Perishable Assets Research Articles

Dynamic Price Dispersion of Seasonal Goods in Bertrand–Edgeworth Competition

The primary distinguishing characteristics of various revenue management systems include fixed capacities, uniform products, and customers' sensitivity to pricing when making purchase decisions. Even with only two or three competitors, the competition remains intense. This study examines the sub-game perfect Nash equilibrium of price competition within an oligopoly market where goods are perishable assets. Each seller possesses a single unit of a non-replenishable good and competes by setting prices to sell their inventory over a finite sales period. Each period, buyers seek to purchase one unit of the good, and the number of buyers entering is random. All sellers' prices are visible to buyers, and there is no cost associated with searching for goods. Through stochastic dynamic programming methods, sellers' optimal responses can be determined by treating the competition as a one-time price-setting game, considering the remaining sales periods and the current demand pattern. Assuming a binary demand model, it is demonstrated that the duopoly model exhibits a unique Nash equilibrium. In addition, it is shown that the oligopoly model does not result in price dispersion based on a discussed metric. Moreover, when a generalized demand model is considered, the duopoly model features a unique Nash equilibrium with mixed strategies, whereas the oligopoly model exhibits a unique symmetric Nash equilibrium with mixed strategies.

Pricing Optimization for Perishable Primary and Ancillary Items with Time-Dependent Inventory Drawdown

There are many industrial applications where attempts are made to sell ancillary products or services with a primary item. For instance, a warranty is often offered as an ancillary product to those who buy television sets (the primary item). This has become even more important in the airline industry where ancillary products such as baggage fees have become crucial to the financial health of the industry. Rapid depletion of available seat inventory, akin to perishable assets, necessitates careful consideration of pricing strategies to maximize revenue. It can make a big difference to revenue if certain fare classes are likely to sell out quickly. For instance, if most of the fares without seat assignment sell out earlier than those with seat assignment, the airline would forego a lot of the revenue from the ancillary item. We formulate the problem allowing for time dependence. In this paper, the question of what price to charge for the primary and ancillary products will be investigated.

Average booking curves draw exponential functions

The booking curve time series in perishable asset industries, including hotels, has been studied to manage a demand-supply condition or revenue management (RM). However, due to changing times, e.g., economy and technology, many RM practitioners have put their efforts into catching on to peoples’ booking pattern shifts, representing macroscopic changes in booking curves. We investigate macroscopic aspects of booking curves with actual sales data across six properties in the hotel and car-rental industries for two years, considering the difference in the economic environment characterized before and during the COVID-19 epidemic. We explain a new cross-industry and cross-economic-environment universal statistical law: average booking curves draw exponential functions (the ABCDEF law). We provide a basis for the ABCDEF law from three perspectives; data validation, modeling in the statistical physics framework, and empirical justification for the causality of the model. The ABCDEF law derives informative statistics to quantitatively measure peoples’ buying behavior even in time or society changes, which is expected to contribute to management in various industries.

Vessel scheduling in liner shipping: Modeling transport of perishable assets

International seaborne containerized trade significantly increased over the last years. Some assets transported in a containerized form by vessels are perishable in nature. Perishable assets deteriorate due to certain operational and environmental factors. This paper proposes a novel mixed integer non-linear mathematical model for the vessel scheduling problem in a liner shipping route with perishable assets, which explicitly captures decay of perishable assets on board the vessels. The objective aims to minimize the total route service cost, including the asset decay cost. The original non-linear mathematical model is linearized using a set of piecewise linear secant approximations. CPLEX is used to solve the linearized mathematical model. Numerical experiments are conducted for the French Asia Line 1 route, served by CMA CGM liner shipping company, to evaluate performance of the suggested solution approach and reveal some important managerial insights. Results demonstrate that the developed mathematical model can serve as an effective planning tool for liner shipping companies in designing efficient vessel schedules and reducing decay of perishable assets on board the vessels.

EM Algorithm and Stochastic Control in Economics

Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new algorithm sequentially updates the control policies in each time period using Monte Carlo simulation in a forward-backward manner; in other words, the algorithm goes forward in simulation and backward in optimization in each iteration. Similar to the EM algorithm, the EM-C algorithm has the monotonicity of performance improvement in each iteration, leading to good convergence properties. We demonstrate the effectiveness of the algorithm by solving stochastic control problems in the monopoly pricing of perishable assets and in the study of real business cycle.

