不完美製程生產存貨系統與聯合補貨模式之研究

An Integrated Production-Inventory System Joint Replenishment Problem with Imperfect Production Process

宋振昌(June-Chun Sung)

指導教授 ： 宮大川

中原大學/工學院/工業工程研究所/博士(2009年)

https://doi.org/10.6840/cycu200900021

摘要

傳統經濟採購批量模式(EOQ)及經濟生產批量模式(EPQ)，為物料採購及生產製造最常採用的存貨控制模式。在過去數十年中，經由放寬理想的假設條件，為數眾多的延伸研究成果已使兩模式趨近於實際的工業界的情況。其中，為同時解決產品及其關聯物料之存貨問題，學者Goyal於1977年已提出一整合生產存貨模式，然而該模式並未考慮製造系統製程退化問題。自此之後，多數不完美製程整合生產存貨模式之延伸研究，聚焦於普通生產製程中的物料耗用，而忽略了重工/重製製程中的物料耗用。忽視生產系統中因不合格品重工/重製製程中的物料耗用所產生缺料影響，可能造成生產遲滯或產生巨額的缺貨懲罰成本。本研究探討可同時決定最佳生產批量及多種物料經濟聯合補貨的單一機器批量生產系統之整合生產存貨模式。假設該生產系統製程為不完美製程，並可能於生產開始後發生劣化情形，並隨機產生一定比率之不合格品；該等不合格品可區分為可修件與報廢件。假設不合格品之重製/重工製程為同質，因此於重製/重工製程後可能仍有一定比例之不合格品產生。由於系統不允許產品缺貨，為滿足需求並補足因不良品報廢所導致的生產缺貨，故將拒收寬放量納入生產數量中。本研究目的在求取無限計畫時間軸下，最小化不完美製程之生產系統期望總成本，以同時決定最佳的系統生產週期時間及各物料之聯合補貨頻率。研究依不合格品所採取的重製或重工策略，以及重製或重工製程是否為不完美製程，建構出四種不同生產存貨模式。由於系統期望總成本函數為片段凸性函數，求解不易。為求取模式之最佳或近似最佳解，研究首先進行成本函數凸性分析，並發展出一搜尋法以利具體求解。研究中以一數值範例舉例說明各模式的正確性及差異，並進行敏感度分析以探討不同參數之影響。

關鍵字

不完美製程 ； 聯合補貨 ； 存貨

並列摘要

The classical Economic Ordering Quantity (EOQ) model and the Economic Production Quantity (EPQ) model are the most frequently adopted inventory control models for material purchasing and product manufacturing. Numerous research efforts have been undertaken over the past few decades to extend both models by relaxing various idealistic assumptions so that the models can resemble the real industry situations closely. One of those extensions for solving the inventory problem of the finished product and its input raw materials simultaneously was the integrated production-inventory model (IPIM) which proposed by Goyal in 1977. But it did not consider the situation where a manufacturing system may deteriorate during the production process. After that, numerous extension studies of IPIM under the imperfect production process condition focused only on the consumption of raw materials in ordinary production processes but neglected the problems of raw materials consumption resulting from the rework/reproduction process for the imperfect items. Ignoring the effect of shortage of raw materials caused by the reproduction/rework of defective items during a production system may make production idle and incur huge penalty of shortage.
This research considers the integrated production-inventory model to determine an optimal production lot size and economic joint replenishment quantity of multi-material simultaneously in a single product, single facility batch production system. The production process is assumed to be deteriorated after it starts and some portion of the products may become defective items randomly. The defective items fall into two groups, the repairable ones and the scrap ones. Since the reproduction or rework process is homogeneous, hence, some portion of the defective items may also be generated during it. Because no shortage of the finished product is permitted, the reject allowance quantity must be added in the initial production quantity in order to fulfill the demand and to supplement the shortage caused by the defective items discarded. Altogether, the objective of this study is to minimize the expected total cost of the system over an infinite horizon in order to decide the optimal production cycle time and the raw material joint replenishment frequency.
According to the manipulation of the defective items, whether by reproduction or by rework and either the process is perfect or imperfect, the study developed four different models. Due to the expected total cost function of each model is a piecewise convex function, it is difficult to derive a global optimal solution directly. For finding out the solutions of these models, a convexity analysis of cost function was held firstly and then a search algorithm is developed to derive the optimal or near optimal solution. To demonstrate each model’s fidelity and learn the differences, same numerical example is used and illustrated. Also, in order to analyze the effects of the various parameters, a sensitivity analysis was held.

並列關鍵字

Imperfect production pr ； Joint replenishment ； Inventory

參考文獻

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