An Advanced Heuristic for Multiple-Option Spare Parts Procurement after End-of-Production

After-sales service is a major profit generator for more and more OEMs in industries with durable products. Successful engagement in after-sales service improves customer loyalty and allows for competitive differentiation through superior service like an extended service period after end of production during which customers are guaranteed to be provided with service parts. In order to fulfill the service guarantee in these cases, an effective and efficient spare parts management has to be implemented, which is challenging due to the high uncertainty concerning spare parts demand over such a long time horizon. The traditional way of spare parts acquisition for the service phase is to set up a huge final lot at the end of regular production of the parent product which is sufficient to fulfill demand up to the end of the service time. This strategy results in extremely high inventory levels over a long period and generates major holding costs and a high level of obsolescence risk. With increasing service time more flexible options for spare parts procurement after end of production gain more and more importance. In our paper we focus on the two most relevant ones, namely extra production and remanufacturing. Managing all three options leads to a complicated stochastic dynamic decision problem. For that problem type, however, a quite simple combined decision rule with order-up-to levels for extra production and remanufacturing turns out to be very effective. We propose a heuristic procedure for parameter determination which accounts for the main stochastic and dynamic interactions between the different order-up-to levels, but still consists of quite simple calculations so that it can be applied to problem instances of arbitrary size. In a numerical study we show that this heuristic performs extremely well under a wide range of conditions so that it can be strongly recommended as a decision support tool for the multi-option spare parts procurement problem.Spare Parts, Inventory Management, Reverse Logistics, Final Order

Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

We consider the canonical periodic review lost sales inventory system with positive lead-times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the Projected Inventory Level (PIL) policy. We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant order policy for any finite lead-time and is therefore asymptotically optimal as the lead-time approaches infinity for the case of exponentially distributed demand per period. Numerical results show this policy also performs superior relative to other policies

An Advanced Heuristic for Multiple-Option Spare Parts Procurement after End-of-Production

After-sales service is a major profit generator for more and more OEMs in industries with durable products. Successful engagement in after-sales service improves customer loyalty and allows for competitive differentiation through superior service like an extended service period after end of production during which customers are guaranteed to be provided with service parts. In order to fulfill the service guarantee in these cases, an effective and efficient spare parts management has to be implemented, which is challenging due to the high uncertainty concerning spare parts demand over such a long time horizon. The traditional way of spare parts acquisition for the service phase is to set up a huge final lot at the end of regular production of the parent product which is sufficient to fulfill demand up to the end of the service time. This strategy results in extremely high inventory levels over a long period and generates major holding costs and a high level of obsolescence risk. With increasing service time more flexible options for spare parts procurement after end of production gain more and more importance. In our paper we focus on the two most relevant ones, namely extra production and remanufacturing. Managing all three options leads to a complicated stochastic dynamic decision problem. For that problem type, however, a quite simple combined decision rule with order-up-to levels for extra production and remanufacturing turns out to be very effective. We propose a heuristic procedure for parameter determination which accounts for the main stochastic and dynamic interactions between the different order-up-to levels, but still consists of quite simple calculations so that it can be applied to problem instances of arbitrary size. In a numerical study we show that this heuristic performs extremely well under a wide range of conditions so that it can be strongly recommended as a decision support tool for the multi-option spare parts procurement problem

Routing and Inventory Allocation Policies in Multi-Echelon Distribution Systems

This paper reviews the previous research in the area of logistics systems, especially in the area of the multi-echelon distribution system with stochastic demand. Many researches in this area emphasize the value of real-time information (which is more readily available nowadays by use of EDS or satellite systems) in distribution-related decisions. Also a great deal of efforts has been taken to study the risk-pooling effect of the various distribution policies in the multi-echelon systems. The objectives of this review are two-folded; (1) to help readers to understand the research paradigm in the multi-echelon area, and (2) to help them to find future research topics not yet explored

Inventory Policy Implications of On-Line Customer Purchase Behavior

In this paper we will examine some implications of online data for a classical operations management model, vis. the Economic Order Quantity model. Customer waiting behavior on individual orders (which occur during stockouts) forms the basis for evaluating the potential backorders. The potential attraction of reducing inventory holding costs must be balanced with the loss due to lost sales. We clearly delineate the conditions under which it is profitable to stock out every ordering cycle, and the conditions under which the traditional economic order quantity model still holds. In order to allow practical application of the model, we develop a number of different approaches to the problem of estimating the backorder function from available on-line transaction data

