One of the most important problems in the production and inventory planning field, is the scheduling of production and work force in a dynamic environment. Although this problem can be formulated as a linear program, it is often quite difficult to solve directly, due to its large scale. Instead, it might be fruitful to use a decomposition approach. Decomposition, in general, means decomposing a difficult problem into several easier, or a sequence of easier problems which are later coordinated to reconstruct the original problem.In this report we discuss several possibilities of applying the most common decomposition principles, namely Benders (primal) and Datnzig-Wolfe (dual), as well as a relatively new decomposition method, called cross decomposition, to the dynamic, multiproduct production and employment planning problem. A number of special cases are also presented.

Initial order quantities1989Inngår i: Engineering Costs and Production Economics, ISSN 0167-188X, E-ISSN 1878-4011, Vol. 15, nr C, s. 307-310Artikkel i tidsskrift (Fagfellevurdert)

Abstract [en]

The paper shows how optimal lot sizes are determined in an initial transient phase where the needed lead time may not be available in the production of a batch. It is assumed that the sales are lost. The transient problem is due to the finite production rate. A case is also considered when the constant demand starts suddenly and production is not started in advance. It is assumed that backlogging is not allowed

In order to obtain higher productivity, investments in the production system are needed. Such investments may lead to improvements of two kinds: (i) increased unit production rate and (ii) reduced set-up times. In this paper the impact of capacity investments on capital tied up in work-in-process and inventories is analyzed. Increased production capacity will usually mean that planning parameters, such as lot sizes, have to be changed. For example, if set-up times are reduced an optimal policy will use smaller order quantities. This will then indirectly lead to lower holding costs. The purpose of this study is to evaluate and compare such consequences.

The classical dynamic lot size problem without backlogging is usually solved with the aid of various heuristics. Most heuristics are sequential, i.e. the demand is considered period for period, and a decision whether to include the demand in a certain period in the preceding batch is taken without regarding the future demand. Recently, it has been shown how to design a sequential lot sizing rule that will optimize the average performance, provided that a typical demand looks like a sequence of independent and identically distributed random numbers. The purpose of this paper is to evaluate if and how this methodology can be implemented in practice. The new lot sizing techniques are evaluated in a simulation study for different types of demand

The classical dynamic lot size problem without backlogging is usually solved with the aid of various heuristics. Most heuristics are sequential, i.e. the demand is considered period for period, and a decision whether to include the demand in a certain period in the preceding batch is taken without regarding the future demand. Recently, it has been shown how to design a sequential lot sizing rule that will optimize the average performance, provided that a typical demand looks like a sequence of independent and identically distributed random numbers. The purpose of this paper is to evaluate if and how this methodology can be implemented in practice. The new lot sizing techniques are evaluated in a simulation study for different types of demand.

This paper studies the disaggregation problem within a hierarchical production planning framework for the case when demands are random variables with known probability density functions. Three different heuristic allocation rules have been proposed in order to provide approximate solutions to the problem. The numerical study shows that it is possible to obtain fairly good results by using heuristic rules instead of the optimizing routine. The additional decision rule for choosing one plan among the set of plans suggested by the heuristic, seems to play an important role as far as the first two heuristics are concerned. The third heuristic is less sensitive' with respect to the additional decision rule and also performs slightly better than the other two heuristics

In the production of metallurgical coke for the steel industry, a mix of several coal blends is used. By mixing different coals it is possible to improve cost efficiency and quality. On the other hand, the use of different coals will increase inventory costs. In this paper we discuss this logistic problem and suggest a heuristic algorithm for minimizing the capital costs of coal inventory. Some results from an implementation are given