INTRODUCTION

The successful application of revenue management in the airline and hotel industries, as well as in other areas of the tourism industry, is well documented (see, eg Baker and Collier, 1999; Ingold et al., 2000). The success, which the firms in these industries derive, stems from their individual efforts to optimally allocate their perishable inventories among different market segments. One would also want to know if they can derive additional benefit by cooperating to improve the allocation of their individual inventories. This is a supply chain management problem.

In a supply chain, different organisations enter into contractual relationships to supply services, products or goods, and the performance of each organisation depends on that of other organisations in the chain. This concept of a supply chain is also applicable to the tourism product. Tourism can be described as an amalgam of different interests, activities, stakeholders and businesses that are functionally linked together to form a distinct supply chain (see Page, 2003). However, unlike manufacturing where consumption of the product follows its production, in a tourism supply chain, production and consumption take place simultaneously at each link in the supply chain.

The tourism product is not a physical item, but it comprises several different services provided by many different suppliers at different points in the tourism supply chain. These suppliers consist of tourism retailers, tourism wholesalers such as tour operators, airlines, hotels, restaurants, visitor attractions and car hire companies (see Page, 2003). Tourists can purchase packages from an intermediary, such as a tour operator or a tourism retailer, which consist of inputs from at least one of these suppliers. Alternatively, they can make their own holiday arrangements by selecting the individual items of the packages themselves. Consumption of these services provides the tourist with a set of experiences and the satisfaction gained is determined by each of these individual experiences. Therefore, an unsatisfactory experience at any point in the chain can mean that the tourist will not consume the product again or recommend it to others.

Normally, the different suppliers of tourism services make independent decisions about pricing and the allocation of their resources among the different market segments. The interdependence among the members of the chain, however, means that decisions made by one member can have an impact on the revenue earned by other members of the chain. This therefore highlights the need for cooperation among members of the supply chain. This cooperation encompasses the three broad areas of market segmentation and product pricing, performance incentives, and demand forecasting. It is therefore necessary to understand the impact of these on the coordination of the tourism supply chain.

Different suppliers of tourism services use different criteria for defining the market segments in which they sell their products, although they may serve the same set of customers; therefore, two airline customers, who purchase identical airline tickets, may purchase different types of hotel rooms. It follows that not taking the market segmentation criteria of other partners into consideration can lead to displacement of customers who will make a greater contribution to the revenue of the supply chain. For example, suppose there are two customers, A and B, each of whom wants to purchase an airline seat and a hotel room. Suppose airline seats are plentiful, while there is only one hotel room available. Suppose also that each customer is willing to pay $400 for an airline seat, but customer A will pay $300 for the hotel room, while customer B will pay $200 for it. Then, if the seat is sold to customer A, the revenue of the chain will increase by $700, while if it is sold to customer B, it will increase by $600. Thus the chain will lose $100 of value by selling the seat to customer B. This scenario highlights how it is possible for the market segmentation decisions of one partner to lead to losses in revenue, when the capacity of one partner is scarce while that of another is plentiful. However, such losses can also occur if both partners have no excess capacities or if both have excess capacities. In all cases, the losses stem from a lack of coordination of pricing decisions between the partners.

Displacement can also occur as a result of the use of inconsistent or conflicting performance incentives by members of the supply chain. Suppose, for example, a tourism retailer rewards its agents on the basis of the number of customers booked, whereas a hotel rewards its agents on the basis of revenue generated. The reservations agent for the retailer will accept bookings on a first-come first-served basis, which can lead to displacement of more valuable hotel customers.

Factors affecting supply and demand at one link in the chain can affect demand at another link in the chain also and therefore these factors should be considered when making demand forecasts. For example, an airline, which forecasts demand for seats without taking into consideration the price of accommodation, may have excess inventory over the planning period, if there is an increase in the price of accommodation. Similarly, a hotel, which neglects transportation capacity in its forecasts, can have an excess inventory of room-nights. In addition, demand forecasts by a hotel that are based on reservations made by an intermediary, such as a tourism retailer, will be inaccurate if they ignore customers who accept upgrades or downgrades, those who decline offers made or turn away because their requests cannot be honoured, and those who defer bookings. One way of addressing these problems is for firms to share demand and inventory data, which will lead to better forecasts.

