An integrated replenishment and production control policy under inventory inaccuracy and time-delay

Inventory inaccuracy has a significant negative impact on the performance of raw materials replenishment and production control. It usually leads to high inventory holding cost or large backlog penalty. To hedge against it, we investigate a replenishment and production control problems for a multiple machines and multiple product-types production/inventory system with inventory inaccuracy. The objective is to minimize the average production cost, including the inventory holding cost and the backlog penalty. In addition to inventory inaccuracy, the lead-time of raw materials replenishment and the unreliability of machines are also taken into consideration. In light of the principle of dynamic programming, a simplified optimal replenishment and production control policy is constructed based on the assumption that the records of inventories are completely accurate. To overcome the shortcomings of the simplified policy in hedging against inventory inaccuracy, a conditional expectation-based replenishment and production control policy is developed based on the fundamental structure of the simplified optimal replenishment and production control policy, and the conditional probability of the physical inventory level. Numerical experiments are conducted to examine the performance of the proposed policy for hedging against inventory inaccuracy, and sensitivity analysis is carried out to study how the parameters of the production/inventory system and the proposed policy affect the average production cost.     

Multiproduct production/inventory control under random demands

Studies the optimal production/inventory control policy for a single machine multiproduct production system. The machine produces to fill the end-product inventory stock and the demand is satisfied from the inventory when available; unsatisfied demand is backlogged until the product becomes available as the result of production. For each product, the demand follows a Poisson process and the unit processing time is known. When the machine switches production from one product to another, it incurs a set-up time and a set-up cost. The relevant costs include the set-up cost, a cost per unit time while the machine is running, and linear costs for inventory and backlogging. This problem is modeled as a semi-Markov decision process using the criterion of minimizing expected total cost with discounting over an infinite horizon. Procedures for computing near-optimal policies and their error bounds are developed. The error bound given by the authors' procedure is shown to be much tighter than the one given by the “norm-based” approach. Computational test results are presented to show the structure of the near-optimal policy and how its accuracy is affected by the system characteristics such as capacity utilization and set-up time     

Considering lost sale in inventory routing problems for perishable goods

This paper presents a mathematical model for an inventory routing problem (IRP). The model is especially designed for allocating the stock of perishable goods. It is assumed that the age of the perishable inventory has a negative impact on the demand of end customers and a percentage of the demand is considered as lost sale. The proposed model balances the transportation cost, the cost of inventory holding and lost sale. In addition to the usual inventory routing constraints, we consider the cost of lost sale as a linear or an exponential function of the inventory age. The proposed model is solved to optimality for small instances and is used to obtain lower bounds for larger instances. We have also devised an efficient meta-heuristic algorithm to find good solutions for this class of problems based on Simulated Annealing (SA) and Tabu Search (TS). Computational results indicate that, for small problems, the average optimality gaps are less than 10.9% and 13.4% using linear and exponential lost sale functions, respectively. Furthermore, we show that the optimality gaps found by CPLEX grow exponentially with the problem size while those obtained by the proposed meta-heuristic algorithm increase linearly.     

Production/inventory systems with a stochastic production rate under a continuous review policy

A single production facility is dedicated to producing one product with completed units going directly into inventory. The unit production time is a random variable. The demand for the product is given by a Poisson process and is supplied directly from inventory when available, or is backordered until it is produced by the production facility. Relevant costs are a linear inventory holding cost, a linear backorder cost, and a fixed setup cost for initiating a production run. The objective is to find a control policy that minimizes the expected cost per time unit.The problem may be modeled as an M/G/1 queueing system, for which the optimal decision policy is a two-critical-number policy. Cost expressions are derived as functions of the policy parameters, and based on convexity properties of these cost expressions, an efficient search procedure is proposed for finding the optimal policy. Computational test results demonstrating the efficiency of the search procedure and the behavior of the optimal policy are presented.     

