In this paper the Discrete Lotsizing and Scheduling Problem (DLSP) is considered. DLSP relates to capacitated lotsizing as well as to job scheduling problems and is concerned with determining a feasible production schedule with minimal total costs in a single-stage manufacturing process. This involves the sequencing and sizing of production lots for a number of different items over a discrete and finite planning horizon. Feasibility of production schedules is subject to production quantities being within bounds set by capacity. A problem classification for DLSP is introduced and results on computational complexity are derived for a number of single and parallel machine problems. Furthermore, efficient algorithms are discussed for solving special single and parallel machine variants of DLSP.

In this paper the Discrete Lotsizing and Scheduling Problem (DLSP) with setup times is considered. DLSP is the problem of determining the sequence and size of production batches for multiple items on a single machine. The objective is to find a minimal cost production schedule such that dynamic demand is fulfilled without backlogging. DLSP is formulated as a Set Partitioning Problem (SPP). We present a dual ascent and column generation heuristic to solve SPP. The quality of the solutions can be measured, since the heuristic generates lower and upper bounds. Computational results on a personal computer show that the heuristic is rather effective, both in terms of quality of the solutions as well as in terms of required memory and computation time.