回收率依赖回收产品质量的再制造EOQ模型

研究回收率依赖回收产品质量情况下制造/再制造混合系统的EOQ模型.该模型假设顾客的需求可通过新产品的制造和回收产品的再制造两种方式满足,且这两种产品无质量差异;需求率是确定的、连续的;总成本包括制造和再制造的固定启动成本,可销售产品和回收品的库存成本,以及缺货成本.当假设缺货成本无限大时给出不允许缺货情况下的模型.给出算例验证模型的有效性.     

回收率依赖价格的再制造EPQ模型研究

研究了考虑回收率依赖于回收品价格,并带有废弃处理的制造和再制造混合系统的(1,R)和(M,1)EPQ模型.在模型中,采用新产品的制造和回收产品的再制造两种方式来满足客户的需要,回收产品部分用于再制造,其余作为废弃处理;总平均成本包括与回收产品、可销售产品有关的库存持有成本,与制造和再制造有关的生产成本和固定成本,与回收品及制造所需原材料的采购成本以及废弃处理成本.模型给出最优生产策略及总平均成本的表达式.算例验证了所建模型的计算方法,并分析了新引人决策变量p(回收产品单价占制造新产品所需原料价格的比例对总平均成本的变化率的影响.     

Joint control of production,remanufacturing, and disposal activities in a hybrid manufacturing–remanufacturing system

To generate insights into how production of new items and remanufacturing and disposal of returned products can be effectively coordinated, we develop a model of a hybrid manufacturing–remanufacturing system. Formulating the model as a Markov decision process, we investigate the structure of the optimal policy that jointly controls production, remanufacturing, and disposal decisions. Considering the average profit maximization criterion, we show that the joint optimal policy can be characterized by three monotone switching curves. Moreover, we show that there exist serviceable (i.e., as-new) and remanufacturing (i.e., returned) inventory thresholds beyond which production cannot be optimal but disposal is always optimal. We also identify conditions under which idling and disposal actions are always optimal when the system is empty. Using numerical comparisons between models with and without remanufacturing and disposal options, we generate insights into the benefit of utilizing these options. To effectively coordinate production, remanufacturing, and disposal activities, we propose a simple, implementable, and yet effective heuristic policy. Our extensive numerical results suggest that the proposed heuristic can greatly help firms to effectively coordinate their production, remanufacturing, and disposal activities and thereby reduce their operational costs.     

On inventory problems with arbitrary cost pattern,demand pattern and demand distribution

A detailed analysis of inventory models without setup costs, arbitrary demand distribution and arbitrary demand and cost pattern is given. First it is shown that the corresponding one-period model without ordering costs may be reduced to another simpler one with appropriately modified demand distribution. Several representations are given for the modified demand distribution. As one of the main results this reduction turns out to be robust in most cases. In a final chapter the results are applied to the determination of an optimal policy for a class of N-period inventory models with convex holding-and shortage costs and without setup costs.     

A multi-product continuous review inventory system with stochastic demand,backorders, and a budget constraint

Common characteristics of inventory systems include uncertain demand and restrictions such as budgetary or storage space constraints. Several authors have examined budget constrained multi-item stochastic inventory systems controlled by continuous review policies without considering marginal shortage costs. Existing models assume that purchasing costs are paid at the time an order is placed, which is not always the case since in some systems purchasing costs are paid when orders arrive. In the latter case the maximum investment in inventory is random since the inventory level when an order arrives is a random variable. Hence payment of purchasing costs on delivery yields a stochastic budget constraint for inventory. This paper models a multi-item stochastic inventory system with backordered shortages when estimation of marginal backorder cost is available, and payment is due upon order arrival. The budget constraint can easily be converted into a storage constraint.     

A multi-product continuous review inventory system in stochastic environment with budget constraint

Common characteristics of inventory systems include uncertain demand and restrictions such as budgetary and storage space constraints. Several authors have examined budget constrained multi-item stochastic inventory systems controlled by continuous review policies without considering marginal review shortage costs. Existing models assume that purchasing costs are paid at the time an order is placed, which is not always the case since in some systems purchasing costs are paid when order arrive. In the latter case the maximum investment in inventory is random since the inventory level when an order arrives is a random variable. Hence payment of purchasing costs on delivery yields a stochastic budget constraint for inventory. In this paper with mixture of back orders and lost sales, we assume that mean and variance of lead time demand are known but their probability distributions are unknown. After that, we apply the minimax distribution free procedure to find the minimum expected value of the random objective function with budget constraint. The random budget constraint is transformed to crisp budget constraint by chance-constraint technique. Finally, the model is illustrated by a numerical example.     

An investigation of lead-time effects in manufacturing/remanufacturing systems under simple PUSH and PULL control strategies

In this paper we extend the PUSH and PULL control strategies defined by van der Laan et al. (E.A. van der Laan, M. Salomon, R. Dekker, Production planning and inventory control for remanufacturable durable products, Working paper 9531/A, Econometric Institute, Erasmus University Rotterdam, The Netherlands, 1995) to evaluate numerically the effects of lead-time duration and lead-time variability on total expected costs in production/inventory systems with remanufacturing. Although both strategies are non-optimal, they are relatively easy to analyse numerically and, more importantly, they are actually used in practice. The most important outcomes of the study are, that for both control strategies: (i) manufacturing lead-times have a larger influence on system costs than remanufacturing lead-times; (ii) a larger remanufacturing lead-time may sometimes result in a cost decrease; and (iii) a larger variability in the manufacturing lead-time may sometimes result in a cost decrease.     

