線性需求下整合性生產存貨模式之最佳批量

An optimal batch size for integrated production-inventory model with a linear trend in demand

歐陽炳昌(Bing-Chang OuYang)

指導教授 ： 黃惠民 ； 饒忻

中原大學/工學院/工業工程研究所/博士(2007年)

https://doi.org/10.6840/cycu200700117

摘要

由於產品需求有淡旺季的現象，過去許多生產或存貨研究的文獻合理地將需求假設為線性函數，且在過去三十年來，大多數文獻皆著重在生產或補貨問題中之最佳解與啟發式演算法的研究，此現象暗示著這類問題的演算法仍有改善空間。
本論文先檢視過去線性需求文獻的演算法，進而提出演算法的改進與其他領域的應用。首先本文將需求為線性函數文獻歸為三類:經濟補貨批量模式、經濟生產批量模式及整合性生產補貨模式。再針對此三種存貨模式個別地提出演算法的改進，簡化過去文獻的複雜運算，本文亦提供完整理論證明彌補過去文獻保留的推測及數值驗證，由結果證實本研究所發展的演算法也是最佳解。
此外，我們還將所發展的演算法延伸到供應鏈管理上單一買賣雙方的應用，發展一個整合性生產存貨模式並提供完整理論證明，驗證本研究建議的模式亦是最佳解，同時也提出範例說明本研究的整合性生產存貨模式與供應鏈整合的重要性。

關鍵字

整合性生產補貨模式 ； 整合性生產存貨模式 ； 線性需求 ； 經濟補貨批量模式 ； 經濟生產批量模式

並列摘要

Due to the usual business cycle of boom and slack, the demand pattern has been assumed to be a reasonably linear trend for production or inventory problems in the literature. In the past three decades, many efforts have made to determine the optimal solution for both production and replenishment problems with a linear trend in demand. However most studies have remained focused on the fundamental methodology and heuristic method development. This implies that a powerful algorithm for these problems is still needed.
In this dissertation, we first provide a simple and accurate algorithm to obtain optimal solutions for previous researches including the replenishment model, production model and integrated production-replenishment for a manufacturing system. Our algorithm is very simple and no complex mathematical calculations such as a cubic equation or power function are required for determining the optimal schedule. In addition, we also develop a general equation to determine the optimal production or replenishment schedule for these three models. The purpose of this study was to provide demonstrations of applicability and completely theoretical proofs to relax some conjectures from previous studies. From the results, we validate that our proposed algorithm is also an optimal solution.
In addition, when considering a supply chain environment, we present an integrated production-inventory model with a linear trend in demand. It is assumed that a vendor makes a single product and supplies it to a buyer with a non-periodic and just-in-time (JIT) replenishment model. The objective is to minimize the joint total cost incurred by the vendor and the buyer. We also provide complete theoretical demonstrations to verify that the Hessian matrix with total cost is positive definite, the solution of the production schedule for a specified production cycles is unique and that the total cost of the production cycles is a convex function of the production cycles. Furthermore, we also show that the performance of integrated consideration in the joint total cost is better than the performance of an independent decision for the buyer or vendor.

並列關鍵字

integrated production- replenishment for a manufacturin ； production model ； replenishment model ； integrated production-inventory model ； linear trend in demand

參考文獻

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