| Abstract: | 在日常生活中，大部份的消費型物品都會產生腐敗或者是衰敗的現象，最常見的就是市場中生鮮蔬果類和酒精類，另外還有化學製品、科技產品等，在正常存放情況下，都會因為時間的流逝導致物品自然發生退化。而退化可分為兩種情況，一種為瞬間退化，一種則為非瞬間退化。瞬間退化即物品在購入的同時，就發生退化；而非瞬間退化則是物品在購入後，經過一段時間後才發生退化。再者，如果期初物品的訂購數量過少，或是當期需求量大增時，往往會發生缺貨的情況。在一家獨佔或數家寡佔的市場，一旦發生缺貨，而且沒有同類型的替代品可供使用時，顧客只好選擇等待補貨或放棄購買，其所造成的損失對公司總利潤的影響並不顯著。然而近幾年，在全球化的影響下，市場多已轉型為完全競爭，亦即，市場上充斥著許多同質性高的物品，除非顧客對該品牌有一定程度的忠誠或特殊的偏好，否則於發生缺貨時，顧客可能選擇購買其他同質性的替代品。此時，因缺貨而產生的損失對公司的總利潤而言，可能會造成嚴重的影響。
傳統的存貨模式，都假設物品是可以永久保存的，而且不允許缺貨的情形發生，為了使模式更能符合真實市場，本研究探討非瞬間退化性物品、允許缺貨且部份欠撥的存貨系統，我們建立兩個不同需求率的單一物品存貨模式。第二章係假設物品的需求與售價呈線性遞減的關係，模式中考慮允許缺貨且部份欠撥，而欠撥率為顧客等候下一次補貨所需時間長度的函數。第三章則是保留第二章部份欠撥的假設，將物品的需求率改為斜坡型且與存貨水準有關。兩個模式皆以單位時間總利潤有最大值為目標，先以傳統的最佳化原理，證明最適解存在而且唯一。接著，分別建立演算法以輔助找出最適解。最後，舉數值範例說明求解過程，並做敏感度分析。
In the real world, most of consumptive products could be decayed or damaged, such as vegetables, fruits, alcohol, chemical products, technical products and others. Normally, the products in storage could be deteriorated by itself as the time going. There are two kinds of deterioration, one is instantaneous deteriorating items, and the other is non-instantaneous deteriorating items. Instantaneous deteriorating means that the product is deteriorated immediately and non-instantaneous deteriorating means that the product is deteriorated after a period of time. Furthermore, if the order quantity is not large enough, or the demand of the product accrues, the backlogging will happen. At a monopoly or oligopoly market, once the shortages occur and there is no substitute to be supplied, customers only have to wait for backorder or give up. The influence caused by shortages is not significant to the company’s total profits. However in recent years, under the influence of globalization, the market has already transformed into perfect competition market and it is filled with the homogeneous products. Unless the customers have the loyalty or special preference to the brand, as the shortage occurs, the customers may probably choose to purchase other homogeneous substitutes. At this situation, the loss caused by shortages will do the serious damage to the company’s total profit.
In classical inventory models, it is generally assumed that the items can be stored indefinitely and occurrences of shortages have never happened. In order to make the model fit to the real market, we discuss the inventory system for non-instantaneous deteriorating items with shortages and partially backlogging. We develop two inventory models for a single product with the different demand rates. In chapter 2, it is assumed that the demand depends on the selling price with a linear decreasing relation. In this model, shortages are allowed and the backlogging rate is variable, which depends on customers’ waiting time for the next replenishment. In chapter 3, we extend the model in chapter 2 with a ramp-type and stock-dependent consumption rate. The objective is to find the maximum total profit per unit time of the inventory system for the two models. First, we prove that the optimal solution is exists uniquely. Then, we establish algorithms to find the optimal solution, respectively. Finally, numerical examples are provided to illustrate the proposed model and sensitivity analysis is carried out. |
