允許缺貨之最佳多項損耗產品經濟生產時間模式

Economic Production Period Model for Multi-Deteriorating Items with Shortage

馮納多(Fhernando)

指導教授 ： 黃惠民

中原大學/電機資訊學院/工業與系統工程研究所/碩士(2017年)

https://doi.org/10.6840/cycu201700414

摘要

在典型的經濟生產數量（EPQ）模型通中常假設相關變數是會一直保持完美的狀態。然而，在現實生活中，一些庫存品會隨著時間的推移而劣化。劣化被定義為隨著時間的推移，產品因而損壞，變差，過時失去價值。這就是為什麼在開發EPQ模型時需要考慮劣化問題。在許多討論庫存模型的文獻，它是假設不允許缺貨發生的。然而，在許多實際情況下，由於各種不確定因性，缺貨情況變為無可避免。因而，庫存缺貨的發生是一個自然現象。但在既有的文獻中不多見有考慮到因庫存品劣化而導致缺貨的庫存模型。由於這種情況，本研究選擇了研究考慮因庫存品劣化而導致缺貨的庫存模型。
在這項研究中，開發了三個生產庫存模型。第一個模型提出了經濟生產週期（EPP）模型，考慮缺貨情境，但不考慮庫存品劣化因素。在這個模型中，我們通過尋找最佳化的補貨週期來取得總成本的最優化。第二個模型提出一個EPP模型，考慮困存品劣化所導致缺貨的情境。該模型在不使用串聯近似解以簡化與忽略劣化函數中θ項的第二或更高階的情況下找到總成本的最優解。第三個模型顯示了一個多庫存品劣化品所導致的缺貨EPP模型。此外，我們在這開發這個模式考慮到限制的存庫存量與限制的預算。
我們為多項庫存劣化所導致缺貨的問題開發了一個EPP庫存模式。這項研究的主要目標是減少總成本。庫存品的劣化的分佈遵循指數分佈。最佳庫存補貨週期和經濟生產週期是決策變量。由於這些數學模型是複雜的，因此不能推導出它們的閉合形式解。為簡化求解方法我們使用Maple 15版的來求解。
我們提供每個模型的數值範例來說明推論。通過呈現靈敏度分析證明了關鍵參數對生產時間和總成本的影響。

關鍵字

庫存 ； 經濟生產批量 ； 多庫存品劣化 ； 缺貨

並列摘要

Classical economic production quantity (EPQ) models usually assume all the items will remain in perfect condition. However, in real life some items will deteriorate over time. Deterioration is defined as damage, decay, obsolescence, and loss of value in a product along time. That is why deterioration needs to be considering when developing EPQ model. Many literatures assume that shortages are not permitted to occur. Nevertheless, in many practical situations, stock out is unavoidable due to various uncertainties. Therefore, the occurrence of shortages in inventory is a natural phenomenon. But only a few inventory models for deteriorating item with considering allowable shortages have been found in the literature. Due to this condition, this research study inventory model dealing with deteriorating item and allowing shortage.
In this research, three production inventory models are developed. The first model presents an economic production period (EPP) model with shortage without deteriorating item. In this model, we get optimal solution of total cost by search the optimal cycle length. The second model gives an EPP model for deteriorating item with shortage. This model find the optimal solution of total cost without using series approximation to simplify and neglecting second or higher order of θ term in the deteriorate function. The third model shows an EPP model for multi-deteriorating items with shortage. Furthermore, we develop this model considering a limited storage capacity for item and a limited budget production.
In this study, we develop an EPP inventory model of deteriorating items for multi-items with shortage. The main objective of this research is to minimize the total cost. Distribution of the deterioration item follows the exponential distribution. The optimum inventory cycle and the economic production period are decision variables. Since these mathematical models are complex, their closed form solutions cannot be derived. We use the simple search method using Maple 15 software to solve the models.
We provide the numerical example for each model to illustrate the theorems. The effects of key parameters changes to production up time and total cost demonstrated by presenting sensitivity analysis.

並列關鍵字

Inventory ； EPQ ； multi-item deteriorating ； shortage

參考文獻

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