# 臺灣博碩士論文加值系統

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 在Hackman and Leachman [1989]所提出的通用生產模型中，對於非整數前置時間(leadtime)非等長規劃期間(planning periods)的問題所建構的離散模型(discrete model)雖然是正確的，由於生產速率僅能在離散點改變，其它部分均強制為固定速率，所以求得並非現實真正最佳解。在Hung[2000]論文中，證明出當延遲時間為非整數時，若採用所有延遲時間的最大公因數作為時間單位及規劃期間長度，則此模型可以求得真正最佳解，但會使問題大小迅速擴大，因而需要很長的求解時間。為了能夠在合理的運算時間內求得真正的最佳解，Hung針對離散模型發展出一套變數分割程序，希望能夠藉著變數的分割以增進目標值。變數的分割原則是在考慮產品存貨平衡以及資源產能限制下所發展出來的。分割方式是將原有的生產變數在原來的規劃期間內的某些時間點一分為二，藉此讓生產速率變數能有彈性地變動以達到提高目標值的目的。不過在Hung的實驗結果中，發現雖然分割可以提高目標值，但求解時間並不如預期。在Hung的論文中，存貨限制式是採用累加的方式，從時間點0累加到時間 ，所以會產生很多的非零係數，增加求解時間。因此本論文的目的在於修改存貨限制式，希望能使求解時間能夠大幅減少。本論文的存貨限制式是採遞迴方式，本期存貨為上期存貨加上本期流入減去本期流出而得，如此可大量減少非零係數，進而縮短求解時間。
 In the general framework for modeling production proposed by Hackman and Leachman [1989], the model with noninteger leadtime and unequal length time periods are accurate under the assumption of constant production rate between two time grids, but not real optimal in practical application. In Hung’s research [2000] has proved that the real optimum can be obtained by converting the formulation using the greatest common divider (G.C.D.) of all the leadtimes as a time unit and planning period, but the problem size of this model will be huge and requires long computation time. Hence, Hung developed variable partition procedures to improve the objective function value under reasonable computation times. The partition rules were developed by considering product inventory levels and resources capacity constraints. The procedure break up the original production variables at time epochs between original time grid in order to give the flexibility for improving the objective value. The result of the Hung’s experiment show that the partition rules improved the objective value but computation time did not decrease as well as we expect. One possible reason is that, in Hung’s formulation, the inventory balance constraints are built by cumulative flow in and flow out form time 0 to time . This generates a huge number of nonzero coefficients and ,thus, increases the computation time. The purpose of this study is to modify the inventory balance constraints and hopefully, to decrease the computation time substantially. In our modified inventory balance constraints, we use a recursive procedure. The inventory at time is equal to the inventory at former time grid , plus the flow in in the interval ( , ), and minus the flow out in the interval ( , ). By doing this, we will be able to decrease the number of nonzero coefficients and, thus, reduce the computation time.
 Abstract ii Chapter 1 Introduction 1.1. Background 1.2. Motivation Chapter 2 Literature Review 2.1. The General Framework 2.2. Linear Programming Models 2.2.1. Basic Linear Programming Models Without Time Lags 2.2.2. Linear Programming Models with Time Lags 2.2.3. A Linear Programming Model with Noninteger Lead Times 2.2.4. A Linear Programming Model with Unequal-Length Time Periods 2.3. Problem Description Chapter 3 Methodology 3.1. The proof of real optimum 3.2. Development of Variables Partition Rules 3.2.1. Consideration of Inventory Level 3.2.2 Consideration of Resources Capacity 3.3. The modification of the inventory balance constraints 3.4. Variables partition procedures Chapter 4 Computational Experiment and Results 4.1. Experiments Design 4.1.1. Factors 4.1.2. Performance Measure 4.2. Computational Experiments Chapter 5 Conclusion and Further Research References
 洪華霜 (2000) 通用生產模式下之最佳生產計劃, 清華大學工業工程與工程管理碩士論文.CPLEX, (1999), Reference Manual, ILOG CPLEX 6.5.Dessouky, M. M. and Leachman, R. C. (1997). “Dynamic models of production with multiple operations and general processing times”, Journal of the Operational Research Society, Vol. 48, pp. 647-654.Hackman, S. T. and Leachman, R. C. (1989), “A general framework for modeling production”, management Science, Vol. 35, pp. 478-495.Leachman, R. C. (1986), “Preliminary design and development of a corporate-level production planning system for the semiconductor industry”, ORC report, Engineering Research Center, University of California, Berkely.Leachman, R. C., Benson, R. F., Liu, C. and Raar, D.J. (1996), “IMPReSS: An automated production-planning and delivery quotation system at Harris Corporation─semiconductor sector, Interfaces, vol. 26, pp. 6-37.
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 1 通用生產模型下之最佳生產計劃

 1 何維莊、黃天祥、賴秀穗。1991。豬瘟疫苗免疫仔豬適期的研究。中華民國獸醫學會雜誌。17: 89-91。

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