In general, there are many situations in which the actions of one partner in the supply chain can result in losses of revenue for another partner. It is being suggested here that, if members of the supply chain cooperate to ensure that resources are used where the opportunity cost is highest, it can result in an increase in revenue for the chain. However, in order to cooperate in this way, a partner will expect to derive at least as much benefit as if it acted on its own, plus an additional amount to account for the opportunity cost of the additional resources required for cooperating. This consideration raises the problem of sharing the increased revenue which is another issue that must be dealt with by the supply chain partners. The problem is to determine a mechanism for coordinating the supply chain which will ensure that a partner is better off, as a result of participating in the coordination process, than when it acts on its own.

This paper introduces a methodology, which utilises bid prices, for coordinating a tourism supply chain. The methodology is used to determine the extent to which a hotel can derive additional revenue from being part of a coordinated supply chain channel involving a hotel and a retailer of hotel services. Simulation is used to compare the hotel's revenue from the coordinated channel with what it receives when the channel is not coordinated. The results indicate that the proposed coordination method can lead to improved revenue for the hotel under certain conditions.

The rest of the paper is organised as follows. A review of contracts for coordinating decentralised supply chains is presented in the next section along with a review of the bid price control methodology. This is followed by a section in which two linear programs (LP) for generating the bid prices are discussed. A discrete event simulation model is presented in the following section along with a discussion of the simulation results. A summary of the paper and discussion of the results are given in the final section.

COORDINATING THE SUPPLY CHAIN

The background to this research encompasses the areas of revenue management and supply chain management. Much work has been done on the application of revenue management in the tourism industry (see, eg Ingold et al., 2000; Harewood, 2006). The work in revenue management has recently been extended to consider alliances of firms in the same industry. The focus of alliance revenue management is on maximising revenue across the alliance network (Vinod, 2005). There are similarities between the alliance revenue management problem and the supply chain management problem, which concerns a number of organisations working together to add value to a product or service and deliver it to the customer (Yilmaz and Bitici, 2005).

The interdependence among the members of the supply chain makes coordination within the chain necessary, and a coordination mechanism is therefore required for managing this interdependence. The coordination mechanism should provide a set of rules for maximising profit and ensuring the fair sharing of benefits and costs among the partners in the supply chain. Xu and Beamon (2006) suggest a methodology, which is based on transactions cost theory, for selecting an appropriate coordination mechanism. This methodology requires identification of all the costs associated with a particular mechanism and then choosing that with the smallest cost.

The tourism supply chain is characterised by a decentralised decision-making style with a high level of resource sharing at the operational level. Tour operators and airlines are the dominant partners in the tourism supply chain, thus leading to an asymmetric relationship with other members of the chain; however, the relationship between partners in the supply chain is naturally cooperative. No firm in the chain exercises a high level of control over any other firm, which favours low coordination cost, but can result in high-risk cost. Uncertainty in the tourism industry results from factors affecting demand for tourism, such as the weather and exchange rates. It can also result from the unreliability of a partner, such as a tour operator who diverts tourists to a competing destination, or a hotel which cannot honour its commitments because it has overbooked. The industry makes great use of information technology, especially for reservations systems, and retailers usually have access to the reservations systems of suppliers. The high usage of information technology is conducive to low coordination and risk costs.

Supply chain contracts

Much of the literature on the coordination of decentralised supply chains concerns two partners, such as a supplier and a retailer, with the supplier providing the retailer with a single product for eventual sale to the consumer. These supply chain contracts can be classified as either demand-dependent pricing schemes or quantity-dependent pricing schemes. Demand-dependent pricing contracts include revenue sharing, buy-backs, quantity flexibility contracts and sales rebate contracts. Quantity-dependent pricing contracts include two-part tariffs and quantity discounts.

With a revenue sharing contract, before any transactions are performed the retailer agrees to pay the supplier a wholesale price and a fixed percentage of revenue. The total revenue generated over a single selling period is determined by the number of items the retailer purchases from the supplier and the retail price. The retailer chooses the price and the quantity that maximise the supply chain's profit. A partner's share of profit may depend on the relative strengths of the partners' bargaining positions, but there will always be some minimum desirable level of profit which will be required for a partner to agree to the contract (Cachon and Lariviere, 2005).

The effectiveness of revenue sharing is limited in a number of situations (Cachon and Lariviere, 2005). When demand depends on the retailer's effort, it might not be possible to coordinate the supply chain with a revenue sharing contract if the effort is costly, if it is not verifiable or if it is costly to verify. Also, if the cost of ensuring that revenues are being shared equitably is high, it can negate any benefits from revenue sharing. When the retailer stocks substitute products, or products that are complements from other suppliers, it can also negate the benefits of revenue sharing for the supplier.

