Stefanus Jasin

A Re-Solving Heuristic with Bounded Revenue Loss for Network Revenue Management with Customer Choice

We consider a network revenue management problem with customer choice and exogenous prices. We study the performance of a class of certainty-equivalent heuristic control policies. These heuristics periodically re-solve the deterministic linear program (DLP) that results when all future random variables are replaced by their average values and implement the solutions in a probabilistic manner. We provide an upper bound for the expected revenue loss under such policies when compared to the optimal policy. Using this bound, we construct a schedule of re-solving times such that the resulting expected revenue loss, obtained by re-solving the DLP at these times and implementing the solution as a probabilistic scheme, is bounded by a constant that is independent of the size of the problem.

Analysis of Deterministic LP-Based Booking Limit and Bid Price Controls for Revenue Management

We study the performance of two popular and widely used heuristics for revenue management known as the booking limit and bid price controls. In contrast to a recent result in the literature where frequent re-solvings of a certain heuristic are shown to significantly reduce revenue loss, we show that the asymptotic revenue loss of either booking limit or bid price control cannot be reduced regardless of the choice of re-solving times and the frequency of re-solving. Moreover, we also show that further variations within the policy classes, such as nested instead of partition booking limit, or certainty equivalent instead of additive bid price, are simply indistinguishable in terms of their order of revenue loss under frequent re-solvings. This negative result highlights the limitation of re-solving deterministic linear programs when the solution is interpreted as either a booking limit or a bid price. Finally, we briefly discuss how to modify the traditional booking limit control to make it more responsive ...

Reoptimization and Self-Adjusting Price Control for Network Revenue Management

We consider a standard dynamic pricing problem with finite inventories, finite selling horizon, and stochastic demands, where the objective of the seller is to maximize total expected revenue. We introduce a simple improvement of the popular static price control known in the literature. The proposed heuristic only requires a single optimization at the beginning of the selling horizon and does not require any reoptimization at all. This provides an advantage over the potentially heavy computational burden of reoptimization, especially for very large applications with frequent price adjustments. In addition, our heuristic can be implemented in combination with a few reoptimizations to achieve a high-level revenue performance. This hybrid of real-time adjustment and reoptimization allows the seller to enjoy the benefit of reoptimization without overdoing it.

An LP-based correlated rounding scheme for multi-item ecommerce order fulfillment

We consider an online multi-item retailer with multiple fulfillment facilities and finite inventory. The challenge faced by the retailer is to construct a fulfillment policy to decide from which facility each of the items in the arriving order should be fulfilled, in a way that minimizes the expected total shipping costs of fulfilling customer orders over a finite horizon. Shipping costs are linear in the size of the package shipped as well as the distance from the facility to the customer. We approximate the stochastic control formulation, which is computationally intractable, with a deterministic linear program (DLP) whose size is polynomial in the size of the input. We then study the performance of two fulfillment heuristics derived from the solution of the DLP. The first heuristic implements the solution of the DLP as fulfillment probability for each item. Since fulfillment decision for each item is made independently of fulfillment decision of other items in the same order, this heuristic does not ha...

Performance of an LP-Based Control for Revenue Management with Unknown Demand Parameters

We consider a standard network revenue management (RM) problem and study the performance of a linear program (LP)-based control, the Probabilistic Allocation Control (PAC), in the presence of unknown demand parameters. We show that frequent re-optimizations of PAC without re-estimation suffice to shrink the asymptotic impact of estimation error on revenue loss. If, in addition to re-optimizations, we also frequently re-estimate the parameters, we prove that the performance of PAC in the unknown parameters setting is almost as good as the performance of PAC in the known parameters setting. Our numerical experiments show that PAC yields a revenue improvement of order 0.5%–1.5% relative to LP-based Booking Limit and Bid Price in most cases. Given the small margin in RM industries, such as the airline industry (about 2%), this level of improvement can easily translate into a significant increase in profit.

Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint

We consider a single-product revenue management problem with an inventory constraint and unknown, noisy, demand function. The objective of the firm is to dynamically adjust the prices to maximize total expected revenue. We restrict our scope to the nonparametric approach where we only assume some common regularity conditions on the demand function instead of a specific functional form. We propose a family of pricing heuristics that successfully balance the tradeoff between exploration and exploitation. The idea is to generalize the classic bisection search method to a problem that is affected both by stochastic noise and an inventory constraint. Our algorithm extends the bisection method to produce a sequence of pricing intervals that converge to the optimal static price with high probability. Using regret (the revenue loss compared to the deterministic pricing problem for a clairvoyant) as the performance metric, we show that one of our heuristics exactly matches the theoretical asymptotic lower bound that has been previously shown to hold for any feasible pricing heuristic. Although the results are presented in the context of revenue management problems, our analysis of the bisection technique for stochastic optimization with learning can be potentially applied to other application areas.

