Crane scheduling in a warehouse storing steel coils

This article studies a single-crane scheduling problem in a warehouse where steel coils are stored in two levels. A given set of coils is to be retrieved from their designated places. If a required coil at the lower level is blocked by one or two coils at the upper level, to retrieve it, the blocking coils must be first moved to other positions. The considered problem is to determine the new positions and the required crane movements so that all coils are retrieved in the shortest possible time. A mixed-integer linear programming model is formulated for the problem and a sequential solution approach is implemented. A dynamic programming algorithm is proposed for optimally solving a restricted case. Based on the analysis of a special case, a heuristic algorithm is proposed for the general case and its worst-case performance is analyzed. The average performances of the solution approaches are computationally evaluated. The results show that the proposed heuristic algorithms are capable of generating good quality solutions.