降低籌置成本已經成爲作業管理的主要課題之一。Zangwill已經探討定量降低籌置成本之影響,結果顯示定量降低籌置成本可以降低總生產成本與總儲存成本之和。本文進一步探討非定量降低籌置成本之影響,結果顯示,當籌置成本降低量非定量增加時,總籌置成本與總儲存成本之和亦會減少。大部份文獻採用文字性敘述討論籌置成本降低量之問題,本文運用數學模式,證明非定量增加籌置成本降低量可以獲得上述結論;但是,卻不一定降低總儲存成本,也不一定降低總籌置成本。更進一步,可以獲得總籌置成本與總儲存成本之和之最低降低率,運用模擬方法,我們計算總籌置成本與總儲存成本之和之降低率,總籌置成本之降低率及總儲存成本之降低率,藉以顯示數學模式的真確性。
One primary focus of Operation management has turned to setup cost reduction. Zangwill examines the effects of stationary setup cost reduction. He presents lowering setup costs should decrease total production and inventory costs with stationary setup reduction. Furthermore, we develop the effects of non-stationary setup cost reduction. Likewise as the amount of setup costs reduction increases the total production and inventory costs decrease with non-stationary setup reduction. Most presentations of setup cost reduction are descriptive with very few mathematical models. Using mathematical approach, we prove that total holding and setup costs will be reduced when non-stationary reduction of setup cost is increased. However, it need not necessarily lower total holding costs or total setup costs. Moreover, we develop the minimal reduction rate of total holding and setup costs by mathematical approach. Using simulation, we compute the range of reduction rate on total setup and holding costs, total holding costs and total setup costs to scrutinize mathematical validity.
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