We study the classic multiperiod joint pricing and inventory control problem in a data-driven setting. In this problem, a retailer makes periodic decisions on the prices and inventory levels of a product that she wishes to sell. The retailer’s objective is to maximize the expected profit over a finite horizon by matching the inventory level with a random demand, which depends on the price in each period. In reality, the demand functions or random noise distributions are usually difficult to know exactly, whereas past demand data are relatively easy to collect. We propose a data-driven approximation algorithm that uses precollected demand data to solve the joint pricing and inventory control problem. We assume that the retailer does not know the noise distributions or the true demand functions; instead, we assume either she has access to demand hypothesis sets and the true demand functions can be represented by nonnegative combinations of candidate functions in the demand hypothesis sets, or the true demand function is generalized linear. We prove the algorithm’s sample complexity bound: the number of data samples needed in each period to guarantee a near-optimal profit is [Formula: see text], where T is the number of periods, and ϵ is the absolute difference between the expected profit of the data-driven policy and the expected optimal profit. In a numerical study, we demonstrate the construction of demand hypothesis sets from data and show that the proposed data-driven algorithm solves the dynamic problem effectively and significantly improves the optimality gaps over the baseline algorithms. This paper was accepted by J. George Shanthikumar, big data analytics.
We study a single product pricing problem with demand censoring in an offline data-driven setting. In this problem, a retailer has a finite amount of inventory and faces a random demand that is price sensitive in a linear fashion with unknown price sensitivity and base demand distribution. Any unsatisfied demand that exceeds the inventory level is lost and unobservable. We assume that the retailer has access to an offline data set consisting of triples of historical price, inventory level, and potentially censored sales quantity. The retailer’s objective is to use the offline data set to find an optimal price, maximizing his or her expected revenue with finite inventories. Because of demand censoring in the offline data, we show that the existence of near-optimal algorithms in a data-driven problem—which we call problem identifiability—is not always guaranteed. We develop a necessary and sufficient condition for problem identifiability by comparing the solutions to two distributionally robust optimization problems. We propose a novel data-driven algorithm that hedges against the distributional uncertainty arising from censored data, with provable finite-sample performance guarantees regardless of problem identifiability and offline data quality. Specifically, we prove that, for identifiable problems, the proposed algorithm is near-optimal and, for unidentifiable problems, its worst-case revenue loss approaches the best-achievable minimax revenue loss that any data-driven algorithm must incur. Numerical experiments demonstrate that our proposed algorithm is highly effective and significantly improves both the expected and worst-case revenues compared with three regression-based algorithms. This paper was accepted by J. George Shanthikumar, big data analytics.
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