產能限制批量排程問題(CLSSP)在製造業中是個很重要的問題，目標是最小化相關生產成本。本研究探討了考量四項重要因素的CLSSP，是目前最困難的CLSSP。這四項因素包含:(1)順序相依的裝設時間、(2)順序相依的裝設成本、(3)允許裝設延續至下一期，亦即，若下期第一個生產產品與本期最後一個產品相同，不需再重新裝設，以及(4)允許裝設時間跨期，亦即，一次裝設不限定於要在同一期內完成，可以跨越多期。由於此問題的困難度高，目前文獻所提出的解決方法大多附帶許多假設，無法完全符合現實情況。而本文針對能夠完善的涵蓋此四個重要因素的CLSSP，提出解決方案。
本研究將總體解決方案分為離散決策和連續決策，離散決策包含總批量個數、各批量所生產的產品種類，以及各批量之開始生產與各批量之結束生產時間所在的時期。而連續決策則是各個批量開始和結束生產的時間點。本研究透過塔布搜尋法來探索離散決策。給定一個離散決策後，再透過求解線性規劃問題得到最佳連續決策值。本研究採用兩種離散決策生成方案，一種是傳統的鄰近解搜尋方法；另一種則是基於當前離散決策所建構之線性規劃問題中的限制式，透過影子價格資訊來修改限制式，得到新的離散決策。本研究之實驗結果是根據不同參數來產生亂數問題及模擬，由實驗結果顯示，本研究提出之塔布搜尋法與影子價格方法，確實能夠求解此複雜的裝設問題。

Capacitated lot sizing and scheduling problem (CLSSP) or, capacitated lot sizing problem (CLSP) in some literatures, with the objective of minimizing total costs is an essential decision in many manufacturing environments. This study aims to investigate the CLSSP with sequence-dependent setup times, costs, setup carryovers, and setup crossovers, which is one of the most complicated CLSSP problems investigated so far. These difficult features include: (1) sequence-dependent setup times, (2) sequence-dependent setup costs, (3) setup carryovers, in which a duplicated setup for an identical product is removed for subsequent periods, and (4) setup crossovers, which allows the duration of a setup running over multiple periods. Due to the difficulty of this problem, many existing proposed solution approaches were developed under various simplifying assumptions, which hence made these techniques not applicable in certain practical environments.
In this study, an overall solution of the problem can be divided into discrete and continuous decisions. Discrete decisions include the number of batches, the products produced in each batch, and the batches with start time contained in each period and the batches with end time contained in each period. Whereas, a continuous decision refers to the start and end times each batch. This study proposes that discrete decisions are explored by tabu search. Then, given a discrete decision, a linear programming problem can be formulated. By solving the LP problem, the optimal continuous decision values can be obtained. There are two discrete decision generation schemes adopted in this study. One is based on traditional neighborhood search methods. The other is based on the shadow prices of precedence constraints of LP problem of a current discrete decision. The computational experiments on randomly generated problem instances show the effectiveness of the proposed approach.

摘要 1
Abstract 2
LIST OF FIGURES 6
LIST OF TABLES 7
1. Introduction 8
1.1 Background and Applications 8
1.2 Capacitated Lot Sizing and Scheduling Problem(CLSSP) 9
1.3 Extension and Complexity of CLSSP 10
1.4 Problem Statement and Research Approach 12
2.Literature Review 14
2.1 Brief History and Classical Papers on CLSSP 14
2.2 CLSSP with Setup Cost and Time 16
2.3 CLSSP with Setup Carryover 17
2.4 CLSSP with Setup Crossover 19
2.5 A Brief Review on Tabu Search and its Application on CLSSP 20
3. Solution Method 22
3.1 MIP Model for CLSP 22
3.1.1 Assumption and Notations 23
3.1.2 Mathematical Model 25
3.2 Generate Initial Solution: Heuristic Method 27
3.3 Discrete Decisions and Continuous Decisions 32
3.4 Continuous Decision: Linear Programming Model 36
3.4.1 Notations 36
3.4.2 Mathematical model 37
3.4.3 An LP model example 40
3.5 Modification of discrete decision (constraint modification) by shadow price information 42
3.6 Discrete Decision: Searching Methods 43
3.6.1 Construction of Neighborhood Solution 43
3.6.2 Tabu Search Algorithm 46
4. Computation Experiments 49
4.1 Experimental Parameters 49
4.2. Problem Generation Procedure 50
4.3. Parameter Setting 51
4.4 Experimental Results 53
4.4.1 Performance Evaluation 53
4.4.2 Factorial Analyses 55
4.4.3 Further Analyses on Shadow Price 60
5. Conclusions and Future Research 62
Reference 63

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