變動的需求和生產對經濟製造批量之影響

Abstract

傳統的經濟製造批量通常假設生產與需求率為常數。事實上從很多情況觀察發現，生產率會隨著需求增減而產生變動之情況。同樣的，生產也會受到存貨的影響而隨著存貨量的增加（減少）而減（增）產。本研究引入產品生命週期的概念，三種市場需求模式：成長、成熟和衰退將一一被推導。 過去的研究通常假設在生產過程中忽略了時間的價值。然而，現今資金的利息不低且生產週期通常很長，生產存貨政策明顯地會影響到公司的利益，因此本論文考慮生產、需求、存貨和折扣現金流量之觀點下來發展出各種生產策略。因此，本研究的主要目的為：(1)考慮生產率同時依賴於存貨和需求時的生產模式，(2)考慮三種不同市場需求的生產模式，(3)考慮退化性存貨下的生產模式，(4)考慮時間價值的生產模式。 基於上述目的建立各種生產排程策略，並推導出單位時間最小化平均成本，最後以數值例子來說明所獲得的模式是有效的。

In the existing literature of classical Economic Manufacturing Quantity (EMQ) models, the rate of production and demand is assumed to be constant. In practice, it has been observed that in many situations, the production rate may go up or down with the demand rate. Similarly, the production may be influenced by the on-hand inventory, namely the production rate may play an opposite role when the on-hand inventory level increases or decreases. This research studies the concept of a product life cycle. Three situations of the market demand patterns, i.e., growth, maturity and decline, are considered. Previous studies have been based on the assumption that the time value of money is negligible during a production run. However, interest rates currently are not low and the planning horizon may or may not be short. Production inventory policies obviously affect profitability and any particular policy choice depends upon relative profitability. Therefore, this study attempts to develop various production policies which consider the effects of production, demand, inventory and the discounted cash flow (DCF). More specifically, the objectives of this research are: (1) Develop a production inventory model by assuming the production rate to be dependent on both on-hand inventory and demand. (2) Develop a production inventory model by considering three situations of the market demand patterns, i.e., growth, maturity and decline. (3) Present a more general model where the inventory is deteriorating at a constant rate. (4) Develop the optimal production inventory policies for a finite production time taking account of time value. Optimal expressions are obtained for the production-scheduling period, resulting in a minimization of the expected average cost per unit time. Finally, numerical examples are given to illustrate the proposed methods’ effectiveness.