With a buy-back contract, the supplier charges a wholesale price per unit and pays the retailer a fixed price for each unit not sold (Pasternack, 1985). Buy-back contracts are equivalent to revenue sharing contracts (Cachon and Lariviere, 2005). Buy-back contracts coordinate the supply chain when the retail price is fixed. These contracts have a number of weaknesses (Taylor, 2002; Krishnan et al., 2004; Cachon and Lariviere, 2005). Returns can provide a disincentive to retailer effort, because they reward the retailer for having unsold inventory. Buy-backs adversely affect supply chain profits and the profits decrease as the buy-back rate increases. Also, returns may cause the retailer to stock more than is required. When the retailer stocks items provided by more than one supplier, a return policy can cause the retailer to put greater effort into selling the products of suppliers who offer more generous buy-back terms. Although buy-backs alone cannot coordinate the channel, coupling buy-backs with another mechanism can provide coordination.

Under the quantity flexibility contract with a fixed retail price, the retailer purchases a given quantity at a fixed wholesale price per unit at the start of the period and may return up to some maximum amount of the quantity at the end of the period for a full refund. Any quantity that is not returned can be salvaged at a fixed price per unit. A quantity flexibility contract can also coordinate a supply chain with a fixed retail price (Tsay and Lovejoy, 1999). However, quantity flexibility contracts can reduce the retailer's effort (Krishnan et al., 2004).

With a sales rebate contract, the supplier charges a fixed wholesale price for each unit purchased by the retailer but gives the retailer a rebate for every unit sold above a threshold quantity (Krishnan et al., 2004; Taylor, 2002). The retailer earns a profit only if the quantity purchased is greater than the threshold. The sales rebate contract can coordinate the supply chain by properly specifying the target rebate terms (Cachon and Lariviere, 2005). The sales rebate contract rewards the retailer for achieving a high volume of sales. It is possible that rebates may provide a stronger incentive for retailer sales effort than buy-backs in many situations (Taylor, 2002).

With a two-part tariff, the supplier charges a wholesale price per unit and a fixed fee. In the case of a supply chain with a single retailer, the two-part tariff is equivalent to a revenue sharing contract (Cachon and Lariviere, 2005; Krishnan et al., 2004).

In the case of a quantity discount contract, the price paid by the retailer is a decreasing function of the quantity purchased. The quantity discount contract also coordinates the supply chain with profit being allocated arbitrarily (Cachon and Lariviere, 2005; Krishnan et al., 2004). Under a quantity discount contract, the supplier's profit is not affected by realised demand.

The focus of this work is on the supply chain channel involving a supplier and a retailer of tourism services. For the sake of simplification, assume that the supplier is a hotel and the retailer is a firm that sells hotel services. For a number of reasons, the contracts reviewed here will not be suitable for a supply chain channel involving these two parties. One reason is that the assumption of a single retail price and a single market segment will be inappropriate. Hotels offer different types of rooms for sale, and there is a natural correspondence between room type and market segment. In addition, according to how a type of room is packaged, a hotel may offer it for sale in different market segments, at the same time. The assumption of a single product comprising an input from a single supplier is also no longer valid. A retailer may sell products from more than one hotel, or a product it offers for sale may comprise inputs from more than one supplier. In the latter case, for example, the retailer may offer for sale a package consisting of a hotel room, and a visit to a tourist attraction. In addition, hotels may offer their products for sale through more than one retailer, who may or may not compete. Normally, the wholesale price of the item is negotiated between the supplier and the retailer, but the retailer sets the retail price and chooses the quantity. The problem is complicated further when market segmentation decisions are made independently by the supplier and the retailer. In such cases, an allocation decision that is optimal for one will not necessarily be optimal for the other. Retailer effort, especially in the form of marketing, also plays a key role in the sale of tourism products. This effort requires the utilisation of some of the retailer's own resources. The effort may be directed at more than one product, and it may therefore be spread over more than one input from the same supplier or from different suppliers.

Bid price controls

In order for the members of the tourism supply chain to cooperate, the profit that each will earn as a result of cooperating must exceed what it can earn on its own. This can be achieved by selecting a coordination mechanism which maximises the profit of the supply chain and which at the same time ensures that each partner is better off, as a result of participating in the coordinated channel. The mechanism should be suitable for a decentralised supply chain with a high level of resource sharing, a low level of control, and should ensure a fair sharing of risk and reward. One way to achieve these goals is through an efficient pricing mechanism.