An integrated fuzzy-stochastic model for revenue management

Revenue management aims at improving the performance of an organization by selling the right product/service to the right customer at the right time. This task is very dependent on uncontrollable external factors. In the hospitality industry, rooms of the hotel represent perishable assets and fixed capacities at the same time. Therefore, in the case of a stochastic process for customers calling in reservations prior to a particular booking date, a common problem for hotels is to devise a policy for maximizing the total expected profit conditional on the set of bookings. We propose a fuzzy model for the hotel revenue management under an uncertain and vague environment. Fuzziness of objective and constraint functions have been incorporated into a stochastic booking model considering multiple-day stays to show the effect of uncertainty on the optimal demand. By changing the relaxation parameters of the objective function, we have found a set of optimal solutions with, in most of the cases, a value of the objective function equal to the optimal solution of the stochastic model, providing several alternative optimal room allocations.

Dynamic Pricing of Perishable Assets Under Competition

We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting p...

여행상품 구매조건의 선호가치에 따른 최적 여행상품 가격설계 연구

Tour products have been recognized as a perishable asset. For tour operation companies (TOCs), improving profitability is a core decision problem for their business. Since package tour products, typical products of TOCs, are perishable after the tour was departed, TOCs have been tried to increase their sales before the departure date with various marketing strategies including price discounts. The pricing problem for perishable assets have been studied in Revenue Management for a long time. However, it is hard to find a research on pricing decisions for tour products. In this paper, we focus on a pricing problem for tour products. In particular, we will consider the pricing scheme with customer preference values on purchasing conditions. With conjoint analysis, we can use the part-worth value as a preference value for each level of purchasing conditions. To construct various discount prices, we use an enumeration method and suggest a mathematical optimization model. With experimental analysis for a sample tour package, we will show that our pricing process is very helpful for designing customer-oriented pricing decision.

Newsvendor Selling to Loss-Averse Consumers with Stochastic Reference Points

We study a newsvendor who sells a perishable asset over repeated periods to consumers with a given consumption valuation for the product. The market size in each period is random, following a stationary distribution. Consumers are loss averse with stochastic reference points that represent their beliefs about possible price and product availability. Given the distribution of reference points, they choose purchase plans to maximize their expected total utility, including gain-loss utility, before visiting the store, and follow the plans in the store. In anticipation of consumers' purchase plans, in each period, before demand uncertainty resolves, the firm chooses an initial order quantity. After the uncertainty resolves, the firm chooses a contingent price depending on the demand realization, with the option of clearing inventory by charging a sale price, and otherwise, posting a full price. Over repeated periods, the interaction of the firm’s operational decisions about ordering and contingent pricing and the consumers' purchase actions results in a distribution of reference points, and, in equilibrium, this distribution is consistent with consumers' beliefs. Under this framework of endogenized reference points, we fully characterize the firm’s optimal inventory and contingent pricing policies. We identify conditions under which the firm’s expected price and profit are increasing in the consumer loss aversion level. We also show that the firm can prefer demand variability over no-demand uncertainty. We obtain a set of insights into how consumers' loss aversion affects the firm’s optimal operational policies that are in stark contrast to those obtained in classic newsvendor models. As examples, the optimal full price increases in the initial order quantity; and the optimal full price decreases, while the optimal sales frequency increases, in the procurement cost.

Newsvendor Selling to Loss Averse Consumers with Stochastic Reference Points

Motivated by the supermarket practice of marking down perishable products daily, we study a newsvendor who sells a perishable asset over repeated periods to consumers with a given consumption valuation for the product. The market size in each period is random, following a stationary distribution. Consumers are loss averse with stochastic reference points that represent their beliefs about possible price and product availability. Given the distribution of reference points, they choose purchase plans to maximize their expected total utility, including gain-loss utility, before visiting the store and follow the plans in the store. In anticipation of consumers' purchase plans, in each period, before demand uncertainty resolves, the firm chooses an initial order quantity. After the uncertainty resolves, the firm chooses a contingent price depending on the demand realization, with the option of clearing inventory by charging a sale price, and otherwise, posting a full price. Over repeated periods, the interaction of the firm's operational decisions about ordering and contingent pricing and the consumers' purchase actions results in a distribution of reference points, and, in equilibrium, this distribution is consistent with consumers' beliefs. We fully characterize the firm's optimal inventory and contingent pricing policies. We identify conditions under which the firm's expected price and profit can be increasing in the consumer loss aversion level. We also show that the firm can prefer demand variability over no-demand uncertainty. We obtain a set of insights into how consumers' loss aversion affects the firm's optimal operational policies that are in stark contrast to those obtained in classic newsvendor models. As examples, the optimal full price increases in the initial order quantity, and the optimal full price decreases while the optimal sales frequency increases in the procurement cost.

