Browsing by Subject "Revenue management"

Now showing 1 - 11 of 11

Open Access
Bundle pricing of inventories with stochastic demand
(Elsevier, 2009) Bulut, Z.; Gürler, U.; Şen, A.
We consider a retailer selling a fixed inventory of two perishable products over a finite horizon. Assuming Poisson arrivals and a bivariate reservation price distribution, we determine the optimal product and bundle prices that maximize the expected revenue. Our results indicate that the performances of mixed bundling, pure bundling and unbundled sales strategies heavily depend on the parameters of the demand process and the initial inventory levels. Bundling appears to be most effective with negatively correlated reservation prices and high starting inventory levels. When the starting inventory levels are equal and in excess of average demand, most of the benefits of bundling can be achieved through pure bundling. However, the mixed bundling strategy dominates the other two when the starting inventory levels are not equal. We also observe that an incorrect modeling of the reservation prices may lead to significant losses. The model is extended to allow for price changes during the selling horizon. It is shown that offering price bundles mid-season may be more effective than changing individual product prices.
Open Access
A comparison of fixed and dynamic pricing policies in revenue management
(2013) Şen, A.
We consider the problem of selling a fixed capacity or inventory of items over a finite selling period. Earlier research has shown that using a properly set fixed price during the selling period is asymptotically optimal as the demand potential and capacity grow large and that dynamic pricing has only a secondary effect on revenues. However, additional revenue improvements through dynamic pricing can be important in practice and need to be further explored. We suggest two simple dynamic heuristics that continuously update prices based on remaining inventory and time in the selling period. The first heuristic is based on approximating the optimal expected revenue function and the second heuristic is based on the solution of the deterministic version of the problem. We show through a numerical study that the revenue impact of using these dynamic pricing heuristics rather than fixed pricing may be substantial. In particular, the first heuristic has a consistent and remarkable performance leading to at most 0.2% gap compared to optimal dynamic pricing. We also show that the benefits of these dynamic pricing heuristics persist under a periodic setting. This is especially true for the first heuristic for which the performance is monotone in the frequency of price changes. We conclude that dynamic pricing should be considered as a more favorable option in practice.
Open Access
Competitive markdown timing for perishable and substitutable products☆
(Elsevier, 2016-10) Şen, A.
We model as a duopoly two firms selling their fixed stocks of two substitutable items over a selling season. Each firm starts with an initial price, and has the option to decrease the price once. The problem for each firm is to determine when to mark its price down in to maximize its revenue. We show that the existence and characterization of a pure-strategy equilibrium depend on the magnitude of the increase in the revenue rate of a firm when its competitor runs out of stock. When the increase is smaller than the change in the revenue rate of the price leader when both firms are in stock for all of the three possible scenarios, neither firm has the incentive to force its rival to run out of stock and if a firm marks its price down after the season starts, its inventory runs out precisely at the end of the season. When the increase is larger than the change of the price leader׳s revenue rate in one particular scenario, waiting until its rival runs out of inventory may be an equilibrium strategy for the larger firm even though this may lead to leftover inventory for itself. In other cases, there may be no pure-strategy equilibrium in the game. In certain regions of the parameter space, a firm׳s revenue may be decreasing in its starting inventory which shows that a firm may be better off if it can credibly salvage a portion of its inventory prior to the game. While most of our analysis is for open-loop strategies, in the final part of the paper, we show that the open-loop equilibrium survives as an equilibrium when we consider closed-loop strategies for an important subset of the parameter space.