Joint optimization of inventory control and product placement on e-commerce websites using genetic algorithms

Prior research had shown that the design of product listing pages has significant influence on the sales volume on an e-commerce website. This study focused on product placement in designing product listing pages; that is, how venders of online stores place their products over the product listing pages for maximization of profit. When trying to increase the sales volume through a better website design, it is imperative to keep a close watch on inventory replenishment so as to reduce business cost. Therefore, this study proposed a visual-attention-dependent demand inventory model for determining the optimal product placement and inventory replenishment decisions that jointly maximize the total profit under the arrangement constraints. This model assumes that visual stimuli such as image size and location have a significant effect on product demand. The substitution effect between products on demand was also examined. Then a genetic algorithms-based search method was employed to solve the model. Finally, the validity of the proposed model was illustrated with example problems.     

持续补货模式下的改良品库存模型研究

改良品的订货问题一直没有引起足够的重视。分别建立持续补货模式下不允许缺货与允许缺货的改良品库存模型,并分析改良率与补货周期、各种费用参数的相关关系,研究表明：改良率与补货周期、单位时间存储费用呈负相关关系,与单位时间订货费用、单位时间改良费用、单位时间缺货费用、单位时间总费用呈正相关关系。同时,对不允许缺货与允许缺货的改良品库存模型单位时间总费用进行比较,并分析库存模型各参数对两种库存模型单位时间总费用差值的影响方式,研究表明：单位时间总费用差值与改良率、补充速率、单次订货费用、单位存储费用、单位改良费用呈正相关关系,与单位缺货费用成呈负相关关系,与需求速率的相关关系取决于补充速率与需求速率的大小关系。     

Economic lot sizing in a production system with random demand

An extended economic production quantity model that copes with random demand is developed in this paper. A unique feature of the proposed study is the consideration of transient shortage during the production stage, which has not been explicitly analysed in existing literature. The considered costs include set-up cost for the batch production, inventory carrying cost during the production and depletion stages in one replenishment cycle, and shortage cost when demand cannot be satisfied from the shop floor immediately. Based on renewal reward process, a per-unit-time expected cost model is developed and analysed. Under some mild condition, it can be shown that the approximate cost function is convex. Computational experiments have demonstrated that the average reduction in total cost is significant when the proposed lot sizing policy is compared with those with deterministic demand.     

不确定环境下三级应急系统部分转运策略

针对应急系统中的多点库存共享问题,研究了需求为随机模糊变量情形下的应急调货策略。考虑一个三级多品种的应急供应系统,当缺货发生时,各供应点之间可依据就近应急转运的原则共享部分库存,据此建立了有需求满足时间约束和各供应点库容空间限制的系统总费用随机模糊期望值模型,提出了一种粒子群优化算法和模拟退火算法相结合的先进计算方法(PSO-SA算法)对模型进行了求解,结合算例分析了转运点、就近转运时间、单位物品库容空间等因素变动对部分转运的影响,并验证了算法的有效性和模型的适用性。     

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.     

VMI for single-vendor multi-retailer supply chains under stochastic demand

This paper discusses how a vendor and multiple retailers interact in a vendor managed inventory (VMI) system under stochastic demand. It is assumed that the vendor replenishes all the retailers at the same time. The vendor replenishment cycle is taken to be an integer multiple of the retailer replenishment cycle. In case of a shortage at the vendor, the available stock is allocated to the retailers on the basis of equal stock out probability. Approximate expressions for minimizing the expected total cost for the VMI system have been developed. Various levers affecting the performance of the system have been analyzed. The validity of the approximate model has been tested through simulation.     

Optimal replenishment policies with allowable shortages for a product life cycle

In this paper, we investigate replenishment policies with allowable shortages by considering a general, time-varying, continuous, and deterministic demand function for a product life cycle. The objective is to optimally determine the number of inventory replenishments, the inventory replenishment time points, and the beginning time points of shortages within the product life cycle by minimizing the total relevant costs of the inventory replenishment system. The proposed problem is mathematically formulated as a mixed-integer nonlinear programming model. A complete search procedure is developed to find the optimal solution by employing the properties derived in this paper and the well-known Nelder–Mead algorithm. Also, several numerical examples and the corresponding sensitivity analyses are carried out to illustrate the features of our model by utilizing the search procedure developed in this paper.     

