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In this study we investigate the desired level of recovery under various inventory control policies when the success of recovery is probabilistic. All the used and returned items go into a recovery process that is modelled as a single stage operation. The recovery effort is represented by the expected time spent for it. The effect of increasing recovery effort on the success probability together with unit cost of the operation is included by assuming general forms of dependencies. Alternative to recovered items, demand is satisfied by brand-new items. Four inventory control policies that differ in timing of and information used in purchasing decision are proposed. The objective is to find the recovery level together with inventory control parameter that minimize the long-run average total cost. A numerical study covering a wide range of system parameters is carried out. Finally computational results are presented with their managerial implications.

As a consequence of the increased awareness on the scarcity of resources and diminishing raw materials, recovery of used products has become an important issue for manufacturers in the past years. In many countries there are laws and law proposals obliging manufacturers to take back their products after their useful life to re-use. Designing recovery systems that bring the used items into an as-good-as new condition has been taking attention of many researches with diverse backgrounds. In this study our main aim is to investigate the desired level of recovery effort in the economical sense. In addition to environmental benefits, product recovery is typically seen as a cost reducing strategy. However, having a recovery practice requires new planning applications; mainly coordinating the traditional purchasing/production sources with recovery options due to the fact that they are used to satisfy the same demand stream. In recent years a vast amount of academic knowledge has been accumulated in coordinating these decisions. de Brito [1, p. 43] provides an up-to-date and extensive review of the literature. One of the issues not investigated in detail is the fact that the recovery process is not perfect in the sense that not all of the items can be successfully recovered. To the best of our knowledge, imperfect recovery is only investigated by Ferrer [2]. Under a deterministic demand, single period setting, he examines a number of distinct situations about the information on the failure of recovery. He includes a number of serial recovery operations and identifies the value of having the yield information in early stages of recovery. In addition the importance of the responsive suppliers as alternative to imperfect recovery is shown by numerical experimentation. Our study, aiming to investigate the desired level of recovery is motivated by an industrial practice in a European refinery (Rijneveld [3]). An important class of items in the inventory consists of expensive, slow moving parts that have high supplier lead time. The system is also subject to returns which cannot be used as-good-as new ones and have to go through a recovery process. The recovery process consists of a set of testing and fixing operations, starting with roughest to the detailed ones. Typically the recovery process is considered to be economical. Therefore the objective of the recovery shop is to maximize the number of recovered items, consequently they have the tendency for practicing recovery into finest detail. Currently, company's purchasing and recovery decisions are not coordinated. Since while making purchasing decisions the returns are not taken into account in a formal way, the recovered items cause inventory accumulation for the serviceables that are used to satisfy demand. As most of these items are slow moving, their effects can be substantial in holding costs. Besides, the objective of maximizing throughput of recovery may not be appropriate considering the effect of increasing recovery effort on the success probability of recovery and costs. The main objective of our study is to investigate the desired level of recovery effort for such a system. Our approach integrates tactical and operational decision making. We consider specification of recovery effort (that can be considered as a system design issue) and purchasing decisions (that is traditionally an operational decision) in a coordinated manner. For the sake of generality and simplicity, we model recovery as a single stage operation with some unit cost and lead time. We consider the expected time spent in recovery operation, i.e., associated expected lead time, as a measure of the amount of recovery effort and focus on the case where the probability of successful recovery increases as the expected lead time increases, i.e., the amount of effort put into recovery. Increasing the expected lead time of recovery operation can be considered as performing further disassembly, testing and fixing operations, in other words increasing the number of steps that get to be more detailed. We also include the effect of increasing recovery effort on associated unit cost. We assume that all of the items completing their usage time (which is stochastic with a known probability distribution) return to the system. We further assume that information on the number of items currently in use is always available. In several practical cases one observes both a 100% return rate and availability of information on the number of items currently in use. For instance consider a specific tool that is occasionally used by service engineers in the maintenance and repair of a certain machinery and that is prone to damage during the use. Whenever a need for use arises, the engineer requests the tool and after the use (s)he returns it. In general, the usage time is stochastic and the quality level of the used tool is not as-good-as new. Similarly, you can think of any commercial product where all of the customers return the products at the end of the useful life time as obliged by legislation or sales agreement. In these cases it is important to keep track of the number of items currently in use, in order to monitor the inventory system correctly. We assume that all of the issues and return information are perfectly recorded. Moreover the number of items currently in use is known. For the system described above we propose four distinct inventory control policies, and the desired level of recovery is investigated under different system conditions: expected life time of the product, expected supplier lead time, unit purchasing cost, sensitivity of success probability and unit cost to the increase in expected lead time of the recovery operation. The outline of the paper is as follows: In Section 2, the technical assumptions are given together with model formulation. In Section 3, the results of the numerical study are presented. Finally managerial insights gained by the study and the effect of employed assumptions are discussed in Section 4.