Open Access
Dynamic pricing under inventory considerations and price protection
(2015-05) Yıldız, Barış
In high-tech industry, customers’ tendency to purchase the newest versions of products forces manufacturers to reduce the prices of older models. This puts the retailers in a vulnerable position as their own sales prices also decrease for these products. For this purpose, manufacturers and retailers compromise over different price commitment terms in their contracts. One such term is price protection. In general, a price protection term obliges a manufacturer refund a retailer a portion of the difference between the new and old wholesale prices for the inventory that the retailer have in stock and that are ordered within a time window. Sometimes, refunds may also be applied on products sold based on their sales price. We study a price protection contract over a finite horizon under stochastic demand. We have a single manufacturer and a single retailer, each endowed with a fixed amount of inventory at the beginning of the horizon. The manufacturer determines the retail price and neither manufacturing nor replenishment is allowed. The objective of the manufacturer is to set the retail price in each period given how much inventory is left at the manufacturer and the retailer. We analyze the structure of the model and provide some analytical results on the effect of different factors on optimal prices and optimal expected profits. Then, we present the results of a numerical study in which we further investigate the effect of different factors to obtain managerial insights.
Open Access
The impact of decision types on revenue management decisions: an experimental study
(Blackwell Publishing, 2018) Kocabıyıkoğlu, A.; Göğüş, Celile Itır; Hekimoğlu, M. H.
In the standard two-class revenue management model, the decision maker allocates a fixed resource between two customer classes with hierarchical prices and uncertain demand. The normative (i.e., expected revenue-maximizing) allocation is given by Littlewood's Rule, but little is known about how decision makers actually form these decisions. We report results of an experimental study that investigates revenue management decision-making. We find that subjects' behavior is influenced by the decision type. In particular, our subjects reserve more units for the high-end segment when they are asked to set the protection level (the number of units to set aside for the higher priced class) compared to when they set the booking limit (the number of units available for the lower priced class). We propose that this behavioral pattern can be explained by our subjects’ different valuations of revenues from the high- and low-end sales. We also observe that when there is a change in segment prices, although decision makers adjust allocations in the direction suggested by normative theory, the magnitude of adjustments is greater (and hence closer to the normative level) when the source of the price change matches the class whose allocation they determine.
Open Access
Missed flight cover design
(2019-07) Çelik, Beyza
Missed flight cover is an option with a price and validity period and is a source of ancillary revenues for the airline companies and helps passengers, who missed their flights, resume their journeys at reduced costs. We study optimal price and validity period of this option to allow a passenger to use missed flight fare towards the purchase of a future airline ticket. Our objective is to maximize the expected ancillary revenues of the airline. The possible actions of passengers are described with a probabilistic graphical model. Within that model, passenger's decision to buy the option and to resume the journey after a missed flight are described with separate hierarchical Bayesian mixed logit regression models. To estimate the parameters of those mixed logit models, an individualized Bayesian choice-based conjoint experiment is designed. In this experiment, each choice set is optimally picked so as to maximize the expected Kullback-Leibler divergence between subsequent posterior distributions of individualized part-worths. The posterior distributions of unknown model parameters, particularly, individualized part-worths, are calculated with a hybrid Markov Chain Monte Carlo (MCMC) algorithm. We developed an R-Shiny online survey web application for six di erent individualized choice experiments (buy or not buy an option for leisure and business travel, resume or not resume a missed leisure or business flight with or without an option) and collected responses of over 300 individuals. Using the MCMC samples of individual part-worths from their posterior distributions, we simulated the market. We searched and found an option design that maximized the average net revenue of the airline over the simulated runs of the market.
Open Access
Optimal bundle formation and pricing of two products with limited stock
(2009) Gürler Ü.; Öztop, S.; Şen, A.
In this study, we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle. Our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm. One of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit. Product demands follow a Poisson Process with a price dependent rate. Customer reservation prices are assumed to have a joint distribution. We study the impact of reservation price distributions, initial inventory levels, product prices, demand arrival rates and cost of bundling. We observe that the expected profit decreases as the correlation between the reservation prices of two products increases. With negative correlation, bundling cost has a significant impact on the number of bundles formed. When the product prices are low, the retailer sells individual products as well as the bundle (mixed bundling), when they are high, the retailer sells only bundles (pure bundling). The expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases. For high starting inventory levels, the retailer reduces bundle price and offers more bundles. The number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases. Impacts of substitutability and complementarity of products are also investigated. The retailer forms more bundles, or charges higher prices for the bundle or both as the products become more complementary and less substitutable.
