We present the Integrated Size and Price Optimization Problem (ISPO) for a fashion discounter with many branches. Based on a two-stage stochastic programming model with recourse, we develop an exact algorithm and a production-compliant heuristic that produces small optimality gaps. In a field study we show that a distribution of supply over branches and sizes based on ISPO solutions is significantly better than a one-stage optimization of the distribution ignoring the possibility of optimal pricing.
We consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon. Customers, whose reservation price distribution changes over time, arrive according to a nonhomogeneous Poisson process. We show that at any given time, the optimal price decreases with inventory. We also identify a sufficient condition under which the optimal price decreases over time for a given inventory level. This sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time. In addition to shedding managerial insight, these structural properties enable efficient computation of the optimal policy.Numerical studies are conducted to show the revenue impact of dynamic price policies. Price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price. For the former, our examples show that using optimal dynamic optimal policies achieves 2.4--7.3 revenue improvement over the optimal single price policy. For the latter, the revenue increase can be as high as 100 . These results explain why yield management has become so essential to fashion retailing and travel service industries.  A firm has inventories of a set of components that are used to produce a set of products. There is a finite horizon over which the firm can sell its products. Demand for each product is a stochastic point process with an intensity that is a function of the vector of prices for the products and the time at which these prices are offered. The problem is to price the finished products so as to maximize total expected revenue over the finite sales horizon. An upper bound on the optimal expected revenue is established by analyzing a deterministic version of the problem. The solution to the deterministic problem suggests two heuristics for the stochastic problem that are shown to be asymptotically optimal as the expected sales volume tends to infinity. Several applications of the model to network yield management are given. Numerical examples illustrate both the range of problems that can be modeled under this framework and the effectiveness of the proposed heuristics. The results provide several fundamental insights into the performance of yield management systems. We propose a game-theoretical model of a retailer who sells a limited inventory of a product over a finite selling season by using one of two inventory display formats: display all (DA) and display one (DO). Under DA, the retailer displays all available units so that each arriving customer has perfect information about the actual inventory level. Under DO, the retailer displays only one unit at a time so that each customer knows about product availability but not the actual inventory level. Recent research suggests that when faced with strategic consumers, the retailer could increase expected profits by making an upfront commitment to a price path. We focus on such pricing strategies in this paper, and study the potential benefit of DO compared to DA, and its effectiveness in mitigating the adverse impact of strategic consumer behavior. We find support for our hypothesis that the DO format could potentially create an increased sense of shortage risk, and hence it is better than the DA format. However, although potentially beneficial, a move from DA to DO is typically very far from eliminating the adverse impact of strategic consumer behavior. We observe that, generally, it is not important for a retailer to modify the level of inventory when moving from a DA to a DO format; a change in the display format, along with an appropriate price modification, is typically sufficient. Interestingly, across all scenarios in which a change in inventory is significantly beneficial, we observed that only one of the following two actions takes place: either the premium price is increased along with a reduction in inventory, or inventory is increased along with premium price reduction. We find that the marginal benefit of DO can vary dramatically as a function of the per-unit cost to the retailer. In particular, when the retailer's per-unit cost is relatively high, but not too high to make sales unprofitable or to justify exclusive sales to high-valuation customers only, the benefits of DO appear to be at their highest level, and could reach up to 20 increase in profit. Finally, we demonstrate that by moving from DA to DO, while keeping the price path unchanged, the volatility of the retailer's profit decreases. In this paper, we examine the research and results of dynamic pricing policies and their relation to revenue management. The survey is based on a generic revenue management problem in which a perishable and nonrenewable set of resources satisfy stochastic price sensitive demand processes over a finite period of time. In this class of problems, the owner (or the seller) of these resources uses them to produce and offer a menu of final products to the end customers. Within this context, we formulate the stochastic control problem of capacity that the seller faces: How to dynamically set the menu and the quantity of products and their corresponding prices to maximize the total revenue over the selling horizon. 