MATHEMATICAL MODELS FOR GROUP REVENUE MANAGEMENT José Guadix, Juan Larrañeta, Luis Onieva Industrial Organization and Management Department Industrial Engineering School – University of Seville Seville, Spain guadix@esi.us.es Abstract – Revenue Management is a technique focus to decision rules for maximizing profit from sale of perish- able inventory units. This paper deals with the special case of hotel revenue management, which can be solved using deterministic and stochastic mathematical programming techniques. We first describe the problem with a theoreti- cal framework that sets the revenue maximization criteria for a hotel. We consider the general case of the problem that accept independent and group guests, with a general mixed integer linear programming model that maximize the total forecasting. Finally, we made comparisons be- tween different proposed models and were found good- quality solutions in short running times. Keywords: Yield Management; Group Revenue Management; Hotels; Mathematical Models. I. INTRODUCTION Recent years have seen an increased interest in using yield management techniques to maximize profitability in capacity constrained situations. Most of the charac- teristics underlying this technique have been used be- fore in different industries. Perishable firms, such as bakers, grocers, fresh fruit sellers or theatre managers, managed demand by varying prices in time. After US Airline Deregulation Act in 1978, any airline could operate any route at any frequency with whatever fares are chose, Smith et al. (1992). Companies adopted dif- ferentiated pricing in order to be able to compete for price sensitive travellers, without giving up the revenue from their existing, full fare customers. Yield management, also referred to as revenue man- agement, is a sophisticated form of supply and demand management that balances both pricing and inventory to maximize revenue for every available unit of capacity. An increasing number of service industries have recog- nized the rapidly growing importance of yield manage- ment in their ability to increase sales, especially profit- ability. Services industries (such as airlines, hotels, rental car agencies, freight transport and broadcast advertising), have been able to market their services (seat on an air- craft, room in a hotel, rent a car, spaces on coaches or advertising time periods) as a perishable product. In this way, Yield Management can be defined as sell the right inventory unit to the right customer at the right time. For Yield Management to be applicable the ser- vice industry needs five conditions (Kimes 2000). 1. Limited capacity. Yield Management is designed for capacity-constrained services firms. The units of inventory are sold in a short time with a fixed capacity, measured by the number of rooms or the number of seats. 2. Market segmentation. Services industries make use of segmentation because these can choose between different types of customers. Arbitrary price is not al- lowed, so the service should have some characteristic that distinguish it. So the same unit of capacity can be used to deliver many different services. 3. Future demand is uncertain. Yield Management must be able to forecast the demand variability so that managers can increase the price during periods of high demand and decrease the price during periods of low demand. Services firms cannot quickly available capac- ity to available demand. 4. Perishable units of inventory. The inventory dis- tinguishes service firms from manufacturing firms. Units of inventory services industries unsold after a specific date are wasted, services cannot be stored. These characteristics decide to sell services in advance. 5. Appropriate cost and pricing structure. Many ser- vices firms present a fixed capacity cost expensive and cannot be rapidly adjusted demand. In the same way additional cost associated to an additional visitor in unused capacity is very low. The revenue management models we study in this paper include group acceptance in hotels. Therefore, in this work we modelled the customer typology as indi- vidual or group. We tested a variety of different rooms optimization algorithms, based on deterministic and stochastic programming techniques. The paper is organized as follow. In Section 2 we study the particular case where the forecasting demand is deterministic, in which groups are allowed or not. In Section 3 we formulate the problem as a stochastic model, without and with groups. That case is close to real-world situations, so the results were better. Compu- tational comparisons are described in Section 4, using linear programming and mixed integer linear program- ming problem. Finally, conclusions are drawn in Sec- tion 5. II. DETERMINISTIC MODEL Yield management has focused mainly on forecast- ing, reservation systems and optimization models. For a International Conference on Knowledge Engineering and Decision Support 375