企業基於種種經濟因素考量，在建置自有倉庫時其容量有一定的限制，一經決定之後便很難再做更動。基於眾多因素，零售端常常會囤積許多商品存貨，而因產品價值有時效性的存在，往往會有損耗的情況發生。
在一個生產與銷售的產銷系統中，針對損耗性商品考慮有限的規劃週期與零售端的自有倉庫有容量限制，建構出製造端與零售端的聯合總成本，以總成本最小化為目標來增加企業的核心競爭力，若無法變更容量限制，則找尋是否有其他替代方案來降低總成本。
藉由數學軟體Mathematica 5.2 的幫助，找出產銷系統中最佳的生產次數、最佳週期時間長度以及每週期的最佳生產批量，達到產銷系統總成本極小化的目標。

An enterprise has some limits on owned warehouse capacity that is constant. Besides retailer often stock a lot of inventories that has characteristic of deterioration. A rented warehouse is used when the ordering quantity exceeds the limited capacity of the owned warehouse, and it is assumed that deterioration rates of items in the two warehouses may be different.
This study minimize retailers and manufactures total cost to consider fixed warehouse capacity with deterioration items in a finite planning horizon.
Mathematic software Mathematica 5.2 is used to derive the optimal production times and lots with minimal total cost. Finally, we use a numerical example to illustrate the model.

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