A study on a probabilistic two-echelon location system for deteriorating items

A special case of the probabilistic multi-locationproblem is studied for deteriorating items. The objective of this study is to determine the location of the minimum number of supply centres among a discrete set of location sites of supply centres under the condition that the probability of each retailer being covered by one of the supply centres is not less than a specified value. A logistic cost function including the deterioration rate is developped for a performance measure of the system.

We have formulated a probabilistic set-covering programming which can be solved by a 0–1 programming. The result of a set of numerical examples well shows the impact of deteriorating rate on the location problems. And also this study will provide a method of a useful guidelines for the location decisions.     

A production lot size inventory model for deteriorating items

In this paper, an attempt has been made to develop a production lot size model which incorporates an unfilled-order backlog for an inventory system with exponential decaying items. Approximate expressions are obtained for the optimum production lot size, the production cycle time and the total cycle time. The theory is illustrated by considering a numerical example of this class. Also it is shown that earlier models developed by Ghare and Schrader [3] and Misra [5] can be obtained as particular cases by choosing appropriate values for the various parameters of the model.     

An integrated production-inventory-marketing model for deteriorating items

Generally, inventory control policies for deteriorating items are very sensitive to different marketing policies especially in chemical, food and pharmaceutical industries. Realizing the importance of such inventory policies in practice, an integrated production-inventory-marketing model is developed for determining the economic production quantity (EPQ) and economic order quantity (EOQ) for raw materials in a multi-stage production system. This model considers the effect of different marketing policies such as the price per unit product and the advertisement frequency on the demand of a perishable item. A search method is employed to determine the values of EPQ and EOQ which would result in the maximum total net profit.     

An inventory model for ameliorating and deteriorating items taking account of time value of money and finite planning horizon

The objective of this study is to develop an optimal replenishment inventory strategy to consider both ameliorating and deteriorating effects taking account of time value of money and finite planning horizon. The amelioration rate and the deterioration rate are assumed to follow a Weibull distribution. The inventory system is particularly useful for young livestock whose utility increase over time. The discounted cash flow and optimisation technique are used to derive an optimal solution. A numerical example and sensitivity analysis are given to illustrate the theory of the inventory system.     

A study on an inventory model for items with weibull ameliorating

This paper is concerned with the development of ameliorating inventory models. The ameliorating inventory is the inventory of goods whose utility increases over the time by ameliorating activation. The term ameliorating inventory is used in this paper at least, since the terminology is not standard well known. This study is performed according to areas; one is an economic order quantity(EOQ) model for the items whose utility is ameliorating in accordance with Weibull distribution, and the other is a partial selling quantity(PSQ) model developed for selling the surplus inventory accumulated by ameliorating activation. The proposed models cannot be solved directly in a closed form, thus we used a computer program and a graphical solution method to obtain the optimal ordering and selling quantity in this paper. Numerical examples to illustrate the effect of ameliorating rate on inventory polices are shown at the end of this paper.     

A production lot size inventory model for deteriorating items with time-varying demand

This paper presents a production lot size model for deteriorating items with time-varying demand. The replenishment cycle and deterioration rates are allowed to vary over a finite planning horizon. A solution procedure for this model is developed to provide the optimal replenishment cycle number. Also three numerical examples are solved for different deterioration rates. Finally, a sensitivity analysis is conducted to study the effect of changes in the related parameters on the objective function.     

折损产品整合生产库存系统优化模型研究

在具有两个不同销售周期的销售市场情形下，当需求率、生产率和折损率为常数时，从供应链整合的角度对折损产品的库存系统进行了优化．通过对供应链中产品生产商和销售商库存系统的各自分析，建立了整合库存系统数学模型，给出了优化方法．     

An EOQ model for deteriorating items with time-varying demand and shortages

The study explores the inventory replenishment policies for the cases with time-varying demand, linearly increasing deterioration rate, partial back-ordering, constant service level and equal replenishment intervals over a fixed planning horizon. Since it is difficult to solve the problem directly, we derive the upper bound of replenishment number for a specific planning horizon and find the solution of service level under a given number of replenishment. The optimal solutions of replenishment number and service level are then determined. Numerical examples and sensitivity analyses are also provided to illustrate the solution procedure.     

一类允许缺货的易变质物品的随机非线性存贮模型

研究了货物存贮问题．考虑到在仓库出空期间一般人们有耐烦与不耐烦两种反应，研究中假设仓库出空期丢失顾客量服从正态分布，据此建立允许缺货的易变质物品的非线性存贮模型，使模型更接近于实际．并给出数值例子，运用Matlab软件求解最优存贮控制策略，得到近似的最佳进货量和最佳出空期长度．     

需求随机的变质性产品生产计划模型

研究了能力约束的有限计划展望期生产计划问题,各周期的需求随机,库存产品存在变质且变质率为常数。建立了问题的期望值模型,目标函数为极小化生产准备成本、生产成本、库存成本的期望值。提出了随机模拟、遗传算法和启发式算法相结合的求解算法。用数值实例对模型和算法进行了验证,优化结果表明模型和算法是有效的。     

On conflict and cooperation in a two-echelon inventory model for deteriorating items

Four scenarios are proposed concerning cooperative behavior for inventory policies between suppliers and retailers: no information is shared; the supplier is dominant during negotiations with retailers; the retailer is dominant during negotiations with suppliers; and the supplier and retailer cooperate. Unlike other studies, we consider deteriorating items and permit completed backorders, with a fixed service rate, in the models for these four scenarios. We explore the optimality of these models and present a procedure to find the optimal solution. Numerical examples are provided to illustrate the procedure, which are also used for sensitivity analysis. The results show that the cooperation scenario with information sharing is the best way to reach a win–win position. However, some compensation programs might be required to persuade suppliers or retailers to cooperate when one of them faces a loss of profits in a cooperative scenario.     

Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts

Retailer promotional activity has become prevalent in the business world. Promotional efforts impact the replenishment policy and the sale price of goods. In this paper, the problem of replenishment policy and pricing for non-instantaneous deteriorating items subject to promotional effort is considered. We adopt a price dependent stochastic demand function in which shortages are allowed and partially backlogged. The major objective is to simultaneously determine the optimal selling price, the optimal replenishment schedule, and the optimal order quantity to maximize the total profit. First, we prove that a unique optimal replenishment schedule exists for any given selling price. Second, we prove that the total profit is a concave function of price. Third, we present an algorithm to obtain the optimal solution and solve a numerical example. Last, we extend the numerical example by performing a sensitivity analysis of the model parameters and discuss specific managerial insights.     

A note on the inventory model for deteriorating items with trapezoidal type demand rate

In this paper, we study the inventory model for deteriorating items with trapezoidal type demand rate, that is, the demand rate is a piecewise linearly function. We proposed an inventory replenishment policy for this type of inventory model. The numerical solution of the model is obtained and also examined.     

Deterministic inventory model for deteriorating items with trade credit financing and capacity constraints

This work presents an inventory model for optimizing the replenishment cycle time for a single deteriorating item under a permissible delay in payments and constraints on warehouse capacity (owned warehouse capacity, with excess inventory stored in rental warehouses). Rented warehouses are assumed to charge higher unit holding costs than owned warehouses. Furthermore, item deterioration rates are assumed to differ between warehouses. This study has two main purposes: First, the mathematical models of the inventory system are established under the above conditions. Second, this study demonstrates that the optimal solution not only exists but is unique, and two theorems are devised for determining the optimal replenishment cycle time. Finally, numerical examples are presented to illustrate the resulting theorems.     

An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate

In this paper, we formulate a deteriorating inventory model with stock-dependent demand by allowing preservation technology cost as a decision variable in conjunction with replacement policy. Moreover, it is assumed that the shortages are allowed and partially backlogged, depending on the length of the waiting time for the next replenishment. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time. For any given preservation technology cost, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total profit per unit time is a concave function of preservation technology cost when the replenishment schedule is given. We then provide a simple algorithm to find the optimal preservation technology cost and replenishment schedule for the proposed model. Finally, we use some numerical examples to illustrate the model.     

A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments

In this study, an appropriate inventory model for non-instantaneous deteriorating items with permissible delay in payments is considered. The purpose of this study is to find an optimal replenishment policy for minimizing the total relevant inventory cost. This mathematical model is a general framework that comprises numerous previous models such as in Ghare and Schrader [Ghare, P. M., & Schrader, G. H. (1963). A model for exponentially decaying inventory system. International Journal of Production Research, 21, 449–460], Goyal [Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 36, 335–338], and Teng [Teng, J. T. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 53, 915–918] as special cases. We have developed some useful theorems to characterize the optimal solutions and provide an easy-to-use method to find the optimal replenishment cycle time and order quantity under various circumstances. Several numerical examples are given to test and verify the theoretical results. Finally, a sensitivity analysis of the optimal solution with respect to major parameters is also included. According to the results of numerical analysis, we provided several ways for the retailer to effectively reduce total annual relevant inventory cost.     

A new order splitting model with stochastic lead times for deterioration items

In unreliable supply environments, the strategy of pooling lead time risks by splitting replenishment orders among multiple suppliers simultaneously is an attractive sourcing policy that has captured the attention of academic researchers and corporate managers alike. While various assumptions are considered in the models developed, researchers tend to overlook an important inventory category in order splitting models: deteriorating items. In this paper, we study an order splitting policy for a retailer that sells a deteriorating product. The inventory system is modelled as a continuous review system (s, Q) under stochastic lead time. Demand rate per unit time is assumed to be constant over an infinite planning horizon and shortages are backordered completely. We develop two inventory models. In the first model, it is assumed that all the requirements are supplied by only one source, whereas in the second, two suppliers are available. We use sensitivity analysis to determine the situations in which each sourcing policy is the most economic. We then study a real case from the European pharmaceutical industry to demonstrate the applicability and effectiveness of the proposed models. Finally, more promising directions are suggested for future research.     

An inventory model for deteriorating items with partial backlogging and permissible delay in payments

The paper deals with an inventory model with a varying rate of deterioration and partial backlogging rate under the condition of permissible delay in payments. The existing literature on the subject generally deal with situations where the payment of an order is made on the receipt of items by the inventory system and shortages are either completely backlogged or fully lost. In this paper, a varying deterioration rate of time and the condition of permissible delay in payments used in conjunction with the economic order quantity model are the focus of discussion. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be inversely proportional to the waiting time for the next replenishment. Numerical examples are presented to illustrate the model.     

需求依赖库存且有时变短缺拖后率的非立即变质物品库存模型

研究了时变短缺部分拖后条件下非立即变质性物品的库存补给模型,其中物品的变质率随时间变化而变化。当库存水平为正值时,市场需求受销售价格影响;当库存为负值时,不能满足的需求被部分拖后,拖后率与在缺货期间已经发生的缺货量有关。通过考虑短缺拖后率和变质率同时随时间变化对库存补给策略的影响,建立具有短缺量部分拖后的非立即变质性物品的库存模型,并且给出模型最优解存在的必要条件,得到一类更加符合实际情形的库存模型。最后,用数值算例说明模型的实际应用。