In response to competitive pressures, firms are increasingly adopting revenue management opportunities afforded by advances in information and communication technologies. Motivated by these revenue management initiatives in industry, we consider a dynamic pricing problem facing a firm that sells given initial inventories of multiple substitutable and perishable products over a finite selling horizon. Because the products are substitutable, individual product demands are linked through consumer choice processes. Hence, the seller must formulate a joint dynamic pricing strategy while explicitly incorporating consumer behavior. For an integrative model of consumer choice based on linear random consumer utilities, we model this multiproduct dynamic pricing problem as a stochastic dynamic program and analyze its optimal prices. The consumer choice model allows us to capture the linkage between product differentiation and consumer choice, and readily specializes to the cases of vertically and horizontally differentiated assortments. When products are vertically differentiated, our results show monotonicity properties (with respect to quality, inventory, and time) of the optimal prices and reveal that the optimal price of a product depends on higher quality product inventories only through their aggregate inventory rather than individual availabilities. Furthermore, we show that the price of a product can be decomposed into the price of its adjacent lower quality product and a markup over this price, with the markup depending solely on the aggregate inventory. We exploit these properties to develop a polynomial-time, exact algorithm for determining the optimal prices and the profit. For a horizontally differentiated assortment, we show that the profit function is unimodal in prices. We also show that individual, rather than aggregate, product inventory availability drives pricing. However, we find that monotonicity properties observed in vertically differentiated assortments do not hold.dynamic pricing, revenue management, perishable products, consumer choice, vertical and horizontal product assortments, efficient algorithm

We study a multicomponent, multiproduct production and inventory system in which individual components are made to stock but final products are assembled to customer orders. Each component is produced by an independent production facility with finite capacity, and the component inventory is controlled by an independent base-stock policy. For any given base-stock policy, we derive the key performance measures, including the probability of fulfilling a customer order within any specified time window. Computational procedures and numerical examples are also presented. A similar approach applies to the generic multi-item make-to-stock inventory systems in which a typical customer order consists of a kit of items.

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Delays in product availability are common in e-commerce where electronic retailers try to manage with very low inventories. While this lowers inventory costs, the negative effect of increased stockouts is to reduce net demand for the product. We analyze the effect of offering a lower price during stockout to compensate for a customer’s waiting time, using an EOQ-type inventory-modeling framework but solving simultaneously for both the optimal prices and the lengths of the in-stock and stockout periods. The lower price recaptures some lost demand and has an important synergistic effect: the increased sales rate leads to lower unit costs for inventory holding and product ordering. Stockout compensation improves market efficiency and increases the retailer’s sales and profit. The optimal stockout-compensation policy is to choose period lengths and prices such that the two periods have equal effective prices (i.e., the optimal stockout compensation equals the average waiting cost for a customer). Compared with the pure wait-free and stockless-operation policies, stockout compensation not only yields greater profits, but also greater revenues, lower unit costs, and increased consumer surplus and market coverage. Compared with a backorder policy without compensation, the stockout compensation policy improves profits and social welfare but at the expense of consumer surplus. Allowing for strategic consumer behavior under knowledge of future prices, the equal-effective-prices solution defines a rational-expectations equilibrium.

In this paper, we propose a new greedy-like heuristic method, which is primarily intended for the general MDKP, but proves itself effective also for the 0-1 MDKP. Our heuristic differs from the existing greedy-like heuristics in two aspects. First, existing heuristics rely on each item's aggregate consumption of resources to make item selection decisions, whereas our heuristic uses the effective capacity, defined as the maximum number of copies of an item that can be accepted if the entire knapsack were to be used for that item alone, as the criterion to make item selection decisions. Second, other methods increment the value of each decision variable only by one unit, whereas our heuristic adds decision variables to the solution in batches and consequently improves computational efficiency significantly for large-scale problems. We demonstrate that the new heuristic significantly improves computational efficiency of the existing methods and generates robust and near-optimal solutions. The new heuristic proves especially efficient for high dimensional knapsack problems with small-to-moderate numbers of decision variables, usually considered as "hard" MDKP and no computationally efficient heuristic is available to treat such problems.

doi 10.1287/mnsc.1030.016

Stochastic models with simultaneous arrivals arise naturally in the areas such as synchronized communication networks, flexible manufacturing systems, production/inventory systems, reliability modeling in random environment, etc., with a wide variety of interpretations. Simultaneous arrivals introduce dependence among various components of the system and make the explicit solutions of joint system performance measures either computationally intensive or intractable. This calls for structural analysis of dependence natures of such systems so that the insight gained from the analysis can suggest plausible approaches to develop tight bounds and efficient approximations to key system performance measures. The usual majorization order on a totally ordered index set and Schur convexity are powerful tools for establishing inequalities, in particular, for stochastic systems. However, the investigation on stochastic systems with simultaneous arrivals leads naturally to the comparison of distributions of parameter values on a tree-structured index set. In this paper, we introduce the notion of majorization with respect to weighted trees. The fundamental strength of tree majorization lies in its ability to make versatile comparisons over two parameter sets defined on a partially ordered index set. We identify several classes of transformations that provide simple characterizations of tree majorization orders. Finally, we apply the new notion to an assemble-to-order system and to a shock model with simultaneous subsystem failures and study the dependence structure of these systems. Our results show that tree majorization and its interplay with various notions of stochastic orders are useful tools to study the dependency of stochastic systems with multivariate, synchronized input processes.

This paper studies the dependence structure and bounds of several basic prototypical parallel queueing systems with correlated arrival processes to different queues. The marked feature of our systems is that each queue viewed alone is a standard single-server queuing system extensively studied in the literature, but those queues are statistically dependent due to correlated arrival streams. The major difficulty in analysing those systems is that the presence of correlation makes the explicit computation of a joint performance measure either intractable or computationally intensive. In addition, it is not well understood how and in what sense arrival correlation will improve or deteriorate a system performance measure. The objective of this paper is to provide a better understanding of the dependence structure of correlated queueing systems and to derive computable bounds for the statistics of a joint performance measure. In this paper, we obtain conditions on arrival processes under which a performance measure in two systems can be compared, in the sense of orthant and supermodular orders, among different queues and over different arrival times. Such strong comparison results enable us to study both spatial dependence (dependence among different queues) and temporal dependence (dependence over different time instances) for a joint performance measure. Further, we derive a variety of upper and lower bounds for the statistics of a stationary joint performance measure. Finally, we apply our results to synchronized queueing systems, using the ideas combined from the theory of orthant and supermodular dependence orders and majorization with respect to weighted trees (Xu and Li (2000)). Our results reveal how a performance measure can be affected, favourably or adversely, by different types of dependencies.