Real-Time Dynamic Pricing with Minimal and Flexible Price Adjustment

We study a standard dynamic pricing problem where the seller (a monopolist) possesses a finite amount of inventories and attempts to sell the products during a finite selling season. Despite the potential benefits of dynamic pricing, many sellers still adopt a static pricing policy because of (1) the complexity of frequent reoptimizations, (2) the negative perception of excessive price adjustments, and (3) the lack of flexibility caused by existing business constraints. In this paper, we develop a family of pricing heuristics that can be used to address all these challenges. Our heuristic is computationally easy to implement; it requires only a single optimization at the beginning of the selling season and automatically adjusts the prices over time. Moreover, to guarantee a strong revenue performance, the heuristic only needs to adjust the prices of a small number of products and do so infrequently. This property helps the seller focus his effort on the prices of the most important products instead of all products. In addition, in the case where not all products are equally admissible to price adjustment (due to existing business constraints such as contractual agreement, strategic product positioning, etc.), our heuristic can immediately substitute the price adjustment of the original products with the price adjustment of similar products and maintain an equivalent revenue performance. This property provides the seller with extra flexibility in managing his prices. This paper was accepted by Noah Gans, stochastic models and simulation .

Real-Time Dynamic Pricing for Revenue Management with Reusable Resources and Deterministic Service Time Requirements

We consider the setting of a firm that sells a finite amount of resources to price-sensitive customers who arrive randomly over time according to a specified non-stationary rate. Each customer requires a service that consumes one unit of resource for a deterministic amount of time, and the resource is reusable in the sense that it can be immediately used to serve a new customer upon the completion of the previous service. The firm’s objective is to set the price dynamically to maximize its expected total revenues. This is a fundamental problem faced by many firms in many industries. We formulate this as an optimal stochastic control problem and develop two heuristic controls based on the solution of the deterministic relaxation of the original stochastic problem. The first heuristic control is static since the corresponding price sequence is determined before the selling horizon starts; the second heuristic control is dynamic, it uses the first heuristic control as its baseline control and adaptively adjusts the price based on previous demand realizations. We show that both heuristic controls are asymptotically optimal in the regime with large demand and large number of resources. Finally, we consider two important generalizations of the basic model to the setting with multiple service types requiring different service times and the setting with advance service bookings.

Power of Dynamic Pricing in Revenue Management with Strategic (Forward-Looking) Customers

The present paper considers a canonical revenue management problem wherein a monopolist seller seeks to maximize revenue from selling a fixed inventory of a product to customers who arrive over time. We assume that customers are forward-looking and rationally strategize the timing of their purchases, an empirically confirmed aspect of modern customer behavior. We consider a broad class of customer utility models that allow customer disutility from waiting to be heterogeneous and correlated with product valuations. Chen et al. (2018) show that the so-called fixed price policy is asymptotically optimal in the high-volume regime where both the sellers initial inventory and the length of the selling horizon are proportionally scaled. Specifically, the revenue loss of the fixed price policy is O(k^{1/2}), where k is the systems scaling parameter. In the present paper, we present a novel real-time pricing policy. This policy repeatedly updates the fixed price policy in Chen et al. (2018) by taking into account the volatility of the historic sales. We force the price process under this policy to be non-decreasing over time. Therefore, our policy incentivizes strategic customers to behave myopically. We show that if the seller updates the price for only a single time, then the revenue loss of our policy can be arbitrarily close to O(k^{1/3} ln k). If the seller updates the prices with a frequency O(ln k / ln ln k), then the revenue loss of our policy can be arbitrarily close to O((ln k )^3). These results are novel and show the power of dynamic pricing in the presence of forward-looking customers, at least for the problem setting considered in this paper.

Asymptotic Optimality of Order-Up-To Control for Stochastic Inventory Systems with Sequential Probabilistic Service Level Constraints

Service level constraint is often used as a metric to directly control the quality of service (e.g., managing the probability of stock-out) in practice. Many inventory problems with service level constraints are often difficult to solve and are typically approximated by deterministic formulations. This raises an important question regarding the quality of such an approach. To shed light on this question, in this paper, we consider two simplified yet fundamental inventory models (with backorder and lost-sales) with independent demands, positive lead times and sequential probabilistic service level constraints, and study the performance of a natural order-up-to policy whose parameters can be calculated using the optimal solution of a deterministic approximation of the backorder inventory system. We show that it is asymptotically optimal for both the backorder and lost-sales systems in the setting with a high service level requirement, with a stronger performance bound for the backorder system. Our analysis for the lost-sales system involves a construction of an alternative backorder system whose expected total cost can be related to that of the analogous lost-sales system. Overall, our result contributes to the growing body of inventory literature that suggests the near-optimality of simple heuristic policies. Moreover, it also gives credence to the use of deterministic approximation for solving complex inventory problems in practice, at least for applications where the targeted service level is sufficiently high.