Four-level closed loop supply chain with remanufacturing

This paper addresses the coordination of order quantities in a four-level closed-loop supply chain (CLSC) with remanufacturing. The levels are multiple buyers and tier-1 and tier-2 suppliers, and a manufacturer. The reverse channel consists of an inspection and disassembly center and a remanufacturing center. Customer demand is met from either newly manufactured items, remanufacturing used items collected from customers for recovery, or from both. Mathematical models are developed to find the production (manufacturing and remanufacturing) and inventory policies that minimize the CLSC total cost. One of the models considers emissions from production and transportation and accounts for energy usage. The results showed that higher collection rates of used items reduce the supply chain costs and improves its environmental performance. A mixed strategy of manufacturing and remanufacturing was found to be best for the chain.     

Simple heuristics for push and pull remanufacturing policies

Inventory policies for joint remanufacturing and manufacturing have recently received much attention. Most efforts, though, were related to (optimal) policy structures and numerical optimization, rather than closed form expressions for calculating near optimal policy parameters. The focus of this paper is on the latter. We analyze an inventory system with unit product returns and demands where remanufacturing is the cheaper alternative for manufacturing. Manufacturing is also needed, however, since there are less returns than demands. The cost structure consists of setup costs, holding costs, and backorder costs. Manufacturing and remanufacturing orders have non-zero lead times. To control the system we use certain extensions of the familiar (s, Q) policy, called push and pull remanufacturing policies. For all policies we present simple, closed form formulae for approximating the optimal policy parameters under a cost minimization objective. In an extensive numerical study we show that the proposed formulae lead to near-optimal policy parameters.     

A production–recycling–inventory system with imprecise holding costs

This paper presents an optimal control recycling production inventory system in fuzzy environment. The used items are bought back and then either put on recycling or disposal. Recycled products can be used for the new products which are sold again. Here, the rate of production, recycling and disposal are assumed to be function of time and considered as control variables. The demand inversely depends on the selling price. Again selling price is serviceable stock dependent. The holding costs (for serviceable and non-serviceable items) are fuzzy variables. At first we define the expected values of fuzzy variable, then the system is transferred to the fuzzy expected value model. In this paper, an optimal control approach is proposed to optimize the production, recycling and disposal strategy with respect so that expected value of total profit is maximum. The optimum results are presented both in tabular form and graphically.     

基于承诺交货期的两阶通用件库存模型

在一个两阶段生产系统中,针对第二阶段应用单通用件的情况,引入承诺交货期因素,分别建立了第一阶段无通用件、单通用件、双通用件库存模型,考查了承诺交货期对通用件库存模型总成本的影响,分析了三类模型相应的最优库存水平。通过算例,说明了在一个第二阶段采用单通用件的两阶段生产系统中,当通用件与非通用件的单位采购成本相同时,并非第一阶段使用越多的通用件,总成本就越低。     

An economic production quantity model with a positive resetup point under random demand

In this paper, an extended economic production quantity (EPQ) model is investigated, where demand follows a random process. This study is motivated by an industrial case for precision machine assembly in the machinery industry. Both a positive resetup point s and a fixed lot size Q are implemented in this production control policy. To cope with random demand, a resetup point, i.e., the lowest inventory level to start the production, is adapted to minimize stock shortage during the replenishment cycle. The considered cost includes setup cost, inventory carrying cost, and shortage cost, where shortage may occur at the production stage and/or at the end of one replenishment cycle. Under some mild conditions, the expected cost per unit time can be shown to be convex with respect to decision parameters s and Q. Further computational study has demonstrated that the proposed model outperforms the classical EPQ when demand is random. In particular, a positive resetup point contributes to a significant portion of this cost savings when compared with that in the classical lot sizing policy.     

Optimal ordering policies for continuous review perishable inventory models

This paper extends the notions of perishable inventory models to the realm of continuous review inventory systems. The traditional perishable inventory costs of ordering, holding, shortage or penalty, disposal and revenue are incorporated into the continuous review framework. The type of policy that is optimal with respect to long run average expected cost is presented for both the backlogging and lost-sales models. In addition, for the lost-sales model the cost function is presented and analyzed.     

Control policies for single-stage production systems with perishable inventory and customer impatience

We consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance.     

