Reverse Logistics: a stochastic EOQ-based inventory control model for mixed manufacturing/remanufacturing systems with return policies

This paper focuses on mixed manufacturing/remanufacturing systems, where manufacturing or purchase of new items integrates product reuse or remanufacturing, with the purpose to achieve a complete and timely demand satisfaction. We formulate a stochastic Economic Order Quantity (EOQ)-based inventory control model for a mixed manufacturing/remanufacturing system. The model is intended to identify the need of placing a manufacturing/purchasing order, to avoid the occurrence of stock-out situations. We then formulate a total cost minimisation problem, to derive the optimal return policy, this latter being a financial incentive paid to customers to increase the flow of returned items. The model developed is investigated through simulations, in order to assess the effect of stochasticity (of demand, return fraction and return delay) on the optimal return policy of the system; then, it is validated through a case study, to derive indications concerning its practical application in real cases. Our study ultimately provides a framework for practitioners to establish EOQ policies in reverse logistics contexts and to evaluate the opportunity of establishing a return policy in those contexts.     

The boomerang returns? Accounting for the impact of uncertainties on the dynamics of remanufacturing systems

Recent years have witnessed companies abandon traditional open-loop supply chain structures in favour of closed-loop variants, in a bid to mitigate environmental impacts and exploit economic opportunities. Central to the closed-loop paradigm is remanufacturing: the restoration of used products to useful life. While this operational model has huge potential to extend product life-cycles, the collection and recovery processes diminish the effectiveness of existing control mechanisms for open-loop systems. We systematically review the literature in the field of closed-loop supply chain dynamics, which explores the time-varying interactions of material and information flows in the different elements of remanufacturing supply chains. We supplement this with further reviews of what we call the three ‘pillars’ of such systems, i.e. forecasting, collection, and inventory and production control. This provides us with an interdisciplinary lens to investigate how a ‘boomerang’ effect (i.e. sale, consumption, and return processes) impacts on the behaviour of the closed-loop system and to understand how it can be controlled. To facilitate this, we contrast closed-loop supply chain dynamics research to the well-developed research in each pillar; explore how different disciplines have accommodated the supply, process, demand, and control uncertainties; and provide insights for future research on the dynamics of remanufacturing systems.     

Analysis of a product recovery system

The continuous growth in consumer waste in recent years has seriously threatened the environment. Environmentally conscious manufacturing and product recovery has become an obligation to the environment and to society. Many countries are contemplating regulations that force manufacturers to take back used products from consumers so that the components and materials retrieved from the products may be reused and/or recycled. We focus on a product recovery system in a remanufacturing system. Product recovery aims to minimize the amount of waste sent to landfills by recovering materials and parts from old or outdated products by means of recycling and remanufacturing. It should be considered when designing and managing the manufacturing systems. We propose a new analytical approach to evaluating the product recovery system with stochastic variability. This model applies the traditional inventory theory to the production/inventory management with consideration for disposal and return. The system is formulated by a discrete time Markov chain. It is composed of the states denoted by the number of the inventory, the transition probabilities between states and the costs associated with the transitions. Using the Markov analysis, we can calculate the total expected average cost per period exactly. Numerical examples are given to show the property of the management system and optimize the product recovery system.     

Dynamic disassembly planning for remanufacturing of multiple types of products

With the increased need for remanufacturing of end-of-life products, achieving economic efficiency in remanufacturing is urgently needed. The purpose of this study was to devise a cost-minimisation plan for disassembly and remanufacturing of end-of-life products returned by consumers. A returned end-of-life product is disassembled into remanufacturable parts, which are supposed to be used for new products after being remanufactured. Each end-of-life product is disassembled into parts at variable levels and through variable sequences as needed, taking into account not only disassembly but also manufacturing, remanufacturing, and holding inventory of remanufacturable parts. This study proposes a mixed integer linear programming (MILP) model for derivation of the optimal disassembly plan for each returned product, under deterministically known demand and return flows. For the purposes of an illustrative example, the proposed model was applied to the formulation of an optimal disassembly and remanufacturing plan of ‘fuser assembly’ of laser printers. The solution reveals that variable-level disassembly of products saves a significant remanufacturing cost compared with full disassembly.     