On inventory replenishment with non-linear increasing demand

We present a consecutive improvement approach to solve the problem of determining the timing and size of replenishments in order to minimize the total inventory costs in the case of a non-linear increasing demand pattern. The proposed procedure is computationally simple compared to other methods. It considers the replenishment in reverse time sequence with the time horizon being exactly the ending point and it thus guarantees to meet the demand over the preestablished time frame. The concept of inventory correspondence is introduced. Numerical examples are also presented and compared with other heuristics using an analytic procedure for replenishment with non-linear increasing demand.Scope and purposeYang et al. [2] is one of the best heuristic algorithms known today for determining the optimal replenishment policy when demand is non-linear increasing. This article proposes a consecutive improvement method which is effective, computationally simple, and intuitively appealing from the graphical illustration. Numerical tests show the proposed method even outperforms Yang's procedure.     

Solving the multi-buyer joint replenishment problem with the RAND method

The multi-buyer joint replenishment problem (MJRP) is the multi-item inventory problem of coordinating the replenishment of a group of items that are jointly ordered from a single supplier. Joint replenishment of a group of items reduces cost by decreasing the number of times that the major ordering cost is charged. The objective of MJRP is to develop inventory policies minimizing the total costs over the planning horizon. The single buyer joint replenishment problem may be solved by techniques using the collectively described as the best available heuristics (e.g. Simulated Annealing, Genetic Procedures, Tabu Search, and others), collectively discussed as the RAND method. In this paper, we propose a new efficient RAND method to solve MJRP.     

Economic Order Quantity model with Weibull deterioration distribution,shortage and ramp-type demand

A single-item single-period Economic Order Quantity model for deteriorating items with a ramp-type demand and Weibull deterioration distribution is considered. The shortages in inventory are allowed and backlogged completely. The model is developed over an infinite planning horizon and the optimal replenishment policy is derived by minimizing the total inventory cost per unit time. The numerical solution of the model is obtained, and the sensitivity of the parameters involved in the model is also examined.     

基于混合果蝇优化算法的选址-库存联合优化策略

针对装备维修保障仓库系统运营费用高、仓库点位布局不合理、备件库存结构不合理等问题,建立以多品种联合补货问题为基础的装备维修备件仓库选址-库存控制决策联合优化模型,模型可用于求解仓库的开设位置、维修活动需求点的指派情况、仓库补货时间以及库存水平等.根据模型的结构特点,利用多种群协同进化的方法改进传统果蝇优化算法的位置更新方式,设计一种内外两层搜索策略的混合果蝇优化算法,外层搜索策略作为算法的主程序用于搜索仓库选址决策变量,内层搜索策略采用改进的RAND算法用于搜索库存控制决策变量.仿真结果表明,混合果蝇优化算法具有良好的求解效率,能够确保库存系统在一定服务水平的基础上有效降低库存运营总成本.     

A study on two-warehouse partially backlogged deteriorating inventory models under inflation via particle swarm optimisation

This paper deals with a deterministic inventory model for linear trend in demand under inflationary conditions with different rates of deterioration in two separate warehouses (owned and rented warehouses). The replenishment rate is infinite. The stock is transferred from the rented warehouse to owned warehouse in continuous release pattern and the associated transportation cost is taken into account. At owned warehouse, shortages, if any, are allowed and partially backlogged with a rate dependent on the duration of waiting time up to the arrival of the next lot. The corresponding problems have been formulated as nonlinear constrained optimisation problems for two different policies (inventory follows shortage (IFS) and shortage follows inventory (SFI)). Finally, the model has been illustrated with a numerical example and to study the effects of changes of different system parameters on initial stock level, maximum shortage level and cycle length with the minimum cost of the system, sensitivity analyses have been carried out by changing one parameter at a time and keeping the others at their original values.     