Economic efficiency is the fundamental criterion used to judge a pricing structure. An efficient or optimal price is one that causes producers to produce products in the exact mix and in the exact quantities demanded by consumers. Efficiency requires that resources be allocated to consumers who are willing to pay the most for them. Following the rules for efficiency allows the partners in the supply chain to maximise their profits. Therefore, the price charged for a tourism product should be equal to the opportunity cost of producing it, in order to make the most efficient use of the resources utilised. The opportunity cost of a product is equal to the sum of the opportunity costs of the resources used in producing it. By this reasoning, the profits of the tourism supply chain can be maximised if each partner in the chain sells its resources in the market segments for which they have the highest values. Implementing an efficient pricing structure is, however, not simple.

Bid pricing has been suggested as a means of ensuring that resources are sold in the market segments for which they have the greatest values. Bid pricing originated in revenue management and is a method that is used for controlling the sale of inventory. By this form of control, threshold values, called bid prices, are set for the item and it is sold only if the price offered exceeds the bid price (McGill and van Ryzin, 1999; Talluri and van Ryzin, 2005). Therefore, the bid price of a resource can be viewed as a measure of its opportunity cost. Bid price controls allow the flexibility of detailed control by product type, market segment and point of sale, without the need for sharing excessive amounts of information between partners (Vinod, 2005). The total bid price for a product is the sum of the bid prices of the resources comprising the product. If the price of the product is greater than the total bid price, then the product is sold, and it is not sold, otherwise. Hence a product is determined to be available if

where P_it is the price of product i on day t, S_i is the set of resources making up product i, and _jt is the bid price for resource j on day t.

The bid price for a resource at a given point in time depends on demand over the rest of the planning period, the available amount of the resource and the time to go until the resource spoils. If a new request is accepted or a cancellation occurs, the change in bid price for resource j will be (see Vinod, 2005).

where z_jt denotes the quantity of resource j demanded on day t.

Demand for a product that requires resource j may also result in demand for resources from other inventories, including those of other suppliers in the tourism supply chain; therefore, demand for resource j can also affect the bid prices for other resources which make up the product of which resource j is a part. The change in the bid price for resource k as a result of a change in the demand for resource j is given by

If resources k and j are complements, then z_kt/z_jt>0, and if they are substitutes then z_kt/z_jt<0. If resource i is plentiful, then _kt/z_kt=0. Therefore changes in the quantity of resource j demanded will not affect the bid price for resource k.

GENERATING THE BID PRICES

Several methods can be used for generating the bid prices. One approach, which has produced good results in revenue management applications, uses the dual prices for the resources constraint from the LP model (see Talluri and van Ryzin, 1998, Baker and Collier, 1999). In this regard, consider the following LP (see Weatherford, 1995; Harewood, 2006).

Model A

where r_it is the hotel's marginal revenue for package i on arrival day t; x_it the number of packages of type i sold for arrival day t; a_ijt the amount of resource j required by one unit of package i on day t; d_it the number of packages of type i demanded for arrival day t; l_i the length of stay for package i; b_jk the amount of resource j available on day k; I the number of packages available and T the length of the planning period.

The objective function (1) maximises the total revenue from the sale of packages over the planning period. Constraint (2) ensures that the amount of each resource used in producing the packages does not exceed what is available on each day of the planning period. Constraint (3) ensures that the number of packages of type i, sold on day t, does not exceed demand for that day.

The previous model assumes that the partner utilises only its own stock of resources to produce the output, which will only be true for the supplier. The retailer may use its own stock of resources along with inputs from the supplier. The retailer therefore has to decide how much of each input to purchase. A slight modification to Model A gives Model B, which is the retailer's LP model.

Model B

where the additional notation used is defined as follows: R_it is the retailer's marginal revenue for package i on day t; c_jt the price of one unit of resource j obtained from the supplier for arrival day t; z_jk the amount of resource j obtained from the supplier for arrival day k.

This model is based on the overbooking models of Harewood (2006) and Baker and Collier (1999). The objective function (5) maximises the total revenue over the planning period, less the total cost of resources purchased. Constraint (6) ensures that the total amount of resource j, which is utilised in all of the packages sold for day k, does not exceed what is available on day k. Note that b_jk=0, if the supplier is the only source of resource j. With an efficient pricing policy, c_jt will be equal to the opportunity cost of resource j on day t.

