Dynamic lot size determination
The term Dynamic lot size determination are economic modeling combined, in contrast to the classical Losformel (EOQ formula), batch sizes as determined for time-varying quantities required that cost , production time and other factors are optimized.
The screen Models with dynamic lot size determination shows an overview of the important models for the formulation of lot size problems with the corresponding procedure for solving the problem.
The basic model of Wagner and Whitin
description
The algorithm according to Wagner-Whitin represents an exact procedure for single-stage uncapacitated lot size problems with only one product . According to a widespread prejudice, exact procedures within the scope of lot size planning form the upper limit of complexity and are too computationally intensive for realistic problem sizes. For this reason, following the presentation of the Wagner-Whitin algorithm (1952), heuristic methods were proposed that achieve adequate results. Of a large number of heuristic methods, the variants Silver-Meal Heuristic and Groff-Heuristic should be mentioned in particular .
Extensions of the basic model
The basic model of Wagner and Whitin has been expanded in many ways:
- Variable planning horizon : In the basic model, the requirements of all T periods are known from the start. If the need for period T + 1 becomes known one period later, it may be that the optimal plan changes or, taking into account period T + 1, would have been different from the start (so-called rolling planning). Calculation tests showed that for this case, which often occurs in practice, heuristics are superior to the exact algorithm. The Groff method and the part-period method performed particularly well.
- Variable production costs or purchase prices : These can be mapped by slightly modifying the standard model. Instead of constant costs C, a specific c t is given for each period .
- Discounts on purchase prices Depending on the type and number, the complexity of the model increases to a greater or lesser extent.
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Capacity restrictions :
- Scarce storage capacity : These models can still be solved in polynomial runtime.
- Scarce production capacity : These models belong to the NP-heavy models and represent a special case of the capacitated lot-sizing problem , in the event that only one product is to be produced.
Models with multiple products
Two standard models for multi-product production have become established in the literature. They almost always belong to the NP-hard problems.
The Capacitated Lot-Sizing Problem
The Capacitated Lot-Sizing Problem (CLSP, eng .: Capacitated Lot Size Problem ) is a model in which several products are manufactured with limited production capacity. Several lots can be issued in one period. The order in which the lots of a period are to be produced is not determined. It is suitable for medium-term planning (weeks to months)
The Discrete Lot-Sizing and Scheduling Problem
In the case of the discrete lot sizing and scheduling problem , only one lot can be issued per (very short) period (so-called micro-period). Fixed lot costs are only incurred if another product is to be manufactured in the subsequent period. Sequence planning takes place at the same time. This model is therefore suitable for short-term planning.
swell
- ^ Wallace J. Hopp and Mark L. Spearman (2001) Factory Physics: foundations of manufacturing management. 2nd ed.Boston: McGraw-Hill, 2001 - ISBN 0-256-24795-1 .
- ^ Hans-Otto Günther and Horst Tempelmeier (2005) Production and Logistics. 6th edition Berlin: Springer, 2005 - ISBN 3-540-23246-X .
- ↑ a b Domschke, Scholl, Voß (1997) Production planning: Process organizational aspects. 2nd edition, Springer, Berlin, 1997.