Optimal tracker for unreliable manufacturing systems

This paper deals with the inventory-production control problem where the produced items are assumed to deteriorate at a rate that depends on the demand rate of the production system. The state of this production system is assumed to be described by a continuous-time Markov process taking values in a finite discrete space. The inventory production control problem is formulated as a stochastic optimal control problem. The optimal policy that solves the optimal control problem is obtained in terms of a set of coupled Riccati equations. The guaranteed cost problem is also treated. A numerical example is provided to show the usefulness of the proposed model.     

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．     

Lot sizing under (Q, R) policy in a capcity constrained manufacturing facility

Traditional approaches to lot sizing and inventory control consider uncertainties in either the demand or manufacturing process but not both. In these models it is usually assumed that the lead times are independent and identically distributed, but this is not realistic in many practical instances. In this paper we consider the lot sizing problem for items with stochastic demands and manufacturing lead times. It is assumed that the inventory of the finished product is controlled by continuous review policy of Q,R type—order quantity, order point system—and the problem is to determine optimal Q and R. We examine the decision parameters under a variety of conditions using exact and approximate methods.     

Multiproduct multiple-buyer single-vendor supply chain problem with stochastic demand, variable lead-time, and multi-chance constraint

In this paper, a multi-product multi-chance constraint joint single-vendor multi-buyers inventory problem is considered in which the demand follows a uniform distribution, the lead-time is assumed to vary linearly with respect to the lot size, and the shortage in combination of backorder and lost-sale is assumed. Furthermore, the orders are placed in multiple of packets, there is a limited space available for the vendor, there are chance constraints on the vendor service rate to supply the products, and there is a limited budget for each buyer to purchase the products. While the elements of the buyers’ cost function are holding, shortage, order and transportation costs, the set up and holding costs are assumed for the vendor. The goal is to determine the re-order point and the order quantity of each product for each buyer such that the chain total cost is minimized. We show the model of this problem to be a mixed integer nonlinear programming type and in order to solve it a particle swarm optimization (PSO) approach is used. To justify the results of the proposed PSO algorithm, a genetic algorithm (GA) is applied as well to solve the problem. Then, the quality of the results and the CPU times of reaching the solution are compared through three numerical examples that are given to demonstrate the applicability of the proposed methodology in real world inventory control problems. The comparison results show the PSO approach has better performances than the GA method.     

Stability conditions of constrained delay systems via positive invariance

A delay system is represented by a linear difference equation. The system parameters and the delays are assumed to be imperfectly known. The output vector is perturbed by an external disturbance vector. The addressed problem is to characterize conditions which guarantee that the output vector remains in a given domain defined by a set of symmetrical linear constraints. This problem is solved by imposing positive invariance conditions. These conditions also imply delay independent asymptotic stability of the associated deterministic system. The possible use of these new robust stability conditions for controlling an input–output delay model is then presented. An application is finally proposed; it concerns an inventory control problem for a simple production loop subject to constraints on inventory levels. © 1998 John Wiley & Sons, Ltd.     

A heuristic method for the inventory routing and pricing problem in a supply chain

The inventory routing problem (IRP) in a supply chain (SC) is to determine delivery routes from suppliers to some geographically dispersed retailers and inventory policy for retailers. In the past, the pricing and demand decisions seem ignored and assumed known in most IRP researches. Since the pricing decision affects the demand decision and then both inventory and routing decisions, it should be considered in the IRP simultaneously to achieve the objective of maximal profit in the supply chain. In this paper, a mathematical model for the inventory routing and pricing problem (IRPP) is proposed. Since the solution for this model is an NP (non-polynomial) problem, a heuristic method, tabu search adopting different neighborhood search approaches, is used to obtain the optimal solution. The proposed heuristic method was compared with two other methods considering the IRPP separately. The experimental results indicate that the proposed method is better than the two other methods in terms of average profit.     

