مشکل رزرو موجودی با اس ام اف و سنجش عملکرد مبتنی بر نرخ

In many inventory settings companies wish to provide customer-differentiated service levels. These may, for example, be motivated by differences in the perceived customer lifetime value or by specific contractual agreements. One approach to provide differentiated service levels is to reserve some portion of the available inventory exclusively for specific customer classes. Existing approaches to inventory reservation are typically based on the assumption that a company can assign a customer specific revenue or penalty cost to any order or unit of demand filled or unfulfilled. In practice, however, it is usually extremely difficult to accurately estimate (especially long term) monetary implications of meeting or not meeting customer demand and corresponding service level requirements. The research presented in this paper addresses the problem of setting appropriate inventory reservations for different customer classes based on fill rate-based performance measures. We model a single period inventory reservation problem with two customer classes and nesting. We develop exact expressions for two conflicting performance measures: (1) the expected fill rate of high priority customers and (2) the expected loss in the system fill rate induced by inventory reservation. With these expressions a decision maker can analyze the tradeoff between the loss in overall system performance and the higher expected fill rates for prioritized customers. We provide analytical insights into the effects of nesting and the impact of relevant problem parameters on these two performance measures. The analytical insights are illustrated and highlighted through a set of numerical examples. Although we limit our analysis to a single period inventory reservation problem, we expect that our results can be utilized in a wide range of problem settings in which a decision maker has to ration a perishable resource among different classes of customers.

In many inventory settings, companies wish to provide different levels of service to different classes of customers. Customer-differentiated service levels may be motivated by differences in the perceived customer lifetime value or by specific contractual agreements that include service level guarantees. One way to provide differentiated service levels is to reserve a certain portion of the available inventory exclusively for individual classes of customers. In the relevant literature, approaches to inventory reservation are typically based on cost and revenue measures. It is assumed that a company can assign a customer specific revenue or penalty cost to any order or unit of demand filled or unfulfilled. In practice, however, it is very difficult to accurately estimate (especially the long-term) monetary implications of meeting or not meeting customer demand and corresponding service level requirements on an individual order basis. For this reason, companies commonly base inventory decisions on service level and fill rate measure targets. If a decision maker chooses to reserve inventory to ensure a higher service level for individual customer classes, he faces a decision making problem with two conflicting objectives: inventory reservation to enhance the fulfillment of demand with higher priority may have a (disproportionate) detrimental impact on the performance of the overall system. A negative impact on the overall system performance occurs if too much inventory is reserved for prioritized customers and, at the same time, the remaining inventory is not sufficient to fulfill the entire demand from customers with lower priority. As a consequence, the decision maker has to evaluate the (non-linear) tradeoff between the benefits of ensuring higher service levels for prioritized customer classes and the (potential) decrease in the overall performance when deciding upon reservation quantities. The research presented in this paper attempts to lend insight into this important tradeoff. We model a single period inventory reservation problem with two classes of customers (with high and low priority) and assume that demand from both customer classes follows a Poisson process. At the beginning of the planning horizon, the decision maker decides on how much inventory to reserve exclusively for high priority customers; there will be no update of the reservation quantity during the planning horizon. We use two non-monetary performance measures to analyze the decision maker's tradeoff when determining the reservation quantity: the expected fill rate for the high priority customer class and the expected loss in the overall system fill rate induced by inventory reservation. We develop exact expressions and establish relevant properties for both performance measures. Based on the developed expressions for the individual performance measures we can fully characterize the decision maker's tradeoff dependent on the reservation level for the high priority customer class, i.e. for any reservation level we can compute the expected fill rate for the high priority customer class and the corresponding loss in the overall fill rate of the system. This information provides valuable decision support to a decision maker, not only when setting specific reservation levels, but also prior to offering certain service level agreements to a class of customers. With our expressions, the decision maker can assess whether it is prudent to “pay the price” of losing some overall system performance to achieve a certain high priority order service level. The results of our research are distinct from prior contributions in multiple ways: first of all, we model a multi-objective inventory reservation problem based on system fill rates rather than assuming a single criterion problem based on (difficult to obtain) penalty cost and revenue measures. Secondly, we do not require strong simplifying assumptions about the arrival structure of demand from different customer classes; for example, we do not impose that demand from low priority customers arrive before demand from high priority customers (as often done in revenue management literature). Not making these simplifying assumptions adds considerable complexity to our analysis because we have to specifically account for the effects of nesting in order to model a realistic problem setting. In our setting, nesting refers to a situation where demand from the high priority customers compete equally with demand from low priority customers for any remaining unreserved inventory once (and if) the high priority customers have exhausted their reserved inventory. To individually capture the “reservation effect” and the “nesting effect” we have to explicitly account for the time structure in the demand arrival processes for both customer classes. To the best of our knowledge, this paper is the first to provide exact expressions for fill rate measures for an inventory reservation problem with nesting. Next to our analytical analysis, we conduct numerical experiments to provide additional insights into the inventory reservation problem. We illustrate the aforementioned tradeoff and show how the effects of inventory reservation (specifically the reservation and the nesting effects) depend on relevant problem parameters. We also illustrate, the conditions under which the decision maker can expect a significant negative impact on the overall system performance when reserving inventory for high priority customers. Although we limit our analysis to a single period inventory reservation problem, we expect that our results can be utilized in a wide range of problem settings in which a decision maker has to ration a perishable resource among different classes of customers. The remainder of this paper is organized as follows: in Section 2 we review the relevant literature related to our research and highlight the contribution of our paper. In Section 3 we provide a formal characterization of the inventory reservation problem, develop exact expressions for the expected high priority fill rate and the loss in the expected overall fill rate of the system, and provide additional analytical insights. The results of a numerical analysis are presented in Section 4 and in Section 5 we summarize our findings and point to future research that may be conducted based on the results of our research.

In this paper we provide exact expressions for the expected high priority fill rate and the expected loss in the overall fill rate in a single period inventory setting where random orders from high and low priority customers are fulfilled following a nested inventory allocation mechanism. We used fill rate-based performance measures to address a multi-objective inventory reservation problem rather than assuming a single criterion problem based on (difficult to obtain) penalty cost and revenue measures. Also, we did not make strong simplifying assumptions about the arrival structure of demand from different customer classes; for example, we do not impose that demand from low priority customers arrives before demand from high priority customers. We formalized the reservation effect and the nesting effect corresponding to alternative inventory consumption cases and showed how relevant problem parameters impact the expected high fill rate and the expected loss in the system fill rate. The results can be utilized to support a decision maker in choosing his “optimal” inventory reservation quantity. We also provided evidence on how the set of potential reservation quantities can be restricted if some (partial) information about the decision maker's preferences is available. Since we are able to formally characterize the tradeoff between the performance measures, our results can also be utilized to support the decision maker in determining such partial preference information. Simple decision rules corresponding to these inventory threshold values can be used to pre-configure an automated inventory reservation engine. In summary, our analysis generates various insights for managers on the impact of inventory reservation using a nesting allocation policy under different system parameters. Future extensions of the research presented in this paper should consider multiple demand classes and different inventory allocation mechanisms. Also, in our analysis we assumed that the demand within the planning horizon is Poisson distributed and stationary. This assumption, although not unreasonable in certain settings and widely used in the literature, may not be generally applicable in practice. Also, we assumed that orders are rejected if the entire available inventory in the planning period has been consumed. Analyzing the performance of a multi-class inventory reservation approach with backorders and multiple planning periods may be of theoretical and practical interest. We believe that the results of our research provide a valuable basis for these modeling extensions.