Open Access
Performance bounds on optimal fixed prices
(2013) Şen, A.
We consider the problem of selling a fixed stock of items over a finite horizon when the buyers arrive following a Poisson process. We obtain a general lower bound on the performance of using a fixed price rather than dynamically adjusting the price. The bound is 63.21% for one unit of inventory, and it improves as the inventory increases. For the one-unit case, we also obtain tight bounds: 89.85% for the constant-elasticity and 96.93% for the linear price-response functions.
Open Access
Pricing and revenue management: the value of coordination
(INFORMS Inst.for Operations Res.and the Management Sciences, 2014) Kocabiyikoǧlu, A.; Popescu, I.; Stefanescu, C.
The integration of systems for pricing and revenue management must trade off potential revenue gains against significant practical and technical challenges. This dilemma motivates us to investigate the value of coordinating decisions on prices and capacity allocation in a stylized setting. We propose two pairs of sequential policies for making static decisions - on pricing and revenue management - that differ in their degree of integration (hierarchical versus coordinated) and their pricing inputs (deterministic versus stochastic). For a large class of stochastic, price-dependent demand models, we prove that these four heuristics admit tractable solutions satisfying intuitive sensitivity properties. We further evaluate numerically the performance of these policies relative to a fully coordinated model, which is generally intractable. We find it interesting that near-optimal performance is usually achieved by a simple hierarchical policy that sets prices first, based on a nonnested stochastic model, and then uses these prices to optimize nested capacity allocation. This tractable policy largely outperforms its counterpart based on a deterministic pricing model. Jointly optimizing price and allocation decisions for the high-end segment improves performance, but the largest revenue benefits stem from adjusting prices to account for demand risk.
Open Access
Revenue management vs. newsvendor decisions: does behavioral response mirror normative equivalence?
(Wiley-Blackwell, 2015) Kocabiyikoglu, A.; Gogus, C. I.; Gonul, M. S.
We study and compare decision-making behavior under the newsvendor and the two-class revenue management models, in an experimental setting. We observe that, under both problems, decision makers deviate significantly from normative benchmarks. Furthermore, revenue management decisions are consistently higher compared to the newsvendor order quantities. In the face of increasing demand variability, revenue managers increase allocations; this behavior is consistent with normative patterns when the ratio of the selling prices of the two customer segments is less than 1/2, but is its exact opposite when this ratio is greater than 1/2. Newsvendors' behavior with respect to changing demand variability, on the other hand, is consistent with normative trends. We also observe that losses due to leftovers weigh more in newsvendor decisions compared to the revenue management model; we argue that overage cost is more salient in the newsvendor problem because it is perceived as a direct loss, and propose this as the driver of the differences in behavior observed under the two problems.
Embargo
Robust resource allocation under uncertainty
(2024-07) Demir, Ali Eren
Current methods for determining optimal capacity controls under uncertainty, such as stochastic optimization, often assume a known distribution for unknown parameters. This paper presents a novel approach using robust optimization to address the stochastic resource allocation problem in airline seat-inventory control. Our static formulations account for demand dependencies, offering a streamlined alternative to existing customer-choice models in revenue management literature. We analyze the structure of our proposed formulations, and provide insights on several robust counterparts of the seat-inventory control problem, considering various measures of robustness. We introduce algorithms based on these robust formulations to derive actionable results. Through extensive simulations focused on seat allocation problems within the revenue management domain, our proposed formulations demonstrate significantly improved worst-case performances. Notably, even under favorable scenarios, the performance of our solutions are comparable to those of the existing methods in the revenue management literature. By providing protection against forecasting errors in demand distribution parameters and offering improved booking limit controls when demand falls below expected value, our formulations demonstrate superior revenue retention compared to existing methods in our comparative analyses.