Investigating imperfect process and demand effects on inspection scheduling and supply chain replenishment policy

The challenge of supply chain management (SCM) is to have a supervision in managing operations that is critical to coordinate with partners and have high quality product. Global companies are now striving to engage in production improvement and product design efficiency to provide a good support for competition in any parts of the world. Recently, the development and improved capability of production and information technology have changed the ways in which companies and manufacturers operate. With the assist of advanced production philosophy and collaborative design and manufacturing (CDM), the quality of product and manufacturing has been notably enhanced. However, a traditional single-stage inventory model considers a case in which depletion of inventory is merely caused by a constant rare. In practice, there is an inventory loss due to deterioration and imperfect production. The purpose of this paper is to investigate the effects of stock- and warranty-dependent demand, and take the relationship among imperfect, warranty policy and inspection scheduling into consideration. An integrated two-stage production inventory deteriorating model for replenishment policy and inspection plan is developed utilizing time-weighted inventory approach. A numerical example is presented to demonstrate the theory. The results show that fixed selling rate, the holding cost and the unit inspection cost are the critical factors in applying the deteriorating inventory model.     

A perishable system with modified base stock policy and random supply quantity

We analyse an inventory system with Poisson demands stocking perishable items having constant hazard rates. Orders are placed at every demand epoch so as to take the inventory position back to its maximum level. The replenishment rate depends on the amount on order and the supply quantity which is random. The assumption on demands during stock out periods cover complete lost sales, partial backordering, and full backlogging as special cases. A matrix recursive scheme is developed to determine the limiting distribution. The computational efficiency of this procedure in the determination of the optimal parameters that minimizes the long run expected cost rate is illustrated with examples.     

Deterministic inventory model with two levels of storage,a linear trend in demand and a fixed time horizon

A deterministic inventory model is developed for a single item having two separate storage facilities (owned and rented warehouses) due to limited capacity of the existing storage (owned warehouse) with linearly time-dependent demand (increasing) over a fixed finite time horizon. The model is formulated by assuming that the rate of replenishment is infinite and the successive replenishment cycle lengths are in arithmetic progression. Shortages are allowed and fully backlogged. As a particular case, the results for the model without shortages are derived. Results are illustrated with two numerical examples.Scope and purposeThroughout the world, the production of food grains is periodical. Normally, in countries where state control is less, the demand of essential food grains is lowest at the time of harvest and goes up to the highest level just before the next harvest. This phenomenon is very common in developing third world countries where most of the people are landless or marginal farmers. At the time of harvest, they share some grain/product with landowners and as soon as the small inventory is exhausted, they are forced to buy food grains from the open market. As a result, demand for food grains increases with time in a period along with the number of the people whose initial stock of food grains gets exhausted.In this paper, a two-storage inventory model with time-dependent demand and fixed time horizon is developed and solved by a mathematical programme based on gradient method. This methodology of model development and its solution are quite general and it can be applied to inventory models of any product whose production is periodical and demand increases linearly with time.     

An integrated decision system for inventory management

Decision rules for inventory control parameters are combined in a microcomputer based information and decision system. Decision rules implemented in IDSIM cover a wide variety of models for deterministic and stochastic demand cases. The system consists of four modules: The determination of economic order and production quantities and the evaluation of any arbitrary ordering rule in terms of carrying and ordering costs are accomplished in the first module. The second module deals with aggregate level decisions for deterministic demand systems, generates Total Cycle Stock curves, and addresses the problems of group replenishment and group discounts for deterministic systems. The third module calculates the optimum safety stock levels and optimum values of control parameters for order/point quantity as well as periodic review/order-up-to-level parameters in stochastic systems with normal and Laplace distributions. Other sophisticated algorithms, which utilize iterative procedures and yield near optimal solutions, are incorporated in the fourth module for the allocation of total safety stock to minimize either the expected number of stockouts or the total value of shortages.