The effect of preservation technology investment on a non-instantaneous deteriorating inventory model

Considering an inventory system with a non-instantaneous deteriorating item, our objective is to study the effect of preservation technology investment on inventory decisions. The generalized productivity of invested capital, deterioration and time-depend partial backlogging rates are used to model the inventory system. The basic results of fractional programming are employed to prove the uniqueness of the global maximum for each case. We also establish several structural properties on finding the optimal replenishment and preservation technology strategies. Further, we use a couple of numerical examples to illustrate the results and conclude the paper with suggestions for possible future researches.     

Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost

In this paper, an economic order quantity inventory model is analyzed, considering that the unit cumulative holding cost has two significant components: a fixed cost which represents the cost of accommodating the item in the warehouse and a variable cost given by a potential function of the length of time over which the item is held in stock. Shortages are allowed and, during the stockout period, only a fraction of demand is partially backordered. The backordering cost includes a fixed cost and a cost linearly dependent on the length of time for which backorder exists. A solution procedure is developed for determining the optimal inventory policy. Moreover, to illustrate the effects of some parameters on the optimal policy and the minimum total inventory cost, a numerical study is developed.     

An optimal replenishment model for inventory items with normally distributed deterioration

This paper deals with the inventory replenishment problem for deteriorating items with normally distributed shelf life, continuous time-varying demand, and shortages under the inflationary and time discounting environment. The reasons of choosing normal are twofold: it is one of the most important probability phenomena in the real world due to the classical central limit theorem, and it is also one of the most commonly used lifetime distributions in reliability contexts. The problem is formulated as a dynamic programming model and solved by numerical search techniques. The solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of the future costs associated with the system is minimized. In the extensive experiments, we validate the model, demonstrate the optimal replenishment schedule and lot-size, and carry out a comparative study to ascertain its contribution. In addition, sensitivity analysis was provided to help identify the most crucial factors that affect system performance. The experimental result shows that the deteriorating problem solved by an appropriate model (i.e. the proposed normal model) can save the total cost up to 2% approximately. It also identifies that the magnitudes of purchase cost per unit and demand rate are the most significant parameters that affect the replenishment decisions and cost.     

Joint pricing and ordering policy for a deteriorating inventory with partial backlogging

In this paper, a deterministic inventory model for deteriorating items with time-dependent backlogging rate is developed. The demand and deterioration rate are known, continuous, and differentiable function of price and time, respectively. Under these general assumptions, we first prove that the optimal replenishment schedule not only exists but is unique, for any given selling price. Next, we show that the total profit is a concave function of price when the replenishment schedule is given. We then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model. Finally, we use a numerical example to illustrate the algorithm.     

An EOQ inventory model for items with Weibull distribution deterioration,ramp type demand rate and partial backlogging

In this paper, an EOQ inventory model is presented depleted not only by demand but also by Weibull distribution deterioration, in which the demand rate is assumed that with a ramp type function of time. In the model, shortages are allowed partial backlogging and the backlogging rate is variable and is dependent on waiting time for the next replenishment. The method is illustrated by three numerical examples, and sensitivity analysis of the optimal solution with respect to parameters of the system is carried out.     

A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule

Due to unreliable production facility and stochastic preventive maintenance, deriving an optimal production inventory decision in practice is very complicated. In this paper, we develop a production model for deteriorating items with stochastic preventive maintenance time and rework using the first in first out (FIFO) rule. From our literature search, no study has been done on the above problem. The problem is solved using a simple search procedure; this makes it more practical for use by industries. Two case examples using uniform and exponential distribution preventive maintenance time are applied. Examples and sensitivity analysis are conducted for each case. The results show that rework and preventive maintenance time have significant affected the total cost and the optimal production time. This provides helpful managerial insights to help management in making smart decisions.     

持有成本和变质率时变的非立即变质品库存策略

本文主要研究非立即变质品的库存策略设计问题。以平均利润最大化为决策目标,构建了一个一般化的库存模型,假设需求受即时库存水平影响且在保鲜期和变质期内库存水平对需求的影响系数不同,持有成本和变质期内的变质率均随时间发生变化,系统允许缺货且短缺量部分延迟订购。进一步证明了当参数满足一定条件时,模型存在唯一的最优解。最后,采用牛顿法给出一些具体的数值算例,并对模型中主要参数的灵敏度进行了分析。结果显示:延长物品的保鲜期将有助于增加系统的平均利润;增加变质期内的需求比增加保鲜期内的需求更有利于增加系统的平均利润;对于变质率高的产品来说,其变质处理成本对最优策略和平均利润的影响不容忽视。此外,本文所构建的模型具有一般性,因此,其应用范围更加广泛。     

短缺量拖后率、需求和采购价均为时变的变质物品EOQ模型

基于需求和采购价均为时变的EOQ模型,进一步考虑时变短缺量拖后率以及资金时间价值等因素对变质物品库存管理的影响,建立了相应的EOQ模型。采用Mathematica4 1对模型进行仿真寻优和主要参数的灵敏度分析,结果显示,最优解存在且库存系统的各参数对最优库存控制策略有不同程度的影响。     

Exact approaches for the pickup and delivery problem with loading cost

In this paper, we propose a branch-and-cut algorithm and a branch-and-price algorithm to solve the pickup and delivery problem with loading cost (PDPLC), which is a new problem derived from the classic pickup and delivery problem (PDP) by considering the loading cost in the objective function. Applications of the PDPLC arise in healthcare transportation where the objective function is customer-centric or service-based. In the branch-and-price algorithm, we devise an ad hoc label-setting algorithm to solve the pricing problem and employ the bounded bidirectional search strategy to accelerate the label-setting algorithm. The proposed algorithms were tested on a set of instances generated by a common data generator in the literature. The computational results showed that the branch-and-price algorithm outperformed the branch-and-cut algorithm by a large margin, and can solve instances with 40 requests to optimality in a reasonable time frame.