Integrated optimization of inventory-distribution systems by random local search and a genetic algorithm

A new model and its solution procedure for the commodity distribution system consisting of distribution centers and consumer points are discussed. Demand is assumed to be a random variable that obeys a known, stationary probability distribution. An integrated optimization model is built where both the order-up-to-R policy, which is one of the typical inventory policies for periodic review models, and the transportation problem are considered simultaneously. The assignment of consumer points to distribution centers is not fixed. The problem is to determine the target inventory and the transportation quantity in order to minimize the expectation of the sum of inventory related costs and transportation costs. Simulation and linear programming are used to calculate the expected costs, and a random local search method is developed in order to determine the optimum target inventory. A genetic algorithm is also tested and compared with the proposed random local search method. The model and effectiveness of the proposed solution procedure are clarified by computational experiments.     

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.     

An inventory model with Weibull demand rate,finite rate of production and shortages

We develop here an inventory model with time-dependent two-parameter Weibull demand rate, allowing shortages in the inventory. The shortages are completely backlogged. The production rate is assumed to be finite and proportional to the demand rate. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples. Sensitivity of the optimal solution with respect to changes in the values of the system parameters is also studied. Special features of time-dependent Weibull demand rate are discussed.     

A mathematical model for order splitting in a multiple supplier single-item inventory system

In this paper we develop a mathematical model which considers multiple-supplier single-item inventory systems. The lead times of the suppliers and demand arrival rate are random variables. All shortages are backordered. Continuous review (s, Q) policy has been assumed. When the inventory level hits the reorder level, the total order is split among n suppliers. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost and shortage cost is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared to the relevant models in the literature. In addition, some managerial insights are observed.     

An integrated replenishment model with quantity discounts, reentry and downward substitution for control wafers

This paper considers control wafers replenishment problem in wafer fabrication factories. A dynamic lot-sizing replenishment problem with reentry and downward substitution is examined in a pulling control production environment. The objective is to set the inventory level so as to minimize the total cost of control wafers, where the costs include order cost, purchase cost, setup cost, production cost and holding cost, while maintaining the same level of production throughput. In addition, purchase quantity discounts and precise inventory level are considered in the replenishment model. The control wafers replenishment problem is first constructed as a network, and is then transformed into a mixed integer programming model. Lastly, an efficient heuristic algorithm is proposed for solving large-scale problems. A numerical example is given to illustrate the practicality for empirical investigation. The results demonstrate that the proposed mixed integer programming model and the heuristic algorithm are effective tools for determining the inventory level of control wafers for multi-grades in multi-periods.     

纺织企业的原料库存控制模型研究

合理控制库存量,降低原料库存成本对纺织企业提高市场竞争力具有重大的意义。通过建立原料库存的不定量不定期控制模型,并采用遗传算法求解,给出了满足平均库存成本最小的(s,S)控制策略,并通过实例验证算法的有效性。     

Retailer's optimal policy under inflation in fuzzy environment with trade credit

Trade credit plays an important role in financing many industries. In the classical inventory model it is assumed that the buyer must pay for the items as soon as the items are received. In this problem, it is considered that the retailer can pay the supplier either at the end of the credit period or later pay interest on the unpaid amount for the overdue period. Here, the retailer's inventory model for the optimal cycle time and payment time for a retailer is developed. The effects of the inflation rate, deterioration rate and delay in payment have been discussed. The whole study is performed in a fuzzy environment by taking the opportunity cost, interest earned and interest paid rate as a triangular fuzzy number. Fuzzy profit functions, which involve fuzzy arithmetic operation, are defined using the function principle. We use the signed distance method to defuzzify the fuzzy profit function. Moreover, numerical and sensitivity analysis is performed to validate the proposed model.     

ABC inventory classification in the presence of both quantitative and qualitative criteria

Organizations classically employ the ABC analysis to have an efficient control on a large number of inventory items. The customary classification method considers just one criterion, i.e., the annual dollar usage to classify inventory items. Recently, several methods have been developed for ABC inventory classification, especially DEA-like models that account for other important criteria leading to more logical results in practice. However, these models assume that all criteria are of quantitative type and hence cannot handle the qualitative criteria which are not stated numerically but as linguistic terms. To alleviate this shortcoming, this paper proposes a modified version of an existent common weight DEA-like model by using of some concepts in the current imprecise DEA (IDEA) models and then applies it for ABC inventory classification in the case where there exist both quantitative and qualitative criteria. The merits of employing the modified model to solve the multi criteria inventory classification (MCIC) problem are discussed. A case example is also illustrated to demonstrate the applicability of the modified model in the context of MCIC problem as well as its superiority over existing approaches.     

