Karl Inderfurth

Simple optimal replenishment and disposal policies for a product recovery system with leadtimes

The paper addresses a problem of product recovery management where a single product is stocked in order to fulfill a stochastic demand of customers who may return products after usage, thus generating also stochastic product returns. The material flow can be controlled by procuring new products on the one hand, and by remanufacturing or disposal of returned items on the other. A situation is considered where all costs are proportional and where remanufacturing as well as procurement needs a fixed deterministic leadtime which can be different for both activities. For periodic review control it is shown how the optimal decision rules for procurement, remanufacturing and disposal can be evaluated by exploiting the functional equations of a dynamic programming formulation. The serious impact of leadtimes on the complexity of the control rule is elaborated, and it is demonstrated for which leadtime situations simple optimal policies can be derived.ZusammenfassungEs wird ein Lagerhaltungsproblem mit stochastischer Nachfrage betrachtet, bei dem Produkte nach Gebrauch wieder zurückgegeben werden können. Diese gebrauchten Güter, deren Rückfluß ebenfalls stochastischer Natur ist, können entweder nach entsprechender Aufarbeitung wiederverwendet oder müssen entsorgt werden. Außer durch Wiederaufarbeitung kann die Versorgung mit marktfähigen Produkten durch Neubeschaffung erfolgen. Es wird davon ausgegangen, daß nur proportionale Kosten für die einzelnen Aktivitäten auftreten und daß sowohl Wiederaufarbeitung als auch reguläre Beschaffung mit festen Durchlaufzeiten bzw. Lieferzeiten verbunden sind. Es wird für den Fall periodischer Kontrolle gezeigt, wie die optimale Entscheidungsregel für Beschaffung, Aufarbeitung und Entsorgung mit Hilfe der stochastischen dynamischen Programmierung untersucht werden kann. Dabei wird der entscheidende Einfluß von Durchlauf- und Lieferzeit auf die Komplexität der Entscheidungsregel herausgearbeitet. Schließlich wird gezeigt, für welche Situationen optimale Regeln einfacher Struktur abgeleitet werden können.

Materials coordination in stochastic multi-echelon systems

This paper reviews the theoretical and numerical analysis of stochastic multi-echelon systems. We discuss both production (assembly) and distribution models, with an emphasis on materials coordination problems. Extensions to capacitated systems are also treated. The emphasis of this paper is on applicability of the models; in particular we characterize environments where multi-echelon models naturally fit. In particular, we discuss numerical procedures which allow for a quick and accurate evaluation of systems of realistic size and show how to use them to arrive at target service levels in serial and assembly systems. Extensions to capacitated systems and more flexible production environments are also discussed.

Product recovery in stochastic remanufacturing systems with multiple reuse options

In many product recovery situations, returned products can be reused in multiple ways. Under these circumstances, the problem arises in which quantities reusable items should be allocated to the different remanufacturing options, especially in case of insufficient stock of returns. For this problem a periodic review model is formulated which also includes a disposal option and incorporates uncertainties in returns and demands for the different serviceable options. The structure of the optimal policy is analyzed, and it is shown that under specific allocation rules a near-optimal policy with a simple structure exists. An efficient computational procedure for determination of the optimal policy parameters is presented. This procedure is applied in a numerical investigation that gives interesting managerial insights into important product recovery issues.

Impact of uncertainties on recovery behavior in a remanufacturing environment

Purpose – Remanufacturing of used products is an emerging business area, which is attractive from both an economic and an environmental point of view. Aims to investigate to what extent profit orientation in product recovery management will stimulate an environmentally conscious behavior in the sense that it promotes high recovery levels. This study also seeks to focus on a product recovery system where, in the context of extended product responsibility, a manufacturer of original products is also engaged in remanufacturing used products taken back from its customers.Design/methodology/approach – For this type of a closed‐loop supply chain the optimal recovery and production policy is evaluated. By a numerical analysis, it is shown how cost‐efficient decision making affects the product recovery behavior. In a sensitivity analysis it is evaluated how various problem determinants influence the preference for product recovery. Specifically, the impact of different sources of uncertainty is investigated.Findi...

