Optimal lot size determination of multistage production system

journal article - other

English

This paper deals with the optimization of total setup plus inventory cost of the multistage inventory-production systems by the lot sizes choice. A certain class of multistage single-product inventory-production systems in which the production stages are arranged in series and the production rates of the individual production stages are finite, fixed and generally different, is described in Section 1. The assumptions include an infinite horizon, constant continuous final product demand and time invariant lot sizes. Some special cases of systems of this class are those estimated by Thomas [8], Schussel [5], Taha and Skeith [7], Crowston, Wagner and Williams [2], Streck [6], Klapka [4] and others. These special cases are shown in Section 2. The problem of the cost optimization of such systems is formulated in Section 3 where the methods are also mentioned that the above authors have used to solve the individual systems. For large-scale systems it appears to be useful to have an apriori estimation of the minimal cost in the form of its analytically expressed lower bound. (An upper bound can be obtained in a trivial way.) In the present paper this lower bound is derived for the class of systems under consideration. For this purpose, first of all, in Section 4 a choice is made of a system from the above class, the optimal cost of which is minimal. The exact cost optimization of the system thus selected, presented in Section 5, is based on dynamic programming. Some elements of this solution are employed in Section 6 to derive a lower bound of the optimal cost of this system (Theorem 3). Another representation of this lower bound based on dynamic programming, which provides a clearer view of the proof of Theorem 3, is presented in Theorem 4 and in the Corollary. Some elements of the proof of Theorem 3 are employed in Theorem 5 to derive a simple formula for another lower bound, more or equally distant from the optimal cost. In the case of special conditions imposed on the production system, the said formula turns into a formula derived for this case by Crowston, Wagner and Williams [2]. Section 7 brings the results of some simple numerical examples of the exact cost optimization by the lot sizes choice and of the lower bounds of the optimal cost. The main results presented in this paper were reported by the author in the seminary [11] held on April 8, 1975, during his stay at the Universita di Pisa.

lot size, multistage production system

KLAPKA, J.

1. 1. 1978

Institute of Mathematics, Academy of Sciences of the Czech Republic

Praha

0373-6725

Application of Mathematics

23

2

Czech Republic

81

97

17

http://hdl.handle.net/10338.dmlcz/103734