When the supplier supplies inputs to more than one retailer and the demand distributions are the same for the markets served by the retailers, then this can be treated as a problem with one supplier and one retailer. If the demand distributions are different for the markets served by different retailers, then each retailer can be used as another characteristic by which to define market segments. The problem can therefore be still treated as a single retailer problem, but with more market segments.

If there is more than one competing supplier supplying substitute inputs at the same price, this will be equivalent to the problem with a single supplier. If, on the other hand, there is more than one supplier who supplies substitute inputs at different prices, then the retailer will want to know how much to purchase from each supplier. The objective function (5) and constraint (6) will become

respectively, where H is the number of suppliers, z_hjt the quantity of input j purchased from supplier h on day t and c_hjt the associated price per unit. If there is a limit on the amount of resource j that can be obtained from each supplier, then the following additional constraints should also be included:

where _hjt is the limit on the amount of resource j that can be obtained from supplier h on day t.

Data and model solution

Data that were obtained from an all-inclusive hotel is used to illustrate the performance of the method. For this purpose, the revenue that the hotel will receive from a coordinated supply chain channel is compared with what it will obtain when the channel is not coordinated.

All services such as meals, entertainment and recreation are equally available to all guests of the hotel, since it is all-inclusive. The hotel also sells certain types of packages that may contain particular services that are not available to all guests. For example, it offers a honeymoon package, which includes features such as pictures and flowers, that is available only to honeymooning couples. Such packages do not differ greatly, in terms of the resources utilised, from the regular packages which are available to all guests. Therefore, in order to simplify the simulation, it is assumed that, except for the type of room, all packages utilise the same resources. The hotel is therefore faced with the problem of allocating its inventory of room-nights among the different market segments in order to maximise its revenue over the planning period. The hotel is assumed to face a demand for packages.

For convenience, it is assumed that the hotel does not engage in the retail sale of packages. Therefore, the recorded prices are assumed to be those paid by the retailer to the hotel; these are the values used for the r_it in Model A. The retailer's prices are unknown and it is therefore assumed that the retailer uses a mark-up pricing policy. A 10 per cent retailer mark-up is used for all packages; therefore, the retailer's marginal revenue for package i on day t is equal to 1.1r_it.

Under an efficient pricing policy, c_jt will be equal to the opportunity cost of resource j on day t. In practice, the opportunity costs of the resources may not be known. In such circumstances, one will want to use values which are good proxies for the opportunity costs. One can use rates published by the supplier, such as the rack rates, or forecasts based on observed prices. Another possibility is to replace the c_jt by the appropriate dual prices from Model A. The dual prices are particularly useful for conveying information on the demand intensities for the resources employed.

Different values are used for the c_jt when solving Model B. One set of solutions uses the dual prices from constraint (2) as proxies for the opportunity costs. The dual prices will be zero for all plentiful resources; however, the hotel will quote a positive price for such resources. Normally, the price quoted will be at least equal to the variable cost of producing one more unit of the item. For example, if the resource is a room, then c_jt will at least be equal to the variable cost of producing an additional room-night. Therefore, a scalar multiple of the rack rate is used for all resources for which the dual prices are zero, and the dual prices are used for all other resources. This gives

where _jt is the dual price from constraint (2) in Model A, w_jt is the rack rate for resource j on day t and a=0 for _jt>0, and a(0, 1] otherwise. For these solutions the values used for a increase in increments of 0.1 from 0 to 1, and the same scalar multiple is used to adjust all rack rates used in a given solution. Another set of solutions to Model B utilises a scalar multiple of the rack rates for all resources. This gives

The values used for a, in this case, increase in increments of 0.1 from 0.1 to 1. Again the same scalar is used to adjust all rack rates used in a given solution.

There are no records of booking requests that are denied or of offers made which are declined by customers. Therefore, the observed bookings for the packages are used to represent the demand for the packages and this gives the values that are used for the d_it. It is assumed that the hotel and the retailer face the same demand; thus d_it is the same for both.

Data for the b_jk in constraint (2) in Model A are obtained from the hotel. Initially, b_jk is equal to the maximum number of rooms of type j available at the start of the planning period. In the case of constraint (6) in Model B, b_jk=0, because it is assumed that the retailer has no rooms of its own.

