Production, Manufacturing and LogisticsSimple heuristics for push and pull remanufacturing policies
Introduction
Environmental considerations, government regulations, and economic incentives motivate many businesses to engage in recovery activities [5]. Recycling of materials is a well-known example. In recent years, more and more companies have initiated value-added recovery operations such as remanufacturing. Remanufacturing brings a product or product part up to an ‘as-new’ quality. Since remanufacturing is often cheaper than manufacturing, this type of recovery can lead to considerable cost savings. Items that are remanufactured nowadays include machine tools, medical instruments, copiers, automobile parts, computers, office furniture, mass transit, aircraft, aviation equipment, telephone equipment, and tires (see [1], [3], [4], [7], [8], [9], [11], [13], [16], [19], [20], [24]).
Across the different industries, product remanufacturing can be done by either the original equipment manufacturers (OEM) or independent remanufacturing companies. An important difference between these two situations is that an OEM, or a third party appointed by the OEM, has to coordinate remanufacturing operations with manufacturing operations, either on a product level or an assembly level. This provides additional complexities for inventory management and is the situation that we consider in this paper.
A typical example of remanufacturing operations is the management of spare car parts. Volkswagen, for instance, retrieves and remanufactures used car parts and resells them as spare parts [26]. Remanufactured parts come with the same quality and warranty as new parts, but are produced for less than half of the cost. Both types are sold for the same price, though. The availability of remanufacturable parts varies through time. Remanufacturing operations generally do not start until the end of the initial phase of the lifetime of a product, due to lack of returns availability before that time. During the following normal phase when design is mature, the number of return is sufficient to set up a remanufacturing operation. However, there are typically less returns than demands, so that manufacturing is still needed as well. During the final phase after the design is retired, there may be more returns than demands, in which case the manufacturing option is no longer required. What we focus on is the normal phase, where remanufacturing operations have to be coordinated with manufacturing operations. Similar examples are reported by Driesch and Flapper [2] (engine remanufacturing at Daimler–Chrysler) and Zuidwijk et al. [30] (copier remanufacturing at Océ).
Fig. 1 gives a graphical representation of the inventory system in the above practical situation. Note that since remanufactured items have the same quality as manufactured items and are sold for the same price in the same market, we do not need to distinguish between the two. Both types are serviceable and are used to satisfy the same customer demands. Clearly, in order to control such a system efficiently, manufacturing and remanufacturing decisions have to be coordinated.
There has been a considerable number of contributions dealing with inventory control for joint manufacturing and remanufacturing. Reviews are provided by Fleischmann et al. [6] and, more recent, by van der Laan et al. [28]. However, only a few authors have proposed heuristic procedures for approximating optimal policy parameters. Such procedures have important practical value, since it is difficult, if not impossible, to exactly optimize inventory order levels and order quantities simultaneously. Indeed, even for easier to handle traditional systems with forward logistics only, heuristic procedures are generally preferred in practise.
In an early account, Simpson [18] studies a periodic review inventory system with general demand and return processes. The remanufacturing process is not modelled explicitly, but the probability density function for the remanufacturing output per time unit is assumed to be fixed and known. Manufacturing lead times are stochastic. The inventory policy is characterized by the order-up-to level for manufacturing. Under both a service objective (minimize holding costs under a fill rate constraint) and a cost objective (minimize holding and backorder costs), Simpson derives a simple newsboy equation for the order-up-to level.
Mahadevan et al. [14] study a slightly modified version of Simpson’s model. Here, returns are remanufactured only at the time of review. The remanufacturing lead time is non-zero, but constant as is the manufacturing lead time. The analysis is restricted to cases with Poisson demand and return processes. Three heuristics for determining the order-up-to level are proposed and tested.
Muckstadt and Isaac [15] model the remanufacturing process explicitly as a queuing system with Poisson arrivals (the returns) and general service times. Manufacturing orders are triggered by a standard (s, Q) policy (reorder Q when inventory position drops to s). The objective is to minimize the average total cost, consisting of manufacturing setup costs, holding costs for serviceable inventory, and backorder costs. Using Markov Chain analysis and approximating the distribution of net inventory with a normal distribution, closed-form formulae for the order level and order quantity are derived.
van der Laan et al. [27] extend the model of Muckstadt & Isaac by including a disposal option for returned items. A returned item is disposed of if there is already a certain number (the dispose-down-to level) of other returns waiting to be remanufactured. They propose an iterative algorithm for calculating a near-optimal order level, order-up-to level, and dispose-down-to level.
The above approaches have one thing in common: the remanufacturing process is autonomous and is not controlled through an inventory policy. In contrast, Kiesmüller and Minner [12] study a discrete time, continuous review inventory system with constant lead times for manufacturing and remanufacturing in which both processes are controlled by order-up-to policies. The objective is to minimize the total average costs, including holding costs and backorder costs, but no fixed costs. Closed-form formulae for the order-up-to levels are derived for cases where (1) lead times are equal, (2) the manufacturing lead time is larger, and (3) the remanufacturing lead time is larger.
We present a heuristical approach for general demand and return processes. The remanufacturing process and remanufacturable inventory are explicitly modeled. Lead times for (re-)manufacturing are equal, non-zero constants. Aside from holding costs, backorder costs and set-up costs for manufacturing, we also include set-up costs for remanufacturing. In order to control such an intricate system, we consider more versatile inventory control policies than the ones mentioned above. Multiple types of policies are analyzed. All use the same (s, Q) type policy for manufacturing, but they differ in the way that they push or pull remanufacturing orders. 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.
The remainder of the paper is organized as follows. In Section 2, the inventory system and the policies are described in detail. The formulae for approximating the optimal order levels and order quantities for the push and pull policies are developed in Sections 3 Heuristics for push control, 4 Heuristics for pull control, respectively, and tested numerically in Section 5. We end with a summary and conclusions in Section 6.
Section snippets
System, policies, and notation
The inventory system is as depicted in Fig. 1. Manufacturing and remanufacturing have the same constant lead time L. Demand and return are driven by independent continuous stochastic processes with (average) rates λ and γ, respectively. It is assumed that demands do not occur in batches and that there is continuous review, so that there is no undershoot of the reorder point. The density function and distribution function of demand during the lead time are denoted by fD and FD, respectively.
The
Heuristics for push control
A stochastic analysis of the system at hand is rather complicated, since we have to deal with a two-dimensional state space (inventory position and remanufacturable inventory) that are mutually dependent. Since the classic EOQ formula has proved to be very robust in stochastic settings, we propose a similar approach and analyze a deterministic model in order to approximate the optimal order quantities (Section 3.1). Given these order quantities, in Section 3.2, we approximate the optimal order
Heuristics for pull control
As was done for push control in the previous section, we first approximate the optimal order quantities under the assumption that demand and return are deterministic (Section 4.1) and then approximate the optimal order level in a stochastic setting (Section 4.2).
Numerical evaluation
The above analysis has lead to the following heuristic expressions.Policy Push – Simple pull General pulla a Provided that .
Studying the table above we observe the following similarities and differences among the heuristics.
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The order quantity for remanufacturing is the same for all push and pull policies.
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The manufacturing
Summary and conclusion
We analyzed an inventory system with product returns, where remanufacturing is an alternative for manufacturing and both have the same lead time. Heuristics were developed for three types of inventory policies: push, simple pull, and general pull. The push policy remanufactures Qr items as soon as they are available. It manufactures Qm whenever the serviceable inventory position drops to sm. The simple pull policy starts a lot if the serviceable inventory position drops to s. A batch of size Qr
Acknowledgment
The research of Dr. Ruud H. Teunter has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.
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