考虑残次品和碳排放的供应链多级库存的EOQ模型

针对供应链多级库存系统,探析残次品与碳排放对该系统的影响作用与供应链库存持有成本、订购成本、运输成本和检查成本的构成函数,建立多级库存的EOQ模型,提供考虑残次品和碳排放的供应链订货经济批量和库存控制策略,并用算例验证了模型的有效性。     

A practical model for managing inventories with unknown costs and a budget constraint

The economic production quantity method is one of the simplest models to control production and inventory. However, the assumptions on which it is based make its application difficult in practical situations. In most companies, set-up and inventory costs are unknown, or may not even exist as such, although other data are known, such as available capacity in machining hours and limits set by the financing subsystem. The present work offers a multi-item inventory model that sets reference values using known values such as inventory investment limits and production capacity. In order to confer the proposed model’s larger practical content, a spreadsheet available to be downloaded has been implemented. Finally, the model dynamics is illustrated as a numerical example obtained from a real company.     

The impact of information transparency on the dynamic behaviour of a hybrid manufacturing/remanufacturing system

A combined manufacturing/remanufacturing system is modelled and its dynamic behaviour is investigated using a control engineering approach. The model is an extension of the automated pipeline, inventory and order based production control system (APIOBPCS), which is well understood from a dynamic perspective. It is assumed that the remanufacturing process is based on a PUSH policy. Utilising different levels of information transparency from the remanufacturing process, three system types are developed and compared. Mathematical and simulation analyses of the system types were undertaken and their robustness to remanufacturing process uncertainties were tested. Our analysis indicates that the greater the degree of information transparency, the greater the robustness of the hybrid system.     

可回复多级库存系统的最优订货和回复策略

本文建立的可回复装配多级库存系统由两部分组成：缺陷零部件库存和产成品库存,其中产成品库存既可以通过零件维修、装配来补充,也可以直接从外部采购产成品获得。模型假设产品由两个可回复零件组成,且回收速率和外部需求是稳定的。通过建模和分析,得到了最优外部采购的经济订货批量,以及最佳装配策略和零件存储策略。     

Determining sequence and ready times in a remanufacturing system

A fundamental scheduling problem is to determine a production start (ready) time for jobs based on customer-specified due dates. Typically, the objective is to delay the ready time in an attempt to minimize work-in-process inventory and maximize production system utilization. In many practical situations, notably remanufacturing operations, highly variable operation times and intricate process plans complicate this problem. In such a case, a specific ready time implies a confidence of on-time completion. Prior analytical results imply the optimal solution is a function of: (i) customer due dates; (ii) desired confidence levels; and (iii) stochastic makespan minimization. This paper proposes the use of a network flow model to represent a remanufacturing flowshop and then presents a structured heuristic approach that is able to develop sequences and ready times for remanufacturing systems by balancing the three factors. A broad experimental design is used to demonstrate that the proposed scheduling method outperforms previous list rules in terms of the calculated mean and robustness values.     

变质率呈Weibull分布的易变质物品的EOQ模型

基于需求和采购价格均为时变的EOQ模型,进一步考虑呈Weibull分布的变质对易变质物品库存管理的影响,建立了相应的EOQ模型,并对该模型进行仿真计算和主要参数的灵敏度分析。结果表明,该模型存在最优解且各主要参数对最优库存控制有不同程度的影响。     

Optimal inventory policies when stockouts result from defective products

An implicit assumption underlying most inventory systems is that the lot ordered will not contain any defective, i.e., unsaleable items when delivered and so there will be no ‘shortages’ in the delivery in the sense that every unit of the product in the accepted lot is of perfect quality and therefore fully acceptable to the customers. Such an assumption is not always tenable in view of the extensive use of acceptance sampling by business and industry in the quality control process. The presence of defective items in the traditional inventory models which foresee no such possibility would certainly disrupt the systems in use, and consequently entail higher operating cost on the inventory management. With an aim to broaden the base of applications, and to demonstrate the impacts of the possible presence of defective products upon the structure and the cost of certain inventory systems, this paper extends two inventory models to the case where the proportion of defective units in the accepted lot is a random variable with known probability distributions. Optimal solutions to the modified systems are developed and comparisons with the traditional models are also presented via numerical examples.     