A flexible model for the pricing of perishable assets

We present a flexible and versatile model which addresses the problem of assigning optimal prices to assets whose value becomes zero after a fixed expiry date. (Such assets include the important example of seats on airline flights.) Our model is broad in scope, in particular encompassing the ability to deal with arrivals of customers in groups. It is highly adaptable and can be adjusted to deal with a very extensive set of circumstances.Our approach to the problem is based on elementary and intuitively appealing ideas. We model the arrival of customers (or groups of customers) according to an inhomogeneous Poisson process. We incorporate into the model time dependent price sensitivity (which may also be described as “time dependent elasticity of demand”). In this setting the solution to the asset pricing problem is achieved by setting up coupled systems of differential equations which are readily amenable to numerical solution via (for instance) a vectorised Runge–Kutta procedure. An attractive feature of our approach is that it unifies the treatment of discrete and continuous prices for the assets.

Pricing and inventory policies under price-tracking behaviour

We develop a demand rate model for the optimisation of retail sales of perishable assets when consumers track prices over the sales horizon. We model this behaviour within an aggregate demand framework, solving the initial joint inventory and pricing problem when the demand is deterministic as well as stochastic. We solve the problem numerically and discuss the specific results as well as the characteristics of the optimal price and inventory levels. We illustrate when firms are likely to choose a penetration vs. skimming pricing policy and describe solution updating procedure as actual sales occur.

The newsvendor problem with an in-season price adjustment

Consider a retailer stocking a seasonal item facing a stochastic demand where information about the demand becomes more accurate as the selling season progresses. The retailer places orders before the start of the season and in-season reorders are not possible. This article extends the classical newsvendor model by allowing the retailer to make an in-season price adjustment after conducting a review and using the realized demand to obtain an accurate estimate of the remaining demand. Our results include answers to the following questions. What price should the retailer choose? How much should the retailer have ordered at the start of the season given the option of adjusting prices in-season? This model was motivated by a problem in car rental revenue management and has applications in perishable assets revenue management (PARM), where price adjustments are needed towards the end of the selling season.

On pricing of perishable assets with menu costs

We consider dynamic pricing of perishable assets in the presence of price-sensitive renewal demand processes. Unlike the existing works in the literature, we explicitly incorporate non-negligible price change costs which reflects the revenue management practice more realistically. These costs are also known as menu costs in the economic literature. The objective is to maximize the discounted expected profit for an initial inventory of Q items by determining the selling prices dynamically. We employ a dynamic programming approach and formulate a model that captures the price–demand relationship. We establish some theoretical results on the properties of the problem at hand. Specifically, we establish the sufficient conditions under which the within-period profit is concave in the selling price and in the remaining shelf life and, furthermore, show the structure of the myopically and asymptotically optimal pricing policy. In a numerical study, we investigate the impact of various system parameters and, in particular, the existence of menu costs, on pricing decisions. We observe that ignoring menu costs may be significantly misleading for the implementation of revenue management. We also propose four implementable policy heuristics and examine their performances. Our findings support some results previously obtained in settings with continuous pricing and negligible price change costs; and, contradict some others.

Dynamic Pricing of Perishable Assets Under Competition

We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice, and then leave immediately with some likelihood of no purchase. The purchase likelihood depends on the time of purchase, product attributes, and current prices. The demand structure includes time-variant linear and multinomial logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of shadow prices measuring capacity externalities that firms exert on each other: equilibrium prices can be solved from a one-shot price competition game under the current-time demand structure, taking into account capacity externalities through the time-invariant shadow prices. The former reflects the transient demand side at every moment, and the latter captures the aggregate supply constraints over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large. This paper was accepted by Yossi Aviv, operations management.

Dynamic Pricing of Perishable Assets under Competition

We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice and then leave immediately with some likelihood of no-purchase. The purchase likelihood depends on the time of purchase, the product attributes and the current prices. The demand structure includes time-variant linear and MultiNomial Logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of shadow prices measuring capacity externalities that firms exert on each other: equilibrium prices can be resolved from a one-shot price competition game under the current-time demand structure, taking into account capacity externalities through the time-invariant shadow prices. The former reflects the transient demand side at every moment and the latter captures the aggregate supply constraint over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide pre-committed and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large.

