New lot-sizing formulations for less nervous production schedules

Previously scheduled production plans frequently need to be updated because of demand uncertainty. After making a comprehensive definition of nervousness which includes costs for changes in production schedule and quantity, we suggest three methodologies. Two methods are modified versions of very well-known methods: the Wagner–Whitin algorithm and the Silver–Meal heuristic. However, our definition of nervousness and its consequences for altering predetermined production volumes make the well-known property of producing either zero or a sum of several periods' demand suboptimal. Therefore a third method, a new mixed integer linear programming formulation, is proposed which is shown to be more effective in some cases. Numerical analyses are carried out for a wide range of possible cases, through which we provide insights to the most appropriate algorithm in a parameterized space.