In this paper, a novel way of modeling uncertainty on demand in the single-item dynamic lot sizing problem is proposed and studied. The not related to quantity, but rather timing, i.e., fully occurs single period given time interval with probability no partial delivery allowed. first motivated modeled. Our naturally correlates uncertain demands different periods contrary most literature sizing....

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...

One of the fundamental problems in operations management is to determine the optimal investment in capacity. Capacity investment consumes resources and the decision is often irreversible. Moreover, the available capacity level affects the action space for production and inventory planning decisions directly. In this paper, we address the joint capacitated lot sizing and capacity acquisition pro...