Overtime vs. regular shift planning decisions in packing shops

Consideration is given to a planning problem arising at the packaging stage of production in several industries (i.e. the packing shop). This, termed economic manpower shift planning with overtime (EMSP-O), seeks the manpower and overtime to be planned at each available workday shift so that production targets are met within a given time horizon at minimum cost. Starting with a practical planning dilemma on the use of overtime, we explore the optimal planning policy together with the performance of two practical policies. An ILP model of EMSP-O is developed and used for determining the optimal policy. Since the problem is shown to be NP-hard, optimal policies were found using a commercial ILP Optimiser. The optimal setting of the practical policies was obtained by existing heuristics. The results show that effective use of overtime leads to workforce reductions and improved utilisation. In many cases, an all-or-nothing property relates overtime and workforce utilisation at optimum. Finally, it is shown that, when indiscriminately used, practical planning policies may have serious cost consequences.