Gp Gudrun Kiesmüller

Inventory models with lateral transshipments: A review

Lateral transshipments within an inventory system are stock movements between locations of the same echelon. These transshipments can be conducted periodically at predetermined points in time to proactively redistribute stock, or they can be used reactively as a method of meeting demand which cannot be satisfied from stock on hand. The elements of an inventory system considered, e.g. size, cost structures and service level definition, all influence the best method of transshipping. Models of many different systems have been considered. This paper provides a literature review which categorizes the research to date on lateral transshipments, so that these differences can be understood and gaps within the literature can be identified.

A new approach for controlling a hybrid stochastic manufacturing / remanufacturing system with inventories and different leadtimes

This paper addresses the control problem of a stochastic recovery system with two stocking points and different leadtimes for production and remanufacturing. For such systems the optimal control policy for a linear cost model is not known. Therefore, in the literature several heuristic policies are investigated and analyzed. In this paper a new approach is provided which differs substantially from the existing ones. Instead of using one inventory position for the production and remanufacturing decisions we base the decisions on two aggregate variables which are defined different for different leadtime relations. By means of numerical examples we illustrate that system performance, measured in average costs per time unit, can be improved substantially by our new approach, especially for large leadtime differences.

An inventory model with dependent product demands and returns

In this paper an inventory model for a single reusable product is investigated, in which the random returns depend explicitly on the demand stream. Further, the model distinguishes itself from most other research in this field by considering leadtimes and a finite planning horizon. We show that neglecting the dependency between demands and returns of products may lead to bad performance with respect to total average relevant costs. Additionally, our results enable us to determine the minimal recovery probability or the minimal length of the planning horizon for which reuse is profitable.

A continuous time inventory model for a product recovery system with multiple options

Abstract Increasing environmental consciousness, limited availability of natural resources to manufacture new products, recovery quotas to avoid disposal, manufacturers assigned to be responsible for used products, and materials value of components included in returned products are incentives for product recovery. The fact that we now have two possible sources to service demand raises new operational questions. For instance, when is remanufacturing of used and returned products preferred to producing the requirements. Most production and inventory management models for reverse logistics are restricted to stationary demands and returns and do not address seasonal effects and product life cycles. Therefore, we consider a deterministic model with dynamic demands and returns. Then there might exist time periods where returns exceed demands and vice versa. The question has to be answered whether excess returns should be stored for future recovery or disposed of. In our work, there are different demand classes, e.g. different product qualities or different markets. This adds yet another aspect to be examined. It has to be determined for which demand class returns should be used. As a result returns can either be stored for later use for a certain demand class or being used instantly for another class. Demands have to be satisfied either from production or remanufacturing of returned products and returns not needed for recovery may be disposed of. In this paper we determine the optimal production, remanufacturing, and disposal policy for a linear cost model by applying Pontryagins Maximum Principle.

Computational issues in a stochastic finite horizon one product recovery inventory model

Inderfurth [OR Spektrum 19 (1997) 111] and Simpson [Operations Research 26 (1978) 270] have shown how the optimal decision rules in a stochastic one product recovery system with equal leadtimes can be characterized. Using these results we provide in this paper a method for the exact computation of the parameters which determine the optimal periodic policy. Since exact computation is, especially in case of dynamic demands and returns, quite time consuming, we also provide two different approximations. One is based on an approximation of the value-function in the dynamic programming problem while the other approximation is based on a deterministic model. By means of numerical examples we compare our results and discuss the performance of the approximations.

Optimal control of a one product recovery system with leadtimes

Abstract In this paper a recovery system for a single product is investigated. Besides a remanufacturing and a manufacturing facility the system consists of one inventory for returned and recoverable items and one for serviceable items. Demands are satisfied from serviceable inventory, which can be replenished by remanufactured returned items, which are as good as new, or by new produced items. Additionally, there is the possibility of disposing of returned items. We determine the cost optimal manufacturing, remanufacturing and disposal rates for the system under the assumptions of a linear cost structure, a finite planning horizon and deterministic and dynamic demand and return rates. Thereby we study two classes of policies, one where backorders are forbidden and another one where they are allowed. In contrast to the existing literature positive leadtimes are considered.

Optimization of component reliability in the design phase of capital goods

We introduce a quantitative model to support the decision on the reliability level of a critical component during its design. We consider an OEM who is responsible for the availability of its systems in the field through service contracts. Upon a failure of a critical part in a system during the exploitation phase, the failed part is replaced by a ready-for-use part from a spare parts inventory. In an out-of-stock situation, a costly emergency procedure is applied. The reliability levels and spare parts inventory levels of the critical components are the two main factors that determine the downtime and corresponding costs of the systems. These two levels are decision variables in our model. We formulate the portions of Life Cycle Costs (LCC) which are affected by a components reliability and its spare parts inventory level. These costs consist of design costs, production costs, and maintenance and downtime costs in the exploitation phase. We conduct exact analysis and provide an efficient optimization algorithm. We provide managerial insights through a numerical experiment which is based on real-life data.

Simple expressions for finding recovery system inventory control parameter values

In recent years considerable effort has been devoted to the development of inventory control models for joint manufacturing and remanufacturing. Optimality of control policies is analyzed and algorithms for the determination of parameter values have been developed. However, there is still a lack of formulae or algorithms that allow for an easy computation of optimal or near optimal policy parameter values. This paper addresses the problem of computing the produce-up-to level S and the remanufacture-up-to level M in a periodic review inventory control model. We provide simple formulae for the policy parameter values, which can easily be implemented within spreadsheet applications. The approach is to derive news-vendor-type formulae that are based on underage and overage cost considerations. We propose different formulae depending on whether lead times for production and remanufacturing are identical or not. A numerical study shows that the obtained solutions provide relatively small cost deviations compared to the optimal solution within the investigated class of inventory control policies.

Dynamic product acquisition in closed loop supply chains

We consider a closed-loop supply chain where demand can either be satisfied by manufacturing new products or by buying back used products from customers and upgrading their functionality by remanufacturing. A joint buy-back pricing and manufacturing–remanufacturing decision model at the operations–marketing interface is presented that allows for dynamic parameters, e.g. product life cycles and seasonal aspects. The model allows the identification of beneficial opportunities for buying back and storing used products for immediate and future recovery. We present a new deterministic, dynamic, continuous-time optimisation model, derive necessary and sufficient optimality conditions, and develop a solution algorithm to find the cost-minimising manufacturing and remanufacturing policies as well as buy-back strategies for used products based on Pontryagins Maximum Principle. It is shown that, in general, an optimal policy will include time intervals where returns are acquired so as to synchronise demand and remanufacturing, where returns are acquired and stored for future remanufacturing, and intervals where demand is satisfied by a mix of manufactured and remanufactured products. Furthermore, we discuss several reactive and proactive acquisition and remanufacturing heuristics and show under which conditions they are optimal. The findings are illustrated by numerical examples.

The benefit of VMI strategies in a stochastic multi-product serial two echelon system

We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.