最佳經濟批量排程問題之延伸研究

Abstract

經濟批量排程問題是針對單一生產設備的數種產品，探討其批量大小，並調整其週期生 產的排程，使其生產計劃為可行，又能滿足顧客的需求，且平均總成本達到最小的存貨 控制問題。在本計畫中，希望配合產品與製造性系統的特性，將經濟批量排程問題進行 延伸研究。在許多產業，決策者正面對產品具有損耗特性下之經濟批量排程問題，例如： (1)蔬菜、水果、生鮮食品等易腐敗之食物；(2)汽油、酒精等揮發性之液體；(3)電子元 件之功能退化、輻射性物質蛻變、底片的變質、藥物過期所導致的失效等。另外，在金 屬沖件、電子裝置、汽車、油漆、飲料、動物食品、紡織品及地毯等產業的生產經理人， 則面對多機經濟批量排程問題。針對上述兩個研究議題，本計畫將提出兩年期的研究計 畫進行探討，內容綱要簡述如下： 第一年計畫名稱：「在產品具損耗特性下之最佳經濟批量排程問題與三種排程策略比較 之研究」 研究主題一：在求解產品具損耗特性下之經濟批量排程問題之最佳解搜尋演算法 因為主持人已經發表論文的研究方法，無法應用於「一般整數策略」下的求解， 而且對於求解大型問題時，收斂速度通常較慢。故在求解方法的設計上，本研 究計畫希望可以直接針對產品具有損耗特性下之經濟批量排程問題的數學模 式，進行比較深入的理論分析，並透過最佳解結構的探討，設計搜尋演算法。 研究主題二：在經濟批量排程問題中，常用的三種排程策略之比較 文獻中未見有學者提出研究論文，對於經濟批量排程問題常用的三種排程策 略，在不同的參數組合下，進行求解品質之比較。因為此關乎決策者面對問題 時，應該選擇何種排程策略，直接影響其求解品質，故為一個非常重要的議題。 第二年計畫名稱：「求解相同與異質平行機台生產系統中最佳經濟批量排程問題之研究」 研究主題一：求解相同平行機台生產系統中之最佳經濟批量排程問題 在本研究主題下，希望運用朝兩個方向進行探討：(1)改採動態批量法的排程策 略，分別在「二冪策略」及「一般整數策略」下進行求解；(2)直接針對數學模 式，進行比較深入的理論分析，並透過最佳解結構的探討，設計搜尋演算法， 使其求解速度比文獻中的解法更快，求解的品質更加穩定。 研究主題二：求解異質平行機台生產系統中之最佳經濟批量排程問題 本研究主題希望探討下列兩個方向：(1)將主持人先前求解相同平行機台生產系 統中之最佳經濟批量排程問題運用的「遺傳演算法」，將其延伸於異質平行機 台生產系統中進行求解；(2)將第一個研究主題中，對於相同平行機台經濟批量 排程問題所得的理論分析與最佳解結構的探討，嘗試延伸於異質平行機台生產 系統中，設計搜尋演算法，尋求另一個效率與品質較好的求解方法。 本計畫的研究成果，將可以提供生產管理經理人，擬行最佳的生產計畫、批量與排 程決策之參考。

The objective of the Economic Lot Scheduling Problem (ELSP) is to determine the lot size and the schedule of production of each item so as to minimize the total cost incurred per unit time. We would like to extend the conventional ELSP to incorporate with the characteristics of products and manufacturing systems in the real world in this proposal. In many industries, the production managers face the ELSP with deteriorating products, e.g., (1) direct-spoilage products, vegetable, fruit and fresh food etc.; (2) physical-depletion products, e.g., gasoline and alcohol etc.; (3) deterioration-products, such as radiation change, negative spoiling and loss of efficacy in inventory, e.g., electronic components and medicine. On the other hand, the decision makers in many industries, e.g., metal press, electronic devices, automobile, paint, drink, pet food, textile and carpet industries, encounter the ELSP with identical or heterogeneous parallel production facilities. Following those two problems discussed above, we state the major concerns of this two-year research project as follows. The first-year project: On the Optimal Strategies of the Economic Lot Scheduling for Deteriorating Products and Comparison Analysis among Three Scheduling Strategies Sub-topic 1: Solving the Economic Lot Scheduling Problem with Deteriorating Products Using an Optimal Search Algorithm We note that the solution approach presented in the author’s past study is not applicable to the problem using the general-integer policy. On the other hand, the convergence rate of the proposed genetic algorithm may turn to be unattractive when the problem size becomes large. We would like to investigate the optimality structure of the problem and design an optimal search algorithm based on our theoretical results. Sub-topic 2: Comparison Analysis among Three Scheduling Strategies for the Economic Lot Scheduling Problem We did not find any research article that compares the three commonly-employed scheduling strategies for the ELSP in the literature. We would like to test the three scheduling strategies using different parameter combinations, and provide suggestions for the decision makers before they solve the ELSP. The Second-year project: On Solving the Optimal Strategies for the Economic Lot Scheduling with Identical and Non-identical Parallel Facilities Sub-topic 1: An Optimal Search Algorithm for Solving the Economic Lot Scheduling Problem with Identical Parallel Facilities In this study, we would like to attack this problem using two approaches: (1) apply the dynamic lot scheduling approach, and (2) conduct full theoretical analysis on the mathematical model and design an optimal search algorithm. Then, we may compare the solution quality and the efficiency of the both solution approaches. Sub-topic 2: New Solution Approaches for Solving the Economic Lot Scheduling Problem with Non-identical Parallel Facilities We employ two approaches to solve the concerned problem in this study: (1) modify the genetic algorithm proposed in the author’s previous study, and apply it to solve the problem here, and (2) conduct full theoretical analysis on the mathematical model and design an optimal search algorithm based on our theoretical results. Then, compare the two approaches using random experiments. We strongly believe that the deliveries of our two-year project shall serve an important foundation for establishing a Decision-Support System (DSS) or an Advanced Planning and Scheduling (APS) for production managers in industries.