線性需求下整合性生產存貨模式之最佳批量

歐陽炳昌

doi:10.6840/cycu200700117

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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 , Ph.D　　Advisor：黃惠民;饒忻　　

英文 DOI： 10.6840/cycu200700117

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

Abstract │ Reference (42) │ Altmetrics

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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.

Reference ( 42 ) 〈TOP〉

1 Armani, M. and Rand, G. K. “An eclectic algorithm for inventory replenishment for items with increasing linear trend in demand,” Engineering Costs and Production Economics, 19(1-3), 261-266, (1990).
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2 Banerjee, A. “A joint economic lot size model for purchaser and vendor,” Decision Science, 17(2), 292-311. (1986).
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3 Bylka, S. “A dynamic model for the single-vendor multi-buyer problem,” International Journal of Production Economics, 59(2), 297-304. (1999).
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4 Donaldson, W. A. “Inventory replenishment policy for a linear trend in demand - an analytical solution,” Operational Research Quarterly, 28(3), 663-670, (1977).
連結：
5 Goyal, S. K. “An integrated inventory model for single-supplier single-customer problem,” International Journal of Production Research, 15, 107-111. (1976).
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