Joern Meissner

Dynamic Pricing Strategies for Multiproduct Revenue Management Problems

Consider a firm that owns a fixed capacity of a resource that is consumed in the production or delivery of multiple products. The firm strives to maximize its total expected revenues over a finite horizon, either by choosing a dynamic pricing strategy for each product or, if prices are fixed, by selecting a dynamic rule that controls the allocation of capacity to requests for the different products. This paper shows how these well-studied revenue management problems can be reduced to a common formulation in which the firm controls the aggregate rate at which all products jointly consume resource capacity, highlighting their common structure, and in some cases leading to algorithmic simplifications through the reduction in the control dimension of the associated optimization problems. In the context of their associated deterministic (fluid) formulations, this reduction leads to a closed-form characterization of the optimal controls, and suggests several natural static and dynamic pricing heuristics. These are analyzed asymptotically and through an extensive numerical study. In the context of the former, we show that resolving the fluid heuristic achieves asymptotically optimal performance under fluid scaling.

Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems

We consider a family of N items that are produced in, or obtained from, the same production facility. Demands are deterministic for each item and each period within a given horizon of T periods. If in a given period an order is placed, setup costs are incurred. The aggregate order size is constrained by a capacity limit. The objective is to find a lot-sizing strategy that satisfies the demands for all items over the entire horizon without backlogging, and that minimizes the sum of inventory-carrying costs, fixed-order costs, and variable-order costs. All demands, cost parameters, and capacity limits may be time dependent. In the basic joint setup cost (JS) model, the setup cost of an order does not depend on the composition of the order. The joint and item-dependent setup cost (JIS) model allows for item-dependent setup costs in addition to the joint setup costs. We develop and analyze a class of so-called progressive interval heuristics. A progessive interval heuristic solves a JS or JIS problem over a progressively larger time interval, always starting with period 1, but fixing the setup variables of a progressively larger number of periods at their optimal values in earlier iterations. Different variants in this class of heuristics allow for different degrees of flexibility in adjusting continuous variables determined in earlier iterations of the algorithm. For the JS-model and the two basic implementations of the progressive interval heuristics, we show under some mild parameter conditions that the heuristics can be designed to be e-optimal for any desired value of e > 0 with a running time that is polynomially bounded in the size of the problem. They can also be designed to be simultaneously asymptotically optimal and polynomially bounded. A numerical study covering both the JS and JIS models shows that a progressive interval heuristic generates close-to-optimal solutions with modest computational effort and that it can be effectively used to solve large-scale problems.

Network Revenue Management with Inventory-Sensitive Bid Prices and Customer Choice

We develop an approximate dynamic programming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a non-linear function which is separable across resource inventory levels. This approximation can exhibit significantly improved accuracy compared to currently available methods. It further allows for arbitrary aggregation of inventory units and thereby reduction of computational workload, yields upper bounds on the optimal expected revenue that are provably at least as tight as those obtained from previous approaches. Computational experiments for the multinomial logit choice model with distinct consideration sets show that policies derived from our approach can outperform some recently proposed alternatives, and we demonstrate how aggregation can be used to balance solution quality and runtime.

Improved bid prices for choice-based network revenue management

One of the latest developments in network revenue management (RM) is the incorporation of customer purchase behavior via discrete choice models. Many authors presented control policies for the booking process that are expressed in terms of which combination of products to offer at a given point in time and given resource inventories. However, in many implemented RM systems—most notably in the hotel industry—bid price control is being used, and this entails the problem that the recommended combination of products as identified by these policies might not be representable through bid price control. If demand were independent from available product alternatives, an optimal choice of bid prices is to use the marginal value of capacity for each resource in the network. But under dependent demand, this is not necessarily the case. In fact, it seems that these bid prices are typically not restrictive enough and result in buy-down effects.

List pricing versus dynamic pricing: impact on the revenue risk

We consider the problem of a firm selling multiple products that consume a single resource over a finite time period. The amount of the resource is exogenously fixed. We analyze the difference between a dynamic pricing policy and a list-price capacity control policy. The dynamic pricing policy adjusts prices steadily resolving the underlying problem every time step, whereas the list pricing policy sets static prices once but controls the capacity by allowing or preventing product sales. As steady price changes are often costly or unachievable in practice, we investigate the question of how much riskier it is to apply a list pricing policy rather than a dynamic pricing policy. We conduct several numerical experiments and compare expected revenue, standard deviation, and conditional-value-at-risk between the pricing policies. The differences between the policies show that list pricing can be a useful strategy when dynamic pricing is costly or impractical.

Risk management policies for dynamic capacity control

Consider a dynamic decision making model under risk with a fixed planning horizon, namely the dynamic capacity control model. The model describes a firm, operating in a monopolistic setting and selling a range of products consuming a single resource. Demand for each product is time-dependent and modeled by a random variable. The firm controls the revenue stream by allowing or denying customer requests for product classes. We investigate risk-sensitive policies in this setting, for which risk concerns are important for many non-repetitive events and short-time considerations.Numerically analysing several risk-averse capacity control policies in terms of standard deviation and conditional-value-at-risk, our results show that only a slight modification of the risk-neutral solution is needed to apply a risk-averse policy. In particular, risk-averse policies which decision rules are functions depending only on the marginal values of the risk-neutral policy perform well. From a practical perspective, the advantage is that a decision maker does not need to compute any risk-averse dynamic program. Risk sensitivity can be easily achieved by implementing risk-averse functional decision rules based on a risk-neutral solution.

