A LAGRANGEAN APPROACH TO DYNAMIC LOTSIZING
The lotsizing problem is probably the most celebrated issue in the production-economic literature, ever since the days of Ford Whitman Harris, who presented his first EOQ formula in 1913. The dynamic lotsizing problem generalises this issue to determine batch quantities when required amounts vary over time. Previously has been demonstrated that inner-corner conditions for an optimum production plan in continuous time reduce the number of possible replenishment times to a finite set of given points at which either a replenishment is made, or not. The problem is thus turned into choosing from a set of zero/one decisions with 1 2n. alternatives, of which at least one solution must be optimal, where n is the number of requirement events. This binary representation of the problem led to the development of the Triple Algorithm, which is of the forward type and is applicable either an Average Cost approach or the Net Present Value principle is applied, and it performs in continuous as well as in discrete time. The two most well-known methods for solving the dynamic lotsizing problem are the Wagner-Whitin dynamic programming algorithm, published by Harvey M. Wagner and Thomson M. Whitin in 1958, which leads to an optimal solution, and the Silver-Meal heuristic (1973), which leads to a near-optimal solution. Also a few other discrete-time algorithms have been presented later, such as by Federgruen and Tzur (1991). It has been shown previously that W-W as well as the Silver-Meal heuristic may be stated both in discrete and continuous time, either the Net Present Value (NPV) or the Average Cost (AC) is applied as the objective function. In this paper we formulate the dynamic lotsizing problem analytically using the binary representation mentioned. A Lagrangean function for each of the two objective functions is stated and the necessary Kuhn-Tucker conditions for an optimum derived. This study analyses properties of the fundamental inequalities of the optimisation conditions. It is also shown that the Kuhn-Tucker conditions will not always generate a unique optimum.
Dynamic lotsizing net present value EOQ Lagrangean approach triple algorithm.
Robert W. Grubbstrom FVR RI
Linkoping Institute of Technology, SE-581 83 Linkoping, Sweden
国际会议
上海
英文
1-6
2009-08-02（万方平台首次上网日期，不代表论文的发表时间）