Joint hybrid repair and remanufacturing systems and supply control

The control of a stochastic manufacturing system that executes capital asset repairs and remanufacturing in an integrated system is examined. The remanufacturing resources respond to planned returns of worn-out equipment at the end of their expected life and unplanned returns triggered by major equipment failures. Remanufacturing operations for planned demand can be executed at different rates and costs corresponding to different replacement and repair modes. The replacement components inventory is provided by an upstream supply with random lead times. The objective is to determine a control policy for both the supply and remanufacturing activities that minimises the average repair/replacement, acquisition and inventory/shortage total cost over an infinite horizon. We propose a suboptimal joint remanufacturing and supply control policy, composed of a multi-hedging point policy (MHPP) for the remanufacturing stage and an (s, Q) policy for the replacement parts supply. The MHPP is based on two inventory thresholds that trigger the use of predefined remanufacturing modes. Control policy parameters are obtained combining analytical modelling, simulation experiments and response surface methodology. The effects of the distribution, mean and variability of the lead time are tested and a sensitivity analysis of cost parameters is conducted to validate the proposed control policy. We also show that our policy leads to a significant cost reduction as compared to a combination of a hedging point policy (HPP) and an (s, Q) policy.     

Continuous review (s,S) policies for inventory systems incorporating a cutoff transaction size

In this paper, a mathematical model is developed for the analysis of optimal replenishment policies for items which experience lumpy demands. In order to avoid disrupting the inventory system, a cutoff transaction size of w units is specified such that customer demands with sizes exceeding w units will be filtered out of the inventory system and treated as special orders to be satisfied by special deliveries. Customer demands with sizes > units will be met From stock. The control discipline is the (s, S) inventory policy with continuous review and the nature of the demands is approximated by a stuttering Poisson distribution. Recursive formulae are developed for the determination of the probabilities of the lead time demand and the available inventory position. The optimal values of the control parameters, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.     

Economic ordering model for deteriorating items with random demand and deterioration

In modern marketplaces, competitive products frequently face volatile demand. In particular, the majority of deteriorating items are frequently subject to dual uncertainty, simultaneously suffering from demand and deterioration. Accordingly, this study attempts to develop an economic ordering model for a newsboy-style deteriorating item with lognormal demand and Poisson-type deterioration. Finally, an effective and practical economic ordering model involving deteriorating inventory is developed for optimising the order quantity of a given deteriorating item during an upcoming selling period to maximise expected profits of retailers. Numerical examples demonstrate that, as expected, the proposed economic ordering model can obtain an optimal solution for the inventory problem involving deteriorating items under uncertain and random demand and deterioration.     

Bullwhip and inventory variance in a closed loop supply chain

A simple dynamic model of a hybrid manufacturing/remanufacturing system is investigated. In particular we study an infinite horizon, continuous time, APIOBPCS (Automatic Pipeline Inventory and Order Based Production Control System) model. We use Åström’s method to quantify variance ratios in the closed loop supply chain. Specifically we highlight the effect of a combined “in-use” and remanufacturing lead-time and the return rate on the inventory variance and bullwhip produced by the ordering policy. Our results clearly show that a larger return rate leads to less bullwhip and less inventory variance in the plant producing new components. Thus returns can be used to absorb demand fluctuations to some extent. Longer remanufacturing and “in-use” lead-times have less impact at reducing inventory variance and bullwhip than shorter lead-times. We find that, within our specified system, that inventory variance and bullwhip is always less in supply chains with returns than supply chains without returns. We conclude by separating out the remanufacturing lead-time from the “in-use” lead-time and investigating its impact on our findings. We find that short remanufacturing lead-times do not qualitatively change our results.     