Risk minimising strategies for revenue management problems with target values

Consider a risk-averse decision maker in the setting of a single-leg dynamic revenue management problem with revenue controlled by limiting capacity for a fixed set of prices. Instead of focussing on maximising the expected revenue, the decision maker has the main objective of minimising the risk of failing to achieve a given target revenue. Interpreting the revenue management problem in the framework of finite Markov decision processes, we augment the state space of the risk-neutral problem definition and change the objective function to the probability of failing a certain specified target revenue. This enables us to obtain a dynamic programming solution that generates the policy minimising the risk of not attaining this target revenue. We compare this solution with recently proposed risk-sensitive policies in a numerical study and discuss advantages and limitations.

Capacitated dynamic lot sizing with capacity acquisition

One of the fundamental problems in operations management is determining the optimal investment in capacity. Capacity investment consumes resources and the decision, once made, is often irreversible. Moreover, the available capacity level affects the action space for production and inventory planning decisions directly. In this article, we address the joint capacitated lot-sizing and capacity-acquisition problems. The firm can produce goods in each of the finite periods into which the production season is partitioned. Fixed as well as variable production costs are incurred for each production batch, along with inventory carrying costs. The production per period is limited by a capacity restriction. The underlying capacity must be purchased up front for the upcoming season and remains constant over the entire season. We assume that the capacity acquisition cost is smooth and convex. For this situation, we develop a model which combines the complexity of time-varying demand and cost functions and of scale economies arising from dynamic lot-sizing costs with the purchase cost of capacity. We propose a heuristic algorithm that runs in polynomial time to determine a good capacity level and corresponding lot-sizing plan simultaneously. Numerical experiments show that our method is a good trade-off between solution quality and running time.

Approximate dynamic programming for lateral transshipment problems in multi-location inventory systems

Companies commonly allocate their inventories across multiple locations based on their historical sales rates. However, random fluctuations in customer purchases, such as those caused by weather conditions and other external factors, might cause significant deviations from expected demand, leading to excess stock in some locations and stockouts in others. To fix this mismatch, companies often turn to lateral transshipments, e.g., the movement of stock between locations of the same echelon. In this paper, we examine multi-location inventory systems under periodic review with multiple opportunities for proactive transshipments within one order cycle. If stockouts occur, demand is lost with no opportunity to backorder. The objective of our model is to find an optimal policy that indicates the sources and the destinations of transshipments as well as the number of units, to maximise the profit of the network. We create a dynamic program that can, in principal, be solved to optimality using Bellmans equation. However, the size of the state and decision spaces makes it impossible to find the optimal policy for real-world sized problem instances. Thereby, we use forward approximate dynamic programming to find a near-optimal transshipment policy. Finally, we conduct an extensive numerical study to gauge the performance of our transshipment policy. For small size instances, we compare our policy to the optimal one. For larger scale instances, we consider other practically oriented heuristics. Our numerical experiments show that our proposed algorithm performs very well compared to state-of-the-art methods in the literature.

The effect of data preprocessing on a retail price optimization system

Revenue management (RM) is making a significant impact on pricing research and practice, from aviation and hospitality industries to retailing. However, empirical data conditions in retail are distinct to other industries, in particular in the large number of products within and across categories. To set profitable static prices with established RM models, the data is often simplified by data pruning (the exclusion of subsets of data that are deemed irrelevant or unsuitable) and data aggregation (the combination of disparate data points). However, the impact of such data preprocessing, despite being ubiquitous in retailing, is insufficiently considered in current RM research. This could induce potential sources of bias for the demand model estimates, as well as subsequent effects on the price optimization system, the optimized price set, and the profit maxima, which have not yet been investigated. This paper empirically studies the impact of two commonly used data preprocessing techniques in retail RM, data pruning and data aggregation, using simulated and empirical retail scanner data. We numerically assess potential biases introduced by data preprocessing using a systems perspective in estimating a two-stage demand model, the resulting price elasticities, optimized price sets, and the ensuing profit that it yields. Results show that both data aggregation and data pruning bias demand model estimates, albeit with different effect, but both produce less profitable price sets than unbiased reference solutions. The results demonstrate the practical importance of data preprocessing as a cause for estimation bias and suboptimal pricing in retail price optimization systems. The effect of the two popular data preprocessing techniques, pruning and aggregation, on a retail price optimization system is analyzed.The study uses real retail scanner data as well as synthetically data generated within empirical valid parameter bounds.The decision support system is based on different configurations of combining a multinomial choice market share model with a linear category model.The interplay of the system components is analyzed and the loss in profit optimality induced by the data preprocessing techniques is quantified.Data pruning and aggregation affect the optimality of retail prices differently, depending on the underlying data and model conditions.