Perishable Items in Multi-Level Inventory Systems

This master thesis studies a two-echelon distribution system for perishable items with two non identical retailers. Each location is managed following a standard continuous (R, Q) ordering policy. The demand occurs solely at the retailers and follows independent Poisson processes. Customers are backordered when the retailer is out of stock. The items are considered as fixed lifetime perishables. Whenever an item perished, it is discarded from the stock. The model includes fix transportation time and the allocation policy at the central warehouse is a First-Come-First-Serve one. This kind of system is very complicated and therefore hard to study. In this master thesis, we focus on a simulation study of 48 different problems with both a FIFO and a LIFO issuing policy at the retailers. The goal of this study is therefore to optimize the values of R in (R, Q) ordering policies considering that the items are perishables. To do so, we try to optimize the values of the reorder points at every location. We also try to find some general behaviour of the system and we compare the FIFO and the LIFO best found solution. More than 1000 hours of computer-time were used for this study. For every problem, we conducted an optimization process to find better values of the reorder points at every location. For the FIFO case, an average cost reduction of more than 20% was found. It exists a good opportunity in term of cost savings while taking into account the perishable characteristic of the items. Another finding of our study is that the LIFO case has good performance comparing to what expected. On average, the costs increase is only 7% while considering a LIFO issuing policy instead of a FIFO one. Moreover, the values of the reorder points for the FIFO best found solution are still the same than the LIFO best found solution in 70% of the problems studied

Inventory control in production-inventory systems with random yield and rework: The unit-tracking approach

This paper considers a single-stage make-to-stock production–inventory system under random demand and random yield, where defective units are reworked. We examine how to set cost-minimizing production/order quantities in such imperfect systems, which is challenging because a random yield implies an uncertain arrival time of outstanding units and the possibility of them crossing each other in the pipeline. To determine the order/production quantity in each period, we extend the unit-tracking/decomposition approach, taking into account the possibility of order-crossing, which is new to the literature and relevant to other planning problems. The extended unit-tracking/decomposition approach allows us to determine the optimal base-stock level and to formulate the exact and an approximate expression of the per-period cost of a base-stock policy. The same approach is also used to develop a state-dependent ordering policy. The numerical study reveals that our state-dependent policy can reduce inventory-related costs compared to the base-stock policy by up to 6% and compared to an existing approach from the literature by up to 4.5%. From a managerial perspective, the most interesting finding is that a high mean production yield does not necessarily lead to lower expected inventory-related costs. This counterintuitive finding, which can be observed for the most commonly used yield model, is driven by an increased probability that all the units in a batch are either of good or unacceptable quality

Exact and heuristic linear-inflation policies for an inventory model with random yield and arbitrary lead times

We investigate a periodic inventory system for a single item with stochastic demand and random yield. Since the optimal policy for such a system is complicated we study the class of stationary linear-inflation policies where orders are only placed if the inventory position is below a critical stock level, and where the order quantity is controlled by a yield inflation factor. We consider two different models for the uncertain supply: binomial and stochastically proportional yield and we allow positive and constant lead times as well as asymmetric demand and yield distributions. In this paper we propose two novel approaches to derive optimal and near-optimal numerical values for the critical stock level, minimizing the average holding and backorder cost for a given inflation factor. First, we present a Markov chain approach, which is exact in case of negligible lead time. Second, we provide a steady state analysis to derive approximate closed-form expressions for the optimal critical stock level. We conduct an extensive numerical study to test the performance of our approaches. The numerical experiments reveal an excellent performance of both approaches. Since our derived formulas are easily implementable and highly accurate they are very valuable for practical application

Inventory Policies and Information Sharing: An Efficient Frontier Approach

We consider a two-tier inventory management system with one retailer and one supplier. The retailer serves a demand driven by a stationary moving average process (of possibly infinite order) and places periodic inventory replenishment orders to the supplier. In this setting, we study the value of information sharing and its impact on the retailer’s optimal ordering strategy. We argue that information sharing affects performance through two key cost drivers: (i) on-hand inventory variability and (ii) replenishment order variability. We characterize a “Pareto frontier” between these two sources of variability by identifying optimal inventory replenishment strategies that trade-off one type of variability for the other in a cost efficient way. For the case in which the retailer is able to share her complete demand history, we provide a full characterization of the efficient frontier, as well as of an optimal replenishment policy. On the other hand, when the retailer is not able (or willing) to share any demand information we provide a partial characterization of an optimal solution and show that information sharing does not always add value. We also show that the question of identifying conditions under which information sharing does offer value reduces to a delicate analysis of the invertibility (in a time series sense) of a specific stationary process.Operations Management Working Papers Serie