中斷式幾何分配生產模式之最適下料演算法研究

An algorithm of the multiple lot sizing problem with rigid demand and interrupted geometric yield

劉芳如(Fang-Ru Liou)

指導教授 ： 古思明

元智大學/工程學院/工業工程與管理學系/碩士(1997年)

摘要

一個生產線必須要生產出訂單所要求之"好的產品數"，下料與成品
數之關係可用機率分配去表示，而要如何在設置成本與變動成本之間做
一權衡，以最小成本做出所有的產品，就要有適當的批量，這就是本文
所要討論的最佳批量。
生產線分配之最佳批量，看似一隨機過程，而實際計算時，是一動
態規畫的問題，二項式分配及離散型均勻分配已有文獻提出其演算法，
而中斷式幾何分配尚無較好的演算法，本文討論在需求量確定、中斷式
分配、呈線性的成本函數之特殊結構下，快速找到其成本相對極小值之
批量的演算法。

關鍵字

確定性需求 ； 中斷式生產 ； 最佳批量

並列摘要

A job shop completely fills an order demand. Production is
conducted in "lot". Lot-sizes that are too large may cause
unnecessarily high production cost. On the other hand, too
small lot-sizes may result in high costs due to frequent
setup. The objective is to determine the first run size to
minimize the expected total cost.

This problem arises in unreliable production systems and
is formulated as a stochastic dynamic program. Although
algorithms have been provided in the literature for
binomial and discrete uniform yields, the interrupted
geometric yield did not have an excellent procedure to
solve for the optimal lot-size. In this research, we
consider the multiple lot sizing problem with interrupted
geometric yield distribution, the customer demand is rigid,
and products cost is linear. An effective algorithm is
developed to search an optimal lot-size for this problem.

並列關鍵字

rigid demand ； interrupted geometric distribution ； optimal lot-size

參考文獻

[1] Anily, S. 1995. "Single Machine Lot-Sizing with Uniform Yields and Rigid Demands: Robustness of the Optimal Solution." IIE Transactions, 27, 625-633.

[2] Beja, A. 1977. "Optimal Reject Allowance with Constant Marginal Production Efficiency." Naval Research Logistics Quarterly, 24, 21-33.

[3] Grosfeld-Nir, A. And Y. Gerchak. 1990 "Multiple Lot-sizing with Random Common-Cause Yield and Rigid Demand." Operation Research Letters, 9,383-388.

[4] Grosfeld-Nir, A. And Y. Gerchak. 1996. "Production to Order with Random Yields: Single-Stage Multiple Lot-Sizing". IIE Transactions, 28, 669-676.

[5] Grosfeld-Nir, A. And B. Ronen. 1993. "A Single Bottleneck System with Binomial Yield and Rigid Demand." Management Science, 39, 650-653.