A Branch-and-Price Algorithm for the Dynamic Inventory Slab Allocation Problem in the Steel Industry

This paper addresses a dynamic inventory slab allocation problem (DISAP), which takes both production and inventory into consideration in a real dynamic processing environment. The particularity is that the holding level of inventory slabs that are generated over a tau-period planning horizon must be zero at the end of period tau. The goal is to schedule the inventory slabs so that the total cost of allocation and inventory holding is minimized. We formulate this problem as an integer problem and then decompose this problem into a master problem with set partitioning constraints and a pricing subproblem which is a knapsack problem. A branch-and-price algorithm is first designed for the proposed problem. The computational results show that our algorithm is capable of solving the medium-sized problem.