Unconstraining demand

I devoted considerable a lot of time for problem of RM tools and constantly used term “demand” as factor in different tools, models and examples. Although, demand is uncertain in future, therefore the only way to predict it with certain probability is to apply appropriate forecasting technique or set of techniques. Before, however we can move to this part of this study, it is necessary to explain difference between constrained and unconstrained demand and ways to calculate the second type.

The reason why forecasting is not developing as fast as other topics in RM is fact that recorded demand is affected by managerial decisions and therefore it doesn’t truly reflect “real” demand. To understand the difference let’s focus on two examples. Firstly, when demand is smaller than supply, the recorded bookings and reservations reflect actual sales (assuming that price rates are correctly set). However, when demand exceed supply, after reaching limit of reservations, further information about demand are lost as customers are turned away. As most information about demand comes from reservation system, such a demand is called “constrained”, while demand in hypothetical situation when supply is limitless is called “unconstrained”. Therefore, the biggest task lays in proper unconstraining demand using following methods summed up by Guo, et. al. (2012).

1. Direct observation – track records of bookings that were accepted as well as those rejected. Rejected bookings could be caused by lack of availability or too high rates. From system point of view, distinguishing the difference is very difficult. Moreover this method has couple of important shortcomings: lack of recognition of multiple inquires from the same customer, incorrect categorization of reject by system, and fact that only small number of reservations are done by channel controlled by hotel. (Queenan et al, 2007)

2. Ignore the censored (constrained) data – even if it sound unwisely, it is unfortunately used in many unsophisticated RM systems. It can lead to following consequences: underestimated future demand, a spiral-down effect on revenue, insufficient number of rooms protected for high-fare customers. (Saleh, 1997)

3. Imputation methods – are used when unconstrained data is incomplete. It is possible to fill in missing data with plausible values, and those values will be treated as unconstrained demand. The most popular mechanisms of calculating missing data are: mean, median or percentile imputation methods.

4. Statistical methodseven if statistical methods are said to be most accurate and became hotspot method in last years, they didn’t achieve much attention in hotel industry (compare to airlines). However, following studies adjusted some techniques used in airlines to hotels.

a) The first statistical method described by Orkin (1998) consists of tracking similar days in the past and compare forecasts with actual number of bookings that day. The difference could be used to correct forecasts and as result calculate unconstrained demand.

b) Liu and Smith et al. ( 2002) method

c) double exponential smoothing method that is easy method to track forecasted unconstrained demand after reservation was closed. It takes number of bookings of every day prior to arrival date (or the day when reservation system was closed and number of bookings reached set level) and then using exponential smoothing calculate projected demand over booking limits between date of reservations’ closed and arrival date. (Ferguson and Crystal et al., 2007)

d) Additive Pick up method – better explained here: Pick Up



The application of this method on our data set is available here: Uncontraining demand *




In order to unconstrain the demand I took raw data and calculated it with formula that was copied on entire dataset (in D column):


To understand what is done in the spreadsheet lets divide this algorithm into parts

  1. I only want to unconstrain demand when final bookins reached limit = 100 -> =IF(C5=100; otherwise I want to have the actual number of bookings ;C5)
  2. The second thing was actually choosing the method that will measure the “extra” bookings that would occur if the capacity was bigger. I chose Additive Pick up method as it is easy and very accurate. It shows on average how many bookigs occured between the arrival date and the day before. And it is calculated as:
    a) sum of final bookings during previous days : SUM($C$4:C5)
    b) sum of bookings that were made one day a prior arrival: SUM($E$4:AH5)
    c) the difference between them is sum of all bookings that occured between those days.
    d) when I divided this sum by COUNT($C$4:C5) I calculated the average increase per day.
  3. Now the interesting part. I cheated a bit :) and checked when the demand closed the limit and I realized that it wasn’t earlier than two days before arrival date (column AI;AJ) so it gives two possibilities:
    a) When IF(E5>0; we add to C5 (100) possible bookings from one day before (SUM($C$4:C5)-SUM($E$4:AH5))/COUNT($C$4:C5);
    b) when bookings were closed one day before. Then the uncontrained demand accounts to C5 (100) + average bookings that occur two days before arrival day and one day before booking (SUM($C$4:C5)-SUM($E$4:AH5))/COUNT($C$4:C5)+(SUM($E$4:AH5)-SUM($F$4:AH5))/COUNT($C$4:C5))





  1. Ferguson, M., Crystal, C., Higbie, J. and Kapoor, R. (2007) A Comparison of Unconstraining Methods to Improve Revenue Management Systems. Georgia Institute of Technology, vol. 3
  2. Guo, P., Xiao, B. and Li, J. (2012) Unconstraining Methods in Revenue Management Systems: Research Overview and Prospects. Advances in Operations Research
  3. Liu, P., Smith, S., Orkin, E. and Carey, G. (2002) Estimating unconstrained hotel demand based on censored booking data. Journal of Revenue and pricing Management, vol. 1, no.2, pp. 121-138.
  4. Orkin, E. B. (1998) Boosting your bottomline with Yield Management. The Corell HRA Quarterly, vol. 28, pp. 52-56
  5. Queenan C. C., Ferguson M., Higbie J., and Kapoor R. (2007) A comparison of unconstraining methods to improve revenue management systems, Production and Operations Management, vol. 16, no. 6, pp. 729–746
  6. Saleh, R. (1997) Estimating lost demand with imperfect availability indicators, Proceedings of the AGIFORS Reservations and Yield Management Study Group, Montreal, Canada, 1997.


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