Online Assortment Optimization with Reusable Resources

We consider an online assortment optimization problem where we have n substitutable products with fixed reusable capacities [Formula: see text]. In each period t, a user with some preferences (potentially adversarially chosen) who offers a subset of products, St, from the set of available products arrives at the seller’s platform. The user selects product [Formula: see text] with probability given by the preference model and uses it for a random number of periods, [Formula: see text], that is distributed i.i.d. according to some distribution that depends only on j generating a revenue [Formula: see text] for the seller. The goal of the seller is to find a policy that maximizes the expected cumulative revenue over a finite horizon T. Our main contribution is to show that a simple myopic policy (where we offer the myopically optimal assortment from the available products to each user) provides a good approximation for the problem. In particular, we show that the myopic policy is 1/2-competitive, that is, the expected cumulative revenue of the myopic policy is at least half the expected revenue of the optimal policy with full information about the sequence of user preference models and the distribution of random usage times of all the products. In contrast, the myopic policy does not require any information about future arrivals or the distribution of random usage times. The analysis is based on a coupling argument that allows us to bound the expected revenue of the optimal algorithm in terms of the expected revenue of the myopic policy. We also consider the setting where usage time distributions can depend on the type of each user and show that in this more general case there is no online algorithm with a nontrivial competitive ratio guarantee. Finally, we perform numerical experiments to compare the robustness and performance of myopic policy with other natural policies. This paper was accepted by Gabriel Weintraub, revenue management and analytics.

Comment on Modified Fare Ratio in a Two-Class Static Revenue Management Model with Buy-up Behavior

We review the optimal booking limit in the two-class static revenue management model with customers’ buy-up behavior. This is when a deterministic fraction of the low-fare customer class that cannot book early are willing to book the higher fare later. This simple model with dependent demands is difficult to analyze. Some well-known publications, such as Talluri and van Ryzin ( 2004 ) and Phillips ( 2005 ), treat this model incorrectly. In this note, we correct an erroneous formula for the modified fare ratio with the proper probabilistic interpretation. The correction was established previously by Brumelle et al. ( 1990 ). Numerical examples reveal that the corrected modified fare ratio provides a lower optimal booking limit, resulting in a higher expected revenue than those obtained by using the incorrect modified fare ratio.

A regret lower bound for assortment optimization under the capacitated MNL model with arbitrary revenue parameters

In this note, we consider dynamic assortment optimization with incomplete information under the capacitated multinomial logit choice model. Recently, it has been shown that the regret (the cumulative expected revenue loss caused by offering suboptimal assortments) that any decision policy endures is bounded from below by a constant times $\sqrt {NT}$ , where $N$ denotes the number of products and $T$ denotes the time horizon. This result is shown under the assumption that the product revenues are constant, and thus leaves the question open whether a lower regret rate can be achieved for nonconstant revenue parameters. In this note, we show that this is not the case: we show that, for any vector of product revenues there is a positive constant such that the regret of any policy is bounded from below by this constant times $\sqrt {N T}$ . Our result implies that policies that achieve ${{\mathcal {O}}}(\sqrt {NT})$ regret are asymptotically optimal for all product revenue parameters.

Dynamic pricing with finite price sets: a non-parametric approach

We study price optimization of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty. Each selling season consists of a finite number of discrete time periods, and demand per time period is Bernoulli distributed with price-dependent parameter. The set of feasible prices is finite, and the expected demand corresponding to each price is unknown to the seller, whose objective is to maximize cumulative expected revenue. We propose an algorithm that estimates the unknown parameters in a learning phase, and in each subsequent season applies a policy determined as the solution to a sample dynamic program, which modifies the underlying dynamic program by replacing the unknown parameters by the estimate. Revenue performance is measured by the regret: the expected revenue loss relative to the optimal attainable revenue under full information. For a given number of seasons n, we show that if the number of seasons allocated to learning is asymptotic to $$(n^2\log n)^{1/3}$$ ( n 2 log n ) 1 / 3 , then the regret is of the same order, uniformly over all unknown demand parameters. An extensive numerical study that compares our algorithm to six benchmarks adapted from the literature demonstrates the effectiveness of our approach.

