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Decision horizons for the capacitated lot size model with inventory bounds and stockouts. (English) Zbl 0790.90027

Summary: We consider the lot size model for the production and storage of a single commodity with limitations on production capacity and storage capacity. There is also the possibility of not meeting demand, i.e. stockouts in the form of lost sales, at a penalty. The stockout option means that horizons can exist and permits the use of orizons to develop a forward algorithm for solving the problem. The forward algorithm is shown to be asymptotically linear in computational requirements, in contrast to the case for the classical lot size model which has exponential computing requirements. Besides the forward algorithm, a number of necessary conditions are derived which reduce the computational burden of solving the model.

MSC:

90B05 Inventory, storage, reservoirs
90B30 Production models
90C90 Applications of mathematical programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C10 Integer programming
90C05 Linear programming
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