SIMULATION MODEL AND RESULTS

Discrete event simulation is used to compare the hotel's revenue from the coordinated channel with the revenue it will obtain when operating in a supply chain that is not coordinated. A decentralised supply chain is assumed. It is assumed that the retailer uses the bid prices obtained from Model B to determine whether to accept or reject a request. If the retailer accepts a request, then the request is passed on to the hotel, which uses bid prices obtained from Model A to determine whether to accept or reject the request. Only requests accepted by the hotel lead to an increase in revenue for the hotel and the retailer. The assumption of independent acceptance and rejection decisions by the hotel and the retailer is consistent with the assumption of a decentralised supply chain. The same bid prices are used for each day of the planning period.

It has been shown that the use of bid prices for accepting requests for bookings can lead to higher revenue, in the hotel revenue management problem, than a first-come first-served approach (see, eg Harewood, 2006). The objective here is to determine whether the use of bid prices to coordinate the tourism supply chain can lead to greater improvements in revenue for the hotel than when it acts alone. To the best knowledge of the author, this is the first time bid pricing is being used to coordinate a supply chain. Vinod (2005), however, suggests the use of bid prices for the airline alliance revenue management problem, which is similar to the tourism supply chain problem being considered here.

It is also assumed that only one request for a booking is received at a time and the time interval between requests is unknown; the demands for the different packages are independent; there are no cancellations and there is no upgrading, downgrading or overbooking. Using these assumptions, bookings are generated sequentially and independently until the end of the planning period is reached. Every time a request is received for a booking, a decision has to be made about whether or not to accept it, without knowing what type of package will be requested next and when the request will arrive. If the request is accepted, then revenue is increased by the price of the package. The simulation starts with the assumption of zero occupancy. Revenue is counted only after the first 14 days of the simulation run and continues for 14 days thereafter. Five hundred independent replications are generated. Total revenue over the planning period is calculated as the average of the 500 replications.

Hotels face a seasonal demand pattern that may vary according to such factors as the day of the week or time of the year. For example, a hotel may realise higher demand on weekends than for the other days of the week, and during the winter months than during the other months of the year. Therefore, the simulations are conducted under different assumptions about the demand intensity, in order to determine how demand intensity affects the outcomes. The demand intensity is measured as the ratio of the demand rate to physical capacity for a given stay-over night. The demand intensities are altered by multiplying the average daily demand rates by a constant. A demand intensity level of 1 is used to denote the demand intensity currently observed by the hotel. A demand intensity level of 2 is achieved by multiplying the observed demand rates for all packages by 2.

The simulation results

The hypothesis that the coordinated channel does not result in any change in revenue for the hotel was tested at the 5 per cent level of significance. The results suggest that the coordination can lead to improvements, but that the improvements depend on the demand intensity level, the method used for computing c_jt and the value used for a in the computation. The findings are illustrated by the results reported in Tables 1, 2 and 3. Table 1 shows the revenue the hotel receives when acting alone, while Tables 2 and 3 give its revenue when it belongs to the coordinated channel, relative to what it receives when it does not.

Table 1 - Standard errors and average revenue when the hotel does not belong to the coordinated channel.

Full table

Table 2 - Standard errors and hotel's revenue from coordinated channel, relative to its revenue from uncoordinated channel, when a times rack rate is substituted for zero dual prices.

Full table

Table 3 - Standard errors and hotel's revenue from coordinated channel, relative to its revenue from uncoordinated channel, when a times rack rate is used for opportunity costs.

Full table

One finding is that there are greater opportunities for increases in revenue at low demand intensity levels than at high demand intensity levels. For example, for demand intensities of 0.75, 1 and 1.25, increases greater than 15 per cent can be achieved, while increases of less than 8 per cent are achieved for a demand intensity level of 1.5, and no increases are observed at a demand intensity level of 2. A possible explanation of this is that at high demand intensity levels, demand for room-nights will exceed capacity and the high demand from high-valued market segments will lead to high bid prices. The high bid prices will reduce the probability of customers, who will make a greater contribution to revenue, being displaced, even if the channel is uncoordinated. On the other hand, when the demand intensity level is low, there is greater room for displacement of high-valued customers, when the hotel acts alone, because of the lower demand rate from these market segments.

