We consider mixed-integer linear programming (MIP) models of production planning problems known as the small bucket lot-sizing and scheduling problems. We present an application of a class of valid inequalities to the case with lost demand (stock-out) costs. Presented results of numerical experiments made for the the Proportional Lot-sizing and Scheduling Problem (PLSP) confirm benefits of such...

This paper represents a long-standing collaboration between Robert Fildes and Brian Kingsman who sadly died before it could be completed. This paper proposes a methodology for examining the effect of demand uncertainty and forecast error on lot sizing methods, unit costs and customer service levels in MRP type manufacturing systems. A number of cost structures were considered which depend on th...