Leadtime effects and policy improvement for stochastic inventory control with remanufacturing

When returns of goods and remanufacturing options have to be taken into consideration in inventory control situations, two additional sources of complexity appear in the traditional approaches of optimizing stochastic inventory control. Firstly, due to uncertainty of returns, an additional stochastic impact has to be regarded. Secondly, with remanufacturing a second mode of supply of serviceable goods is given, so that coordination with the regular mode of procurement becomes necessary. It can be shown that under these conditions we face extremely complicated optimal control rules if the leadtimes for remanufacturing and regular procurement differ. This holds for both the structure of the control policy and the inventory information necessary for optimal stock adjustment. In this context, the meaning of the inventory position, which is well-defined in traditional inventory control, is no longer evident. In practice, in these situations usually simple (suboptimal) decision rules are applied that only use a few control parameters and additionally do not take into consideration the complexity of defining the inventory position appropriately. For such a simple (4-parameter) control rule it is shown that by determining the inventory position in a proper way the performance of the policy can be improved considerably. This effect is equivalent to using the remanufacturing leadtime as a decision variable which has to be fixed in an optimal way.

Safety stocks in multi-stage inventory systems under different service measures

In this paper, we treat the problem of determining safety stocks in multi-stage inventory systems with normally distributed demands. The system follows a periodic review base-stock control policy. Assuming that every stockpoint satisfies a service level constraint and that no internal delays occur, we formulate the optimization problem for a general inventory system and derive properties of the optimal policy, which depend on the structure of the multi-stage system and the service measure used. Considering stockout occurrence related service levels, we find that the safety stock coverage times can only obtain values resulting from the extreme points of the solution set. Service levels representing size and duration of stockouts need less protection and are connected with problem reduction properties. The analysis of the reduced problems leads to similar extreme point properties as for stockout occurrence related service.

Planning and control of rework in the process industries: A review

For all kinds of reasons, rework, i.e. the transformation of products not fulfilling preset specifications into products that do, is an important issue in process industries. Despite a considerable amount of published research on planning and control of rework, and in addition many papers referring to the existence of rework in the process industries, hardly any attention has been paid to the consequences of many process industries specific characteristics for execution, planning and control of rework operations. Here are identified the characteristics of the process industries that influence the possibilities for rework in these industries, based on a framework provided by Flapper and Jensen ( International Journal of Production Research , 1999, to be published). How the available operations management literature assists in determining operational strategies for planning and control of rework in process industries is assessed. It is concluded that many relevant and interesting problems have not been addressed.

Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution

Abstract In hybrid control systems for simultaneous remanufacturing of used products and manufacturing of new ones, the two operations are not directly interconnected if remanufactured items are downgraded and have to be sold in markets different from those for new products. Sometimes a connection between these markets is given by a downward substitution property which allows the producer to offer a new item instead of a remanufactured one in case of a shortage of a remanufactured product. Thus, shortage costs can be avoided, but a loss in profit due to sale of a high-graded product at the price of a low-graded one has to be accepted. For a single-period problem with stochastic returns of used products and stochastic demands of serviceable ones, it is shown how the manufacturing and remanufacturing decisions have been coordinated in order to maximize the total expected profit. It turns out that under strictly proportional costs and revenues a medium-simple ‘order-up-to policy’ with two parameters and two parameter functions is optimal. However, optimal policies in situations where manufacturing leadtimes exceed leadtimes for remanufacturing turn out to be different from those in the opposite leadtime case. The research presented combines methods for policy analysis in stochastic manufacturing/remanufacturing problems and in stochastic inventory control problems with substitutable products.

How to set the holding cost rates in average cost inventory models with reverse logistics

Among both inventory theorists and practitioners, it is common use to include an opportunity cost rate in the holding cost rate. In that way, the cost of capital can be roughly incorporated in an average cost (AC) inventory model. The traditional way for calculating the opportunity cost rate is to multiply the interest rate (or discount rate) by the marginal cost for producing/ordering an item. For single source inventory systems with only forward logistics, this method is easy to use, and leads to near-optimal policies from a discounted cash flow (DCF) point of view. For inventory systems with reverse logistics, however, the method is no longer straightforward. In this paper we compare different methods for calculating the opportunity cost rates of returned non-serviceable, remanufactured, and manufactured items. We discuss which method gives the best results for a specific reverse logistics model with setup costs, non-zero lead times, and disposal.

Safety stock optimization in multi-stage inventory systems

Abstract Determining appropriate safety stocks in stochastic multi-state production/distribution systems is a very difficult task. Approaches for optimal determination of safety stocks regarding cost objectives and service level restrictions which are suitable for practical applications can only be found for a very limited class of multi-stage inventory problems like problems of strictly serial structure or special two-stage production/distribution systems. In this paper a procedure for determining the optimal size and distribution of safety stocks in a general serial or divergent production/distribution process ruled by a base-stock control policy is presented. This approach especially allows for taking into account the impact of end-item demand correlation on distribution and size of safety stocks by using risk-pooling effects in divergent systems. A powerful dynamic programming algorithm for solving the safety stock optimization problem is developed, and impacts of problem parameter variations on the optimal solution are discussed.