There are a number of interesting observations concerning the impact of the method used for computing c_jt on the changes in revenue. Values of a, which are close to zero, do not yield statistically significant improvements in revenue. This is so because small values of a can result in the underestimation of the opportunity cost of an unsold room-night. For example, suppose demand for a room is less than the number of rooms available for Friday night, while it exceeds the number of rooms available for Saturday and Sunday nights. Then the dual prices for the room will be zero for Friday night and greater than zero for Saturday and Sunday nights. Suppose customer A wants a room for Friday and Saturday nights, while customer B wants one for Saturday and Sunday nights. If A arrives first, then A will get it, as long as the price offered exceeds the dual price for Saturday night. Thus customer B will be displaced for small enough values of a, and therefore, result in lower revenue for the hotel. This type of displacement will always occur for a>0, if c_jt=_jt+aw_jt is used. This particular example helps to emphasise the additional benefit that the hotel can derive from the coordination, as a result of the network characteristics of the hotel revenue management problem. The results also show that values of a that are too high can lead to reductions in revenue and that the values of a for which this happens depend on the demand intensity and the method used for computing c_jt. For example, when c_jt=_jt+aw_jt, at a demand intensity level of 1.5, improvements in revenue can be obtained for values of a between 0.3 and 0.7, but no improvements are realised for a greater than 0.7. When the demand intensity level is 2, reductions in revenue are realised for a greater than or equal to 0.7. Reductions in revenue in these situations occur because the hotel will have unsold room-nights when the values of a are too high. This outcome is especially likely at high demand intensity levels, because the high dual prices combined with the high values of a will lead to greater displacement of customers when c_jt=_jt+aw_jt. In addition, c_jt=_jt+aw_jt yields statistically significant improvements in revenue for smaller values of a than c_jt=aw_jt. This is so because c_jt=aw_jt can underestimate the opportunity cost of the hotel's scarce room-nights for small values of a. However, if the value of a is sufficiently large, it will not be possible for low valued customers, who arrive first, to displace higher valued customers who arrive later, in either case.

SUMMARY AND DISCUSSION

A bid price approach to coordinating the tourism supply chain is proposed in this paper. Under the method, the retailer and supplier use bid prices for sharing information. They also use them to independently make acceptance and rejection decisions for bookings requested. If the retailer accepts a request on the basis of its bid prices, the request is then passed on to the hotel, which then uses its own bid prices to make an acceptance decision. The proposed method possesses a number of benefits.

• The bid prices convey information about the demand distribution with respect to the market segments and the inventory on hand, over the remainder of the planning period. Their use therefore removes the need for sharing large quantities of information between partners in the supply chain.
• It can help to reduce uncertainty resulting from factors affecting demand.
• The method is suitable for a decentralised supply chain, such as the tourism supply chain, where there is a low level of monitoring and control.
• It ensures a fair sharing of benefits and costs, even in an asymmetric supply chain.
• It ensures coordination of performance incentives, through focusing on maximising revenue at each link in the supply chain.
• Its adoption is facilitated by the extensive use of information technology in the tourism industry.

A simulation was conducted so as to compare the hotel's revenue from a coordinated supply chain channel with that from an uncoordinated channel. The results show that the method proposed for coordinating the supply chain channel can yield improvements in revenue for the hotel. The extent of the improvements, however, appears to depend on the demand intensity and the method used for computing the opportunity costs of the hotel's resources.

One problem with this approach to coordinating the supply chain is determining appropriate values for the bid prices which the supplier uses for sharing information with the retailer. Use of the dual prices from the resources constraints in Model A is one choice; the principal weakness of this approach is that the dual prices are zero for all plentiful resources. In order to overcome this weakness, one can use the dual prices, with the zero values replaced by a scalar multiple of the rack rates. Another choice is to use a scalar multiple of the rack rates for all resources. Various choices for the bid prices can lead to improved revenue for the hotel; however, the extent of the improvements seems to depend on the method used for calculating the opportunity costs. The results also suggest that the greatest improvements can be obtained at low demand intensity levels and that at high demand intensity levels, revenue may remain the same or it may even fall.

The scenario used in this paper to illustrate the benefits of coordinating the tourism supply chain is not typical of the relationship between a hotel and retailer, in practice. In practice, a retailer may pass each request as it is received to the hotel, which then makes a decision about whether or not to accept it. The methodology of this paper is not relevant to this type of supply chain channel. An alternative type of arrangement is for an intermediary, such as a tour operator, to negotiate an allotment of rooms and a price for the rooms with the hotel, before the start of the season. The tour operator only pays for the rooms after the demand is realised. The tour operator uses the rooms along with other inputs to make up packages, which are then sold to customers. The tour operator alone determines the retail price of the packages. Normally, the tour operator reserves a large number of rooms, in case demand is high. However, if demand is low, it will be unable to satisfy its allotment; this will cause the hotel to have unsold room-nights, but it does not penalise the tour operator. The hotel will have similar arrangements with different tour operators. Each tour operator will be aware of the demand intensities for its allotment of room-nights but not of those for other tour operators, while the hotel will be aware of the demand intensities for all room-nights. It is therefore possible that the revenue of the supply chain can be improved by coordinating the supply channel with each tour operator. The supply chain scenario that is depicted in this paper is a simplification of this type of problem; however, it provides some insight into the benefits that can be derived. This is an area for future research.