Single-vendor single-buyer with integrated transport-inventory system: Models and heuristics in the case of perishable goods

We consider the problem of shipping a set of products from a single origin (the vendor) to a common destination (the buyer) with the objective of minimizing the sum of the inventory and transportation costs, when a set of shipping frequencies is given and products are assumed to be perishable. We provide a mixed integer linear programming model for the problem and propose the modification of known heuristic algorithms to solve it. Extensive computational results show how some of the modified heuristics are extremely efficient and effective.     

基于遗传算法的纺织企业机配件库存控制

合理压缩库存量,降低库存成本对于纺织企业来说意义重大.建立了在非平稳需求下的库存控制模型,并采用遗传算法求解,给出了满足库存成本最小的(s,S)控制策略.通过求解某配件的(s,S)控制策略,验证了算法的有效.     

A heuristic method for the vehicle routing problem with backhauls and inventory

The purpose of this paper is to determine the route of the vehicle routing problem with backhauls (VRPB), delivering new items and picking up the reused items or wastes, and resolve the inventory control decision problem simultaneously since the regular VRPB does not. Both the vehicle routing decision for delivery and pickup, and the inventory control decision affect each other and must be considered together. Hence, a mathematical model of vehicle routing problem with backhauls and inventory (VRPBI) is proposed. Since finding the optimal solution(s) for VRPBI is a NP-hard problem, this paper proposes a heuristic method, variable neighborhood tabu search (VNTS), adopting six neighborhood searching approaches to obtain the optimal solution. Moreover, this paper compares the proposed heuristic method with two other existing heuristic methods. The experimental results indicate that the proposed method is better than the two other methods in terms of average logistic cost (transportation cost and inventory cost).     

An application of fuzzy set theory to inventory control models

A method for solving an inventory control problem, of which input data are described by triangular fuzzy numbers will be presented here. The continuous review model of the inventory control problem with fuzzy input data will be focused in, and a new solution method will be presented. For the reason that the result should be a fuzzy number because of fuzzy input data, and the certain number about order quantity is prefered in the real-world, it is necessary to transform the fuzzy result to crisp one. The interval mean value concept is used here to help to solve this problem. Under the condition of total cost minimum, the interval order quantity maximum can be obtained.     

Inventory policy of a deteriorating item with variable demand under trade credit period

In this paper, an inventory model of a deteriorating item with stock and selling price dependent demand under two-level credit period has been developed. Here, the retailer enjoys a price discount if he pays normal purchase cost on or before the first level of credit period, or an interest is charged for the delay of payments. In return, retailer also offers a fixed credit period to his customers to boost the demand. In this regard, the authors develop an EOQ model incorporating the effect of inflation and time value of money over all the costs. Keeping the business of seasonal products in mind, it is assumed that planning horizon of business is random and follows a normal distribution with a known mean and standard deviation. The model is formulated as retailer’s profit maximization problem for both crisp and fuzzy inventory costs and solved using a modified Genetic Algorithm (MGA). This algorithm is developed following fuzzy age based selection process for crossover and gradually reducing mutation parameter. For different values of MGA parameters, optimum results are obtained. Numerical experiments are performed to illustrate the model.     

3级网状随机性库存控制策略的仿真优化

研究了多制造商,多分销商和多零售商的3级网状随机性库存系统的(r,Q)库存控制策略问题.由于该系统具有顾客到达时间服从泊松分布,随机顾客需求量,随机顾客购买行为,随机订货时间和制造商生产容量有限制等特点,使得解析方法很难描述系统中的多种复杂随机因素并无法求解有效的库存控制策略.为此建立了以总成本最小为目标的数学模型,运用了基于仿真的优化方法,通过将仿真方法与粒子群优化算法相结合对问题进行求解.最后通过仿真实例与比较,验证了模型和基于仿真的粒子群优化方法的可行性和有效性.也表明了基于仿真的优化方法在供应链管理中的适用性.