Research on Decision Optimization Model of Microgrid Participating in Spot Market Transaction

The development of electricity spot trading provides an opportunity for microgrids to participate in the spot market transaction, which is of great significance to the research of microgrids participating in the electricity spot market. Under the background of spot market construction, this paper takes the microgrid including wind power, photovoltaic (PV), gas turbine, battery storage, and demand response as the research object, uses the stochastic optimization method to deal with the uncertainty of wind and PV power, and constructs a decision optimization model with the goal of maximizing the expected revenue of microgrids in the spot market. Through the case study, the optimal bidding electricity of microgrid operators in the spot market is obtained, and the revenue is USD 923.07. Then, this paper further investigates the effects of demand response, meteorological factors, market price coefficients, and cost coefficients on the expected revenue of microgrids. The results demonstrate that the demand response adopted in this paper has better social–economic benefits, which can reduce the peak load while ensuring the reliability of the microgrid, and the optimization model also ensure profits while extreme weather and related economic coefficients change, providing a set of scientific quantitative analysis tools for microgrids to trade electricity in the spot market.

Equity-based incentive to coordinate shareholder-manager interests under information asymmetry

<p style='text-indent:20px;'>The shareholder's interest oriented from business operation relies on opportunism regulation of the manager under asymmetry. Effective motivation incentives should be exploited to facilitate the manager's effort devotion enthusiasms. This paper establishes a theoretic model in which the shareholder offers equity-based incentive to a fairness-preferred manager to coordinate their interest conflicts and maximize her expected revenue. The manager exerts unverifiable levels of efforts toward both decision and coordination tasks making the most of his private information about fairness preference. Two interrelated performance measures on different hierarchical levels are considered for contracting purposes. In each situation, we derive the equilibrium effort choices and incentive coefficients of both participants, and investigate how these decisions are affected by fairness preference. Research findings suggest that the incorporation of firm equity dominates pure profit incentive in eliciting high effort levels toward two distinctive managerial tasks. Besides, the equity-based incentive weakens the perceived unfairness and facilitates the participants' expected revenue. Comparative statics and numerical analysis are conducted to demonstrate our results and the effectiveness of the proposed equity-based incentive. Finally, we summarize the contributions of this paper and put forward directions for further study.</p>

Mixed Mechanisms for Auctioning Ranked Items

This paper deals with the problem of designing and choosing auctioning mechanisms for multiple commonly ranked objects as, for instance, keyword auctions in search engines on Internet. We shall adopt the point of view of the auctioneer who has to select the auction mechanism to be implemented not only considering its expected revenue, but also its associated risk. In order to do this, we consider a wide parametric family of auction mechanisms which contains the generalizations of discriminatory-price auction, uniform-price auction and Vickrey auction. For completeness, we also analyze the Generalized Second Price (GSP) auction which is not in the family. The main results are: (1) all members of the family satisfy the four basic properties of fairness, no over-payment, optimality and efficiency, (2) the Bayesian Nash equilibrium and the corresponding value at risk for the auctioneer are obtained for the considered auctions, (3) the GSP and all auctions in the family provide the same expected revenue, (4) there are new interesting auction mechanisms in the family which have a lower value at risk than the GSP and the classical auctions. Therefore, a window opens to apply new auction mechanisms that can reduce the risk to be assumed by auctioneers.

Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints

We examine the revenue–utility assortment optimization problem with the goal of finding an assortment that maximizes a linear combination of the expected revenue of the firm and the expected utility of the customer. This criterion captures the trade-off between the firm-centric objective of maximizing the expected revenue and the customer-centric objective of maximizing the expected utility. The customers choose according to the multinomial logit model, and there is a constraint on the offered assortments characterized by a totally unimodular matrix. We show that we can solve the revenue–utility assortment optimization problem by finding the assortment that maximizes only the expected revenue after adjusting the revenue of each product by the same constant. Finding the appropriate revenue adjustment requires solving a nonconvex optimization problem. We give a parametric linear program to generate a collection of candidate assortments that is guaranteed to include an optimal solution to the revenue–utility assortment optimization problem. This collection of candidate assortments also allows us to construct an efficient frontier that shows the optimal expected revenue–utility pairs as we vary the weights in the objective function. Moreover, we develop an approximation scheme that limits the number of candidate assortments while ensuring a prespecified solution quality. Finally, we discuss practical assortment optimization problems that involve totally unimodular constraints. In our computational experiments, we demonstrate that we can obtain significant improvements in the expected utility without incurring a significant loss in the expected revenue. This paper was accepted by Omar Besbes, revenue management and market analytics.