模糊環境下總體生產計劃之隸屬函數解法

Solving Aggregate Production Planning Problems in Fuzzy Environments: A Membership Function Approach

黃文隆(Wen-Lung Huang)

指導教授 ： 陳世彬

國立中正大學/管理學院/企業管理學系/博士(2015年)

摘要

總體生產計劃 (Aggregate Production Planning, APP) 在作業管理扮演重要的角色，引起許多關注於探討模糊環境中的總體生產計劃問題。然而，之前的研究僅提供明確解，容易造成不是低估或者是高估的現象，導致使用者決策錯誤。本研究在探討多期生產下，不同糢糊不確定性型態的總體生產問題。相較於現有其他研究，由於本研究所提出的模式及求解程序可以保有模糊特性，因此所獲得的總體生產計劃問題解更具有效性。本研究首先考量單產品、單目標總體生產計劃模式，主要概念是基於延展原則(extension principle)和α截集(α-cuts)的應用基礎上，將模糊總體生產計劃模式轉換為明確的總體生產計劃模式。再基於延展原則，建構出模糊最小總成本的隸屬函數，並求出模糊解。透過可能性水準建構出一對二階(two-level)參數規劃，再藉由不同的可能性水準α值計算出模糊總體生產計劃總成本的上界和下界，隨之建構模糊總體生產計劃總成本的隸屬函數(membership function)，並舉例以驗證說明本研究所提出方法的有效性。再者，本研究所提出方法在成功地延伸應用在不同特性的多產品總體生產計劃問題後，進而結合「極大-極小」方法，處理不同型態模糊數的多目標總體生產計劃問題。
相較其他研究，本研究所提出的方法可對不明確或模糊參數求出更合理解，因此可提供決策者有關加班、存貨、缺貨、雇用、解雇人力替代策略更寬範圍的決策資訊以因應模糊環境的變動；再者，可協助製造業決策者降低無效率績效(例如缺貨、延遲)的生產影響與無法吻合正確需求產量的風險。因此，本研究結果可提供決策者更多有效益的總體生產計劃與更可能達到最佳分項計劃 (disaggregate plan)。
本研究所提出的方法亦可應用於其他不同結構的總體生產計劃模式，例如多站、不同目標權重、資源利用限制及供應鏈管理上的總體生產-配銷計劃(Aggregate Production-Distribution Planning, ADPD)。
關鍵字：總體生產計劃、模糊理論、線性規劃、隸屬函數、參數規劃

關鍵字

參數規劃 ； 隸屬函數 ； 線性規劃 ； 總體生產規劃 ； 模糊理論

並列摘要

Aggregate production planning (APP) plays a critical role in operations man-agement (OM) and has attracted considerable attention to investigate the APP problem in fuzzy environments. However, previous studies provided only crisp solutions that are prone to either be under- or over-estimated, thus leading its users to make faulty decisions. This study investigates multi-period APP problems with several distinct types of fuzzy uncertainties. In contrast to the existing studies, the modeling and solution procedure proposed in this work conserves the fuzziness such that the obtained APP is more effective. First, the single-product APP with single-objective is considered. the main concept is based on the application ofα-cuts and Zadeh’s extension principle to transform the fuzzy APP model into a family of crisp APP models. The membership function of the fuzzy minimum total cost is constructed based on Zadeh’s extension principle and fuzzy solutions are provided. A pair of two-level mathematical programs parameterized by the possibility level is formulated to calculate the lower and upper bounds of the fuzzy total cost at each possible level of . By enumerating different values of , the membership function of the fuzzy total cost is constructed. To illustrate the validity of the proposed approach, the example studied by Lai and Hwang (1992) using Chanas’s approach is investigated. Next, the proposed approach is applied to APP problems with other characteristics. It is extended to the multi-product APP successfully. Moreover, combining Zimmermann’s max-min operation, the proposed approach is modified for dealing with the multi-objective APP problems with several fuzzy parameters of different types.
Compared with other studies, the proposed approach can obtain a more reasona-ble solution for imprecise/fuzzy parameters, and so more wide-range decision infor-mation on alternative strategies for overtime, inventory, backorder, and hiring and layoffs workers is provided for decision-makers in response to variations in fuzzy environments. Furthermore, the proposed approach helps decision-makers in manufacturing industry reduce the production impacts of performance inefficiency (e.g. backorder, delay) and risks that demand might not be met with the right products. Thus, the results can provide decision-makers with more effective and informative APPs and more chance to achieve the optimal disaggregate plan.
The proposed approach can also be applied to other APP models with different structures, such as multi-site, different goal priorities, resource utilization constraint, and aggregate production-distribution planning (ADPD) in supply chain management (SCM).
Keywords:aggregate production planning; fuzzy sets; linear programming; member-ship function; parametric programming

並列關鍵字

parametric programming ； membership function ； linear programming ； fuzzy sets ； aggregate production planning

參考文獻

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