需求双向替代与生产转换下动态批量决策及预测时阈研究

doi:10.16381/j.cnki.issn1003-207x.2021.0044

Abstract

Abstract:

Demand （or product） substitution allows a customer who comes to purchase a specific product to accept or choose another available product when her original choice is unavailable or not offered. The notion of substitution has recently been recognized as an effective tool to improve the efficiency of multi-product inventory systems by taking advantage of the inherent flexibility. There are a large number of settings in which costs are incurred only when the product being produced is changed. Such a cost is referred to as the changeover cost. The flexibility associated with demand substitution can be used to address inefficiencies resulting from significant changeover costs.The dynamic lot sizing problem and forecast horizon under production changeovers and two-way demand substitution are analyzed. The optimal decisions of the production for a T-period problem are computed to minimize the production changeovers cost，variable production cost， substitution cost and holding cost. Based on the structural properties of the optimal solution， a forward dynamic programming algorithm is developed to solve the problem. By the marginal cost analysis method， the sufficient condition is given to establish the monotonicity of production points for two products， then the regeneration set is established for two products and the sufficient condition is given to obtain the forecast horizon. Finally， a computational experiment is used to compare the length of forecast horizon under one-way and two-way demand substitution. The length of forecast horizon under at most one changeover and multiple changeovers in a period are also compared. The length of forecast horizon will be lengthened under two-way demand substitution， and will be shortened under multiple changeovers in a period. In addition， the length of forecast horizon increases with changeover costs， and decreases with the parameters of growth and variability and substitution costs.

Key words: forecast horizon, two-way demand substitution, production changeovers, dynamic lot sizing

CLC Number:

F253.4

Fu-ying JING,Yin-ping Mu,Xiang-rui CHAO. Forecast Horizon of Dynamic Lot Sizing Model Under Production Changeovers and Two-Way Demand Substitution[J]. Chinese Journal of Management Science, 2023, 31(8): 226-238.

Figures/Tables 14

符号	定义
$T$	时间周期；
$P (t)$	$t$ -周期问题
$d i t$	第 $t$ 期产品 $i$ 的需求， $d i t ≥ 0$ ， $i = 1,2$ ， $1 ≤ t ≤ T$
$x i t$	第 $t$ 期产品 $i$ 的生产数量， $x i t ≥ 0$ ， $i = 1,2$ ， $1 ≤ t ≤ T$
$I i t$	第 $t$ 期期末（第 $t + 1$ 期期初）产品 $i$ 的库存数量， $I i t ≥ 0$ ， $i = 1,2$ ， $1 ≤ t ≤ T$
$y i j t$	第 $t$ 期产品 $i$ 替代产品 $j$ 的数量， $y i j t ≥ 0$ ， $i, j = 1,2$ ， $i ≠ j$ ， $1 ≤ t ≤ T$
$c i t$	第 $t$ 期产品 $i$ 的单位生产成本， $c i t ≥ 0$ ， $i = 1,2$ ， $1 ≤ t ≤ T$
$K i j t$	第 $t$ 期生产由产品 $i$ 转换到产品 $j$ 的转换成本， $K i j t ≥ 0$ ， $i = 1,2$ ， $i ≠ j$ ， $1 ≤ t ≤ T$
$ω i j t$	第 $t$ 期产品 $i$ 替代产品 $j$ 的替代成本， $ω i j t ≥ 0$ ， $i = 1,2$ ， $i ≠ j$ ， $1 ≤ t ≤ T$
$h i t$	第 $t$ 期产品 $i$ 的单位库存持有成本， $h i t ≥ 0$ ， $i = 1,2$ ， $1 ≤ t ≤ T$

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Forecast Horizon of Dynamic Lot Sizing Model Under Production Changeovers and Two-Way Demand Substitution

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