本文考量一個不完美製程下劣化產品的生產存量模式。在產品的生產週期中,假設前期處於管制狀態,且需求平穩、已知,縱使產品本身有劣化現象,但在固定的劣化率下,生產策略仍為在一定的時間內生產一定的庫存量,以因應所需。由於不允許缺貨,因此,至所有庫存耗盡,新生產即開始。然而在生產過程中,生產系統可能隨機偏移至非管制狀態,造成所生產的產品會出現較高的劣化率。本文所發展模式之目的,在於求解符合單位時間期望總成本最小化的生產期,所涵蓋的成本項目有設置成本、持有成本、劣化成本,而系統至非管制狀態的時間和產品至劣化的時間均假設呈指數分配。本文並提供一個近似最佳解的式子,以利快速求解。
This paper considers a production-inventory model for deteriorating items subject to an imperfect production process. A product is to be manufactured in cycles on a system that is assumed to be in an in-control state at the beginning of a production run. The demand rate of the product is assumed to be fairly stable and known. For each production cycle, the production is run for a predetermined amount of time during which items produced are used to meet the demand and to build inventories. Items produced in this state are subject to a constant rate of deterioration. After a production run is completed, the system will be kept idle until all on-hand inventories are depleted. Since no shortages are allowed, a new production run will begin only when the inventory level reaches to zero. During a production run, the production system may shift at random from an in-control state to an out-of-control state. Subsequently, items produced in the out-of-control state are subject to a higher deterioration rate than those units produced during the in-control state. The objective of the model is to determine a production uptime so as to minimize the expected total cost per unit time including the setup, the inventory holding, and the deterioration cost. The time-to-shift of the productions system and the time-to-deterioration of an item are assumed to be exponentially distributed. A closed-form solution of a near optimal production uptime is derived.