The dominance of the foreign tour operator in the tourism supply chain is also an issue that should be addressed, because of its implications for the effectiveness of the methodology which is being proposed here. A number of authors have highlighted the consequences of this dominance for the tourism destination (see, eg Tapper, 2001). Tour operators have a lot of market power which they use to generate demand for tourism. They also exercise a lot of influence and control over this demand. They have great influence over the volume of tourism, the destinations chosen by the tourists and the facilities which are used. They are able to use their bargaining power and their dominance in the market to extract low prices from the providers of tourism services in the destinations. The overall result of the role of the foreign tour operators in determining demand and associated earnings from tourism can be large losses in revenue for the destination. Consequently, local providers of tourism services in the destination are often forced to operate with low rates of return (Curtin and Busby, 1999). Laws (2000) reports that in the case of Majorca, the forcing down of hotel rates resulted in increased numbers of tourists; however, the low room rates meant that hotels could not afford to modernise or refurbish their facilities in line with competing destinations.

Tour operators have come to realise that an exploitative relationship with the destination is not in the best interest of either, and they have therefore started to emphasise and support sustainable tourism. This new approach arises out of a need to address broader environmental, socio-economic and cultural issues in the context of sustainable tourism development (Tapper, 2001; The Tour Operators Initiative for Sustainable Tourism Development, 2003). The objective of maximising the revenue of the tourism supply chain and that of ensuring a fair distribution of risk and reward among partners in the supply chain are consistent with the economic objectives of the Tour Operators Initiative for Sustainable Development. Therefore, the methodology introduced in this paper can assist with achieving these economic objectives. This is also an area for further research.

The survival of many tourist destinations depends on air transport. Large airlines, which are owned in the tourists' country of origin, provide almost all of the transport to many of these destinations. If the routes are not profitable for the airlines, they will reduce the level of service or even withdraw it altogether, which can lead to a considerable fall in tourist arrivals. In order to avoid this outcome, some tourist destinations in the Caribbean have paid subsidies to airlines so that they will continue their services. It is possible that the methodology proposed in this paper can be applied to coordinating the channel involving hotels and airlines in order to ascertain the extent to which it can help to improve their profitability.

In an asymmetric supply chain, problems can arise with respect to sharing the increased revenue resulting from the coordinated channel. One possibility is to share it in proportion to the risk undertaken by each partner (Xu and Beamon, 2006), but it may be difficult to measure the risk undertaken by a partner. However, if the opportunity cost of a product is viewed as a measure of the risk associated with its production, then the bid prices of the resources employed can be used to account for the risk undertaken by the partners.

Intangible factors, which influence the revenue of the supply chain, such as the retailer's market power, are of special interest when sharing revenue. Such factors often result from effort utilised. Sometimes, effort can be accounted for through a resource constraint; however, it will not always be possible to account explicitly for the retailer's effort in this way. That will be the case, for example, if the retailer's effort is an integral part of its market share or if its effort is spread over more than one resource input. Nevertheless, in such cases the supplier will still benefit from the effort, as long as it results in an increase in the bid prices of the supplier's resources. Furthermore, the sharing of the increased revenue will be fair as long as each earns the opportunity cost of its resources.

One other shortcoming of the simulations is that the bid prices were not updated whenever new demand data became available. One will expect that updating the bid prices can lead to improved revenue. One will also have to decide how often to update the bid prices. They can be updated whenever a new demand occurs, but such a high frequency can be costly and will not necessarily lead to any improvements over updating them less frequently.

There are a number of other possible directions in which this work can be extended. The obvious direction is to consider a supply chain consisting of more than one supplier of each resource, and where there are competing retailers. It was assumed in solving the models that the retailer does not utilise any of its own resources; future work can relax this assumption and consider situations where the retailer utilises its own resources also. The work can also be extended to consider alliances between other types of tourism supply chain partners. Many airlines and hotels practise upgrading, downgrading and overbooking, and therefore these practices can also be considered in future work.

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