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

For large multi‐division firms, coordinating procurement policies across multiple divisions to leverage volume discounts from suppliers based on firm‐wide purchasing power can yield millions of dollars of savings in procurement costs. Coordinated procurement entails deciding which suppliers to use to meet each division's purchasing needs and sourcing preferences so as to minimize overall purchasing, logistics, and operational costs. Motivated by this tactical procurement planning problem facing a large industrial products manufacturer, we propose an integrated optimization model that simultaneously considers both firm‐wide volume discounts and divisional ordering and inventory costs. To effectively solve this large‐scale integer program, we develop and apply a tailored solution approach that exploits the problem structure to generate tight bounds. We identify several classes of valid inequalities to strengthen the linear programming relaxation, establish polyhedral properties of these inequalities, and develop both a cutting‐plane method and a sequential rounding heuristic procedure. Extensive computational tests for realistic problems demonstrate that our integrated sourcing model and solution method are effective and can provide significant economic benefits. The integrated approach yields average savings of 7.5% in total procurement costs compared to autonomous divisional policies, and our algorithm generates near‐optimal solutions (within 0.75% of optimality) within reasonable computational time.

As firms embrace collaborative principles, partners of varying strengths and standing are coming together to deliver products effectively to consumers. In a two-tier collaborative channel, a partner's relative standing is manifest in the order in which wholesale and retail prices are determined; in turn, standing influences a partner's ability to achieve profits. We propose a framework, based on two factors that specify the strength of partners across channel tiers (channel leadership) and within a tier (echelon dominance) and together determine a partner's standing in the pricing process, to effectively study various channel strength scenarios. Our analysis of Stackelberg games corresponding to these scenarios reveals interesting insights regarding the impact of channel leadership and echelon dominance, both individually and jointly. For instance, we show that the presence of a dominant player in the upstream manufacturing tier benefits both the dominant and the weak manufacturers. The leadership-dominance framework also allows us to study the effect of a retailer's sequencing of its pricing of the two manufacturers' products. By embedding the retailer's timing choices in channel strength scenarios, we find that both the retailer and weak manufacturer prefer that the retailer set prices for the two products simultaneously; in contrast, the echelon-dominant manufacturer benefits from the retailer sequentially pricing the manufacturers' products. Our analysis also covers preeminent channel leaders that control both wholesale and retail prices, finding that preeminent partners achieve significant gains and consumers benefit from low retail prices. Moreover, the weak manufacturer benefits from the presence of a preeminent manufacturer.

Disruptions in infrastructure networks to transport material, energy, and information can have serious economic, and even catastrophic, consequences. Since these networks require enormous investments, network service providers emphasize both survivability and cost effectiveness in their topological design decisions. This paper addresses the survivable network design problem, a core model incorporating the cost and redundancy trade-offs facing network planners. Using a novel connectivity upgrade strategy, we develop several families of inequalities to strengthen a multicommodity flow-based formulation for the problem, and show that some of these inequalities are facet defining. By increasing the linear programming lower bound, the valid inequalities not only lead to better performance guarantees for heuristic solutions, but also accelerate exact and approximate solution methods. We also consider a heuristic strategy that sequentially rounds the fractional values, starting with the linear programming solution to our strong model. Extensive computational tests confirm that the valid inequalities, added via a cutting plane algorithm, and the heuristic procedure are very effective, and their performance is robust to changes in the network dimensions and connectivity structure. Our solution approach generates tight lower and upper bounds with average gaps that are less than 1.2% for various problem sizes and connectivity requirements.

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