On the Effect of Product Variety in Production–Inventory Systems

In this paper, we examine the effect of product variety on inventory costs in a production–inventory system with finite capacity where products are made to stock and share the same manufacturing facility. The facility incurs a setup time whenever it switches from producing one product type to another. The production facility has a finite production rate and stochastic production times. In order to mitigate the effect of setups, products are produced in batches. In contrast to inventory systems with exogenous lead times, we show that inventory costs increase almost linearly in the number of products. More importantly, we show that the rate of increase is sensitive to system parameters including demand and process variability, demand and capacity levels, and setup times. The effect of these parameters can be counterintuitive. For example, we show that the relative increase in cost due to higher product variety is decreasing in demand and process variability. We also show that it is decreasing in expected production time. On the other hand, we find that the relative cost is increasing in expected setup time, setup time variability and aggregate demand rate. Furthermore, we show that the effect of product variety on optimal base stock levels is not monotonic. We use the model to draw several managerial insights regarding the value of variety-reducing strategies such as product consolidation and delayed differentiation.     

Optimal Inventory Policies with Service-Level Constraints

In a practical situation it is often difficult to determine the value of the shortage costs for use in in ventory-control systems. However, in cost-minimization problems including service-level constraints, shortage costs are implicitly prevailing. With the purpose of exploring these relations, a continuous review (Q, r) stock-control system is considered, where the order points and lot sizes are computed simultaneously. Instead of explicitly expressing the shortage cost in the objective function, it is taken into consideration through a service-level constraint. The shadow price of this constraint can in some sense be interpreted as the shortage cost corresponding to the requested service level. By changing the value of the service level, interesting relations between shortage costs and service levels can be viewed for different sets of other inventory parameters. In order to investigate the sensitivity for probabilistic variations in the input data, two different probability distributions are used to describe the lead-time demand.     

Optimisation of integrated reverse logistics networks with different product recovery routes

The awareness of importance of product recovery has grown swiftly in the past few decades. This paper focuses on a problem of inventory control and production planning optimisation of a generic type of an integrated Reverse Logistics (RL) network which consists of a traditional forward production route, two alternative recovery routes, including repair and remanufacturing and a disposal route. It is assumed that demand and return quantities are uncertain. A quality level is assigned to each of the returned products. Due to uncertainty in the return quantity, quantity of returned products of a certain quality level is uncertain too. The uncertainties are modelled using fuzzy trapezoidal numbers. Quality thresholds are used to segregate the returned products into repair, remanufacturing or disposal routes. A two phase fuzzy mixed integer optimisation algorithm is developed to provide a solution to the inventory control and production planning problem. In Phase 1, uncertainties in quantity of product returns and quality of returns are considered to calculate the quantities to be sent to different recovery routes. These outputs are inputs into Phase 2 which generates decisions on component procurement, production, repair and disassembly. Finally, numerical experiments and sensitivity analysis are carried out to better understand the effects of quality of returns and RL network parameters on the network performance. These parameters include quantity of returned products, unit repair costs, unit production cost, setup costs and unit disposal cost.     

Dynamic lot-sizing with setup cost reduction

One of the fundamental tenets of the Just-in-Time (JIT) manufacturing philosophy is that reduction or even elimination of inventory conserves valuable resources and reduces wasteful spending. In many cases, to achieve inventory reductions requires investment in reduction of setup costs. For this reason, certain proposals for incorporating means for reducing setup costs into classical production-inventory models have been offered in recent years. This article considers a dynamic lot-sizing model M where the values of the setup costs can be reduced by various amounts depending upon the level of funds R committed to this reduction. We show that for each fixed value of R, the model can be represented as a shortest path problem. By minimizing the optimal value function V(R) of the shortest path problem over R, model M can, in theory, be solved. In practice, the viability of this approach depends crucially upon the properties of the function V. Since these properties depend upon the nature of the setup cost function K used in model M, we analyze how V varies as K varies. This allows us to propose two exact, finite algorithms for solving model M, one for the case when K is a concave function, the other for the case when K is convex. Computational results for the convex case are presented. The problems solved demonstrate that, in practice, setup cost reductions chosen according to model M have the potential to significantly reduce both inventory levels and total costs.     

再制造能力有限的多产品混合系统库存决策

为确定各产品的制造与再制造策略,对再制造能力有限的多产品混合系统进行研究.在系统中,对多种产品进行制造和再制造.每种产品在顾客使用后都会以恒定速率返回,但因再制造能力有限,有些产品无法用于再制造而被处置.每种产品需求恒定且由服务性产品来满足,服务性产品由制造品和再制造品组成,不允许缺货.在一次制造准备和至少一次再制造准备策略下构建了库存决策模型,利用拉格朗日乘数法和贪婪算法分别确定了各产品的再制造顺序和再制造比率.并当再制造比率一定时,给出了再制造准备次数为正整数时各产品制造与再制造策略的求解程序,得到了各产品制造和再制造批量、再制造准备次数等求解公式.最后,应用算例对模型及求解方法进行了验证.     

Simultaneous optimization of classical objectives in JIT scheduling

Just-in-time production models have been developed in recent years in order to reduce costs of diversified small-lot productions. The methods aim at maintaining the production rate of each type of part as smooth as possible and therefore holding small inventory and shortage costs. Different ways of measuring the slack between a given schedule and the ideal no-inventory no-shortage production have been considered in the literature. This paper compares the three most studied objective functions and refutes several conjectures that have been formulated in the last few years.