In this study we investigate the level of the desired recovery effort when the recovery process is not perfect. The effect of increased recovery effort on both the unit costs and the success of recovery operation is included in an abstract model where the recovery operation is represented by a single stage. Increasing the expected lead time of this operation corresponds to an increase in the number of steps of recovery in real life applications. Four distinct inventory control policies are proposed. They differ in the moment that the purchasing decision is made and in the way the inventory position is defined. Our computational experience reveals the following managerial insights. ••Recovery is most attractive for the systems where ∘∘ the recovery operation is efficient in terms of gain obtained in success by increasing its lead time, ∘∘ the magnitude of unit recovery cost is small with respect to purchasing cost, ∘∘ the unit recovery cost is not very sensitive to an increase in its lead time For these systems maximizing the recovery success is almost equivalent to minimizing expected costs. Therefore, before trying to maximize the output of the recovery shop, the pros in terms of gains in recovery success and cons in terms of increased unit costs should be well assessed. In addition, the sensitivity of the desired level of recovery with respect to efficiency shows the importance of process improvement studies that involves various research areas from material science, design for disassembly to disassembly planning. •• When the expected life time of the product is long with respect to the supplier lead time, considering the recovery operation as a primary source of satisfying demand does not make economic sense, even if the recovery operation is cost attractive and efficient.Under these cases, considering items currently in use, and making purchasing decisions upon failures at recovery, increase costs in the long run. In addition, when the recovery operation is not cost attractive and inefficient, the desired recovery probability is very low. In these cases, we expect that the exclusion of the items in process at the recovery operation will improve the performance of the systems. For a very restricted number of problems, inclusion of items in use in inventory position information lowers costs. Since we assume that all of the items completing their life time return to the system, our model does not include any costs incurred for keeping track of these items. When the return process itself is stochastic in terms of the number of items return to the system, the source of recovery is smaller in terms of inflow to the recovery operation. Our result on the value of this piece of information in terms of costs and the sensitivity of the solutions with respect to demand rate (in our case it determines the inflow to the recovery operation in the long run) shows the importance of estimating the return intensity rather than potential returns in the future. ••We assume an age independent success probability at the recovery operation. In real life, we expect that as the age of the used items increase and the number of previous recoveries increase, the probability of success at recovery operation decreases. Similarly, the sensitivity of success with respect to the increased recovery effort will be lower for the items used for a longer duration and that have been already recovered. In that sense, the desired recovery levels that we present constitute an upper bound for real life. Ferrer [2] already shows the importance of having the failure information as soon as possible. Under these cases, imposing rules restricting the age of the items that go through recovery operation will improve the system performance. •• We have ignored all possible effects of the workload on the throughput of recovery operation. When the resources carrying out recovery is limited in number, queuing effects occur. In that case, effective lead times increase, and consequently the inventory value of returns has a more significant effect. We expect that when the recovery shop is capacitated, the desired level of recovery decreases compared to uncapacitated case.