation strategy to avoid search process being tapped in local optimum. Computational results on randomly generated instances show that the proposed algorithm is effective.