An inventory model of instantaneous deteriorating items with controllable deterioration rate for time dependent demand and holding cost

Purpose: The purpose of this paper to develop an inventory model for instantaneous deteriorating items with the consideration of the facts that the deterioration rate can be controlled by using the preservation technology (PT) and the holding cost & demand rate both are linear function of time which was treated as constant in most of the deteriorating inventory model. Design/methodology/approach: Developed the mathematical equation of deterministic deteriorating inventory model in which demand rate and holding cost both is linear function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged and obtain an analytical solution which optimizes the total cost of the proposed inventory model. Findings: The model can be applied for optimizing the total inventory cost of deteriorating items inventory for such business enterprises where they use the preservation technology to control the deterioration rate under other assumptions of the model. Originality/value: The inventory system for deteriorating items has been an object of study for a long time, but little is known about the effect of investing in reducing the rate of product deterioration and their significant impact in the business. The proposed model is effective as well as efficient for the business organization that uses the preservation technology to reduce the deterioration rate of the instantaneous deteriorating items of the inventory.Peer Reviewe

Using optimal control to adjust the production rate of a deteriorating inventory system

AbstractThis work represents is another contribution to the application of optimal control theory to production inventory systems. We consider a firm that produces some product at a certain rate and aims at improving this rate. We successfully formulated the model as an optimal control problem and obtained an explicit solution using the maximum principle. An illustrative example is provided and the sensitivity of the model to some of the system parameters was addressed

[[alternative]]A Comparison between Two Pricing and Lot-Sizing Models with Partial Backlogging and Deteriorated Items

計畫編號：NSC93-2416-H032-007研究期間：200408~200507研究經費：374,000[[abstract]]最近，Abad（2003）討論了退化性產品在有限生產率、指數退化率、部分欠撥和 銷售損失下的售價和批量問題。他的模式是週期開始時即生產，由於生產率大於需求 率，存貨逐漸累積；當存貨數量達到某一水準時，便停止生產。接著，庫存量隨著市 場的需求及退化逐漸減少並產生缺貨現象；此時，只有部分顧客願意等待欠撥。當欠 撥數量達到某一水準時，便又開始生產，缺貨數量逐漸被補足。本研究，我們首先將 推廣他的模式，在目標函數中加入欠撥成本和商譽損失成本。接著，對相同的售價和 批量問題，我們建立一個類似於Goyal and Giri（2003）的新模式。此模式是週期開始 時不生產，造成缺貨，而只有部分顧客願意等待欠撥，當欠撥數量達到某一水準時， 便開始生產，缺貨數量逐漸被補足，接著產生存貨。當存貨數量累積到某一水準時， 便停止生產，庫存量隨著市場的需求及退化，逐漸降至零為止。我們以分析的方法比 較這兩個模式的總利潤，並且指出在某些條件下，其中一個模式優於另一個模式。最 後，舉一些例子說明上述的結論。[[sponsorship]]行政院國家科學委員

Development of an EPQ Model for Deteriorating Product with Stock and Demand Dependent Production rate under Variable Carrying Cost and Partial Backlogging

In the present article, an economic production quantity (EPQ) model is developed for deteriorating product with time dependent demand and the time dependent inventory carrying cost. Here,it is assumed that the production rate at any instant depends on both the stock and the demand of the product. To make the model more realistic, the shortages are allowed and partially backlogged. The backordering rate is taken as a decreasing function of waiting time for the next refill.The main objective of the present study is to find the optimal total cost per unit time of the production system. To validate the optimal resuts, numerical example is provided. To analyze the effect of variations in the optimal resuts with respect to change in one parameter at a time, sensitivity analysis is carried out and the results are presented graphically

Comprehensive Analysis and Review of Particle Swarm Optimization Techniques and Inventory System

The main aim of this study work is to discuss the applications of Particle Swarm Optimization (PSO) Techniques and inventory system in engineering and science. Holding and dealing with of a stock item is one of the crucial work for minimum cost and the control running of any commercial enterprise corporation to be it a five-star hotel, a publication house, a production enterprise or a hospital. PSO has numerous application in the area of commercial enterprise and industries. Inventories constitute a huge part of the entire belongings of a corporation, and enormous attempt is needed to manipulate the inventories. In the provision of very restrained assets in nations like India, Sri Lanka, Nepal, Bhutan, Bangladesh, Pakistan, etc., then an obligation of usage of assets with the most efficient way need to be prioritized. Therefore, the control of the substances and stock manipulate play an essential position with the control of productivity. It is hoped that this discussion would be important for researchers using PSO with inventory control

Development of Fuzzy Inventory Model under Decreasing Demand and increasing Deterioration Rate

This research study proposed an inventory model with both the time varying variable deterioration and demand rate under the fuzzy environment. Fuzzy set theory is generally consider with imprecision and uncertainty nature of quantitative coefficients. In this system, we assumed the linearly increasing and decreasing function of time  for deterioration and demand respectively. In this research work, we discuss a fuzzy inventory model solving by signed distance method where demand follow time varying.&nbsp

[[alternative]]Retailer's Optimal Ordering Policy under Supplier Credits

計畫編號：NSC93-2416-H032-005研究期間：200408~200507研究經費：280,000[[abstract]]在現今變動快速且競爭激烈的社會中，為鼓勵零售商增加購買數量，供應商往往 會提供一些獎勵消費行為的策略，如給予現金折扣或延遲付款的寬限期。此有別於傳 統的存貨模式(EOQ)中，零售商在收到貨品的當時即須支付貨款。本研究首先將建立一 數學模式，探討在廠商給予現金折扣或允許延遲付款的條件下，零售商該如何訂定最 佳訂購策略。其次，深入討論此最佳訂購策略的特性。最後，以實例來驗證說明此最 佳訂購策略及其相關性質。 In the traditional inventory economic order quantity (or EOQ) model, it was assumed that the customer must pay for the items as soon as the items are received. However, in practices, the supplier frequently offers a cash discount and/or a permissible delay to the customer especially when the economy turns sour. As a result, in this paper, we establish an optimal ordering policy for a retailer when the supplier provides not only a cash discount to avoid the default risk but also a permissible delay to increase sales. We then characterize the optimal solution and provide an easy-to-use algorithm to find the optimal order quantity and replenishment time. Furthermore, we also compare the optimal order quantity under supplier credits to the classical economic order quantity. Finally, several numerical examples are given to illustrate the theoretical results and make the sensitivity of parameters on the optimal solution.[[sponsorship]]行政院國家科學委員

Existence of EOQ and its evaluation: some cases of stock blow down dynamics depending on its level

The EOQ mathematical models usually deal with the problem of a wholesaler who has to manage a goods restocking policy, settling his best amount of goods to be procured. Best means capable of minimizing all the costs concerning the trade of the stored goods. The relevant seminal contributions are due to Harris, and Wilson, who analyzed an easy scenario with a certain demand uniform all over the time so that its instantaneous change rate is fixed, with stocking charges not dependent on time. In such a field, our own contribution consists of establishing sufficient conditions on the well posedness to the minimum cost problem and relationships providing either closed form solutions or, alternatively, quadrature formulae, without ex ante approximations. All this allows a numerical solution to the transcendental (or algebraical of high degree) equation solving to the most economical batch. In short, such our paper is concerning the special family of EOQ mathematical models with different deterministic time-dependent demands