개인수요의 상.하 이동을 고려한 좌석할당모형 개발

최근 수입경영은 항공운송산업뿐만 아니라 이와 유사한 일회성상품(perishable assets)의 성격을 갖는 산업 전 부문에서 널리 활용되고 있다. 본 논문은 항공산업에서 활용되고 있는 정태적 좌석할당모형을 기반으로 시점마다 무작위로 발생하는 고 저가의 항공수요가 각 요금수준별 사전 할당된 좌석의 유무에 상관없이 필요에 따라 상하 이동을 하며 고가수요가 저가의 좌석을 선택할 수도, 저가의 수요가 고가의 좌석을 구입할 수도 있다는 전제로 기존의 한 방향 좌석할당모형과 대별되는 양방향 좌석할당모형을 개발한다. 또한 본 모형을 기반으로 항공사 수입이 기존의 한 방향 수요이동을 고려한 모형과 비교하여 수입을 더욱 극대화 시킬 수 있다는 사실을 실증한다. 실증방법은 C-프로그램을 활용하여, 수요의 가격수준을 국내 K항공사에서 한국지역 판매를 위해 활용되고 있는 4가지 운임으로 구분하고, 수요분포는 최대값과 최소값을 발생확률에 따라 난수를 이용하게 되며, 요금수준은 한국지역의 요금수준분포를 참조하여 고가를 100, 90, 85, 80 수준으로 하여 모의실험을 시행한다. 그 결과 고가의 수요에 지나친 좌석할당을 시행하는 경우를 제외하고는 수요의 양방향을 고려한 항공좌석할당 방법이 높은 수준의 수입을 창출할 수 있다는 결론을 얻게 된다. The concepts of static seat allocation model has been used widely in the air transportation industry, and proven as a good concepts for managing perishable assets. The paper analyzed, in realistic environment, the volume of Accept Demand and Reject Demand through several times' simulation experiments at each fare level by using C-Program analyzing process applied to upward and downward models of demand, to analyze the change of fare level when upward and downward shifts of fare levels' demand happen at once. As a consequence, I concluded that the revenue of the case to consider the both shifts of demand at each fare level is bigger than that of the case to consider the single shift of demand at each fare level, except the case to downsize the seat allotment at very low price when supply is bigger than demand, with developing a general model concerned with plural fare levels.

OPTIMAL CONSTANT PRICE POLICY FOR PERISHABLE ASSET YIELD MANAGEMENT

Perishable asset yield management has wide applications in airlines seat inventory control, rental car and hotel room reservations. In contrast to the research on optimal dynamic pricing that has taken place in the past decade, we examine the practical merit of a constant price policy. This means a single price is applied to an item throughout the sales cycle.. We present procedures to identify the optimal constant price for two different applications. In the first, there is full dilution and in the second there is no dilution (dilution is when a customer that is willing to pay a high price is satisfied at a low price). We also propose a more flexible constant price policy (hybrid method) in which prices can be changed at discrete intervals and we present a method for its optimal policy. Furthermore, this hybrid method is capable of incorporating the costs associated with price change explicitly.

Optimisation of perishable asset revenue management problems that allow prices as decision variables

This paper addresses a new slant to a problem which is general to the service industries - perishable asset revenue management. Traditional approaches have assumed that prices are fixed and solved for the optimal allocation quantities. Our approach recognises that prices affect demand and should therefore be included as decision variables to be optimised. We solve three different types of problems: a) up to n price classes, distinct asset control mechanism, and no diversion, b) up to three price classes, nested asset control mechanism, and no diversion, c) up to three price classes, nested asset control mechanism, and diversion. Analytical results are provided in most cases and examples illustrate the results as well as the time required to solve these complex problems. Finally we look at the trade-off involved between computational time and expected contribution when using heuristic decisions obtained from less realistic assumptions relative to the true optimal decisions. On average, the suboptimality ranged from 0.84% to 8.3% with a corresponding decrease in computing time required on the order of several minutes. Some trends are presented to help determine a priori which type of problems would tend to benefit most from the more accurate formulation. This should help managers decide when it is worth the extra computing time to come up with the true optimal solution.

Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices

Consider a continuous-time inventory problem in which a retailer sets the price on a fixed number of a perishable asset that must be sold prior to the time at which it perishes. The retailer can dynamically adjust the price between any of a finite number of allowable prices. Demand for the product is Poisson with an intensity that is inversely related to the price. The optimal policy is piecewise-constant. The maximum expected revenue is nondecreasing and concave in both the remaining inventory and the time-to-go. For a given inventory level the optimal price declines as the time at which the products perish approaches. At any given time the optimal price is nonincreasing in the number of items remaining unsold. These results are extended to (i) the case in which the prices and corresponding demand intensities depend on the time-to-go; and (ii) the case in which the retailer can restock to meet demand at a unit cost after the initial inventory has been sold.