Resource Allocation and Pricing in the Absence of a Demand Forecast

This work is motivated by our collaboration with a large consumer packaged goods (CPG) company. We have found that whereas the company appreciates the advantages of dynamic pricing, they deem it operationally much easier to plan out a static price calendar in advance. We investigate the efficacy of static control policies for revenue management problems whose optimal solution is inherently dynamic. In these problems, a firm has limited inventory to sell over a finite time horizon, over which heterogeneous customers stochastically arrive. We consider both pricing and assortment controls, and derive simple static policies in the form of a price calendar or a planned sequence of assortments, respectively. In the assortment planning problem, we also differentiate between the static vs. dynamic substitution models of customer demand. We show that our policies are within 1-1/e (approximately 0.63) of the optimum under stationary demand, and 1/2 of the optimum under nonstationary demand, with both guarantees approaching 1 if the starting inventories are large. We adapt the technique of prophet inequalities from optimal stopping theory to pricing and assortment problems, and our results are relative to the linear programming relaxation. Under the special case of stationary demand single-item pricing, our results improve the understanding of irregular and discrete demand curves, by showing that a static calendar can be (1-1/e)-approximate if the prices are sorted high-to-low. Finally, we demonstrate on both data from the CPG company and synthetic data from the literature that our simple price and assortment calendars are effective. This paper was accepted by Hamid Nazerzadeh, big data analytics.

In “Bifurcating Constraints to Improve Approximation Ratios for Network Revenue Management with Reusable Resources,” Baek and Ma provide a unified framework for dynamically allocating reusable resources over time in the general network revenue management setting. That is, each incoming query is allowed to request an arbitrary combination of resources for different unknown durations, capturing applications like cloud computing and the dispatching of human resources. Through this framework, they derive simple algorithms that achieve the same approximation ratios as existing algorithms, which only allow queries to request one resource. Their framework also suggests a meta-algorithm for “bifurcating” the resources depending on the network structure and then using two different algorithms for controlling the capacities of two different groups of resources. This contrasts existing “one-size-fits-all” approaches to network revenue management and is demonstrated to improve both theoretical guarantees and empirical performance over a wide variety of instances.

We study the multi-armed bandit problem with arms which are Markov chains with rewards. In the finite-horizon setting, the celebrated Gittins indices do not apply, and the exact solution is intractable. We provide approximation algorithms for the general model of Markov decision processes with nonunit transition times. When preemption isn’t allowed, we provide a (1/2 − ε)-approximation, along with an example showing this is tight. When preemption is allowed, we provide a 1/12-approximation, which improves to a 4/27-approximation when transition times are unity. Our model captures the Markovian Bandits model of Gupta et al., the Stochastic Knapsack model of Dean et al., and the Budgeted Learning model of Guha and Munagala. Our algorithms improve existing results in all three areas. In our analysis, we encounter and overcome to our knowledge a new obstacle: an algorithm that provably exists via analytical arguments, but cannot be found in polynomial time.

In optimization problems, decisions are often made in the face of uncertainty that might arise in the form of random costs or benefits. In “Distributionally Robust Linear and Discrete Optimization with Marginals,” Louis Chen, Will Ma, Karthik Natarajan, David Simchi-Levi, and Zhenzhen Yan study a robust bound of linear and discrete optimization problems in which the objective coefficients are random and the set of admissible joint distributions is assumed to be specified only up to the marginals. They provide a primal-dual formulation for this problem, and in the process, unify existing results with new results. They establish NP-hardness of computing the bound for general polytopes and identify two sufficient conditions—one based on a dual formulation and one based on sublattices that provide a class of polytopes where the robust bounds are efficiently computable.