This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems. The Lagrangian dual costs are updated by subgradient optimization, and the single-item problems are solved by dynamic programming. A heuristic smoothing procedure constructs feasible solutions (production plans) which do not require overtime. The algorithm solves problems with setup time or setup cost. Problems with extremely tightly binding capacity constraints were much more difficult to solve than anticipated. Solutions without overtime could not always be found for them. The most significant results are that (1) the tightness of the capacity constraint is a good indicator of problem difficulty for problems with setup time; and (2) the algorithm solves larger problems better than smaller problems, although they are more time consuming to solve. This indicates that larger problems may be easier despite the greater computational effort they require.inventory/production: deterministic models, inventory/production: material requirements planning, programming: large scale systems
This paper investigates a multi-item, multi-level production scheduling problem with linear costs and production and inventory constraints at one key facility. Two multi-item problems---one in which the constraint was on shipping capability and one in which there was a final stage bottleneck machine---motivated the paper. A multi-item facilities-in-series problem is formulated, in standard fashion, as a linear program. Then we show that in certain important cases the 3-period problem is a network problem. This 3-period result is used as the basis for a rolling heuristic for T-period problems. The conditions under which this heuristic fails to find optimal solutions are discussed and computational comparisons to standard linear programming are given. Finally, we discuss ways of dealing with two constrained facilities and with setup costs.inventory/production: deterministic models, material requirements planning, networks/graphs: multi-commodity
This paper presents an easily understood and computationally efficient heuristic algorithm for the capacitated lot sizing problem (CLSP), the single machine lot-skiing problem, with nonstationary costs, demands, and setup times. The algorithm solves problems with setup time or setup cost. A variation of the algorithm can solve problems when limited amounts of costly overtime are allowed.Results of experimentation indicate that the most significant effects on solution quality are due to the level of setup costs relative to holding costs and the size of the problems as determined by the number of items. Also affecting solution quality are tightness of the capacity constraint and variability of demand in a problem. When the capacity constraint is atremely tightly binding, it sometimes has difficulty finding solutions that do not require Overtime Subject Amax Rvduction/Oprmtions Management.
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