Effects of carbon emission regulations on remanufacturing decisions with limited information of demand distribution

Policy-makers are developing regulation policies to drive down carbon emissions from industries. Independent remanufacturers (IRs), which remanufacture recycled products/components/parts, must manage and evaluate economic costs generated by the production under future carbon emission regulations. We present three optimisation models to determine the remanufacturing quantity that maximises the total profits under three common carbon emission regulation policies: (a) mandatory carbon emissions capacity, (b) carbon tax and (c) cap and trade. These models include sales revenue, remanufacturing cost, disposal cost, inventory holding cost, shortage cost and carbon emission cost. The max–min approach is used to solve the models, which assume limited information on demand distribution. We investigate how the three regulation policies affect remanufacturing decision-making for IRs and we also solve some numerical examples where we vary the magnitudes of incentives, penalties and stringency of constraints to provide implications to policy-makers. The results indicate that remanufacturers should aim to improve yield rate to maximise the profit irrespective of the implemented carbon emissions policy. Policy-makers should prefer the carbon tax policy, if any of the other two policies must be performed, a remanufacturing discount such as a higher carbon emission cap or lower penalty should be implemented to better promote the development of remanufacturers.     

Product acquisition management: Current industry practice and a proposed framework

Remanufacturing requires that used products (cores) be obtained from the enduser at the end of their current life cycle so that the value-added may be recovered and the products returned to functional use again. The acquisition of cores to be remanufactured in such recoverable manufacturing systems is a complex set of activities that requires careful coordination to avoid the uncontrolled accumulation of core inventory, or unacceptable levels of customer service. The authors report on current industry practice via an extensive survey of North American remanufacturing firms. The authors propose a formal framework for Product Acquisition Management (PrAM) to coordinate, monitor, and provide an interface between reverse logistics and production planning and control activities. Finally, a series of managerial guidelines for the organization of PrAM activities is proposed. We conclude that managers should take actions that consistently reduce the variance inherent in a remanufacturing environment.     

应用作业成本法的模糊EPQ模型

应用作业成本法,研究了库容有限且缺陷产品可修复的经济生产批量问题。考虑企业自身库容有限及缺陷产品可修复,在系统中存在多个模糊参数的情况下,建立了一个基于作业成本法的模糊期望值模型,通过求解该模型确定出最佳生产批量和最大缺货量。最后的数值例子说明了所建模型是有效可行的。     

Set-up and production planning in hybrid manufacturing–remanufacturing systems with large returns

Hybrid systems that use both raw materials and returned products in the production process are considered. The system contains one facility, and undergoes set-ups each time it switches between two production modes. In particular, we address systems engaged mainly in remanufacturing and having a large percentage of return. This situation is encountered in companies with mature remanufacturing channels. The targeted application area is comprised of hybrid systems that uses leasing as a business model with manufacturing serving to attenuate return uncertainty. To evaluate the system performance, we take into account manufacturing and remanufacturing costs, holding costs in serviceable and return inventories, backlog and set-up costs. Our analysis of hybrid systems with high return levels reveals features that are peculiar to such systems and that differentiate them from systems with lower return rates. We first present analytical solutions for optimal production and set-up schedule, and determine the possible cycle shapes for reliable systems. Optimal policies contain intervals of manufacturing and remanufacturing at maximal rate, and intervals of on-demand and on-return remanufacturing. Failure-prone systems are studied next, using the formalism of stochastic dynamic programming. Optimal policies give rise to the trajectories converging to the patterns similar to the analytically calculated cycles.     

Optimal acquisition policy in remanufacturing under general core quality distributions

The quality of acquirable used products (cores) is highly variable, which has made production planning and control of remanufacturing systems difficult. This paper studies an acquisition problem in presence of uncertain core quality. In order to derive optimal acquisition policy, the problem is formulated as a non-linear integer programming model in the framework of order statistics. The model is a strictly discrete convex problem with a unique global minimal solution. Then, a single bisection method is developed to obtain the optimal solution under a general continuous quality distribution. Moreover, the expressions of the optimal solution in some frequently used quality distributions are derived. Furthermore, the model is extended to the case of a general remanufacturing cost function, and corresponding results are presented. Finally, numerical experiments are conducted to test the effects of quality distribution, cost relationships of acquirable cores and remanufacturing cost function.