Quiz 16: Revenue Management With Capacity Controls

Business

Revenue management is concerned with maximizing the revenue by making optimal choice of capacity and pricing strategy given the supply or demand is fairly constant. In case of protection level/ booking limit is a capacity control tool. In this case, generally, two types of reservations are used to cater two types of customer arrivals. The arrival occurs in a staggered manner i.e. the low fare or discounted price offers are given the first priority is arrival. The concept from a newsvendor model from single period inventory model is borrowed in computing the optimal choice of capacity reserved for the full-priced offers. a. The available total capacity is 150 rooms. Since 50 rooms are reserved for full-price rooms, the available capacity for the discounted rooms img b. Compute the optimal reserved capacity for the full-price rooms as follows: Full price, img Half price, img img For optimal reserved capacity of high-fare rooms, the probability of high-fare demand being less than or equal to reserved quantity equals the critical ratio. In other words, img Or, img Compute the value of the standard normal variable z using the following Excel function: img With the given full-price demand distribution, compute the value of Q using the following formula: img Rounding off the value of Q , the optimal level of full-priced rooms is img c. After responding to the competitor's move the prices are as following: Full price, img Half price, img img Since the critical ratio reduces, the protection level for the full-price will also reduce. d. Given the protection level, compute the left-over inventory level as follows: Protection level, Q = 61 img The corresponding loss function, img Expected lost sales, img So, img img The expected left-over inventory is img e. Note that on an average, 70 full-price rooms will be booked. Compute the expected revenue using the following equation: img So, the expected revenue will be img f. If there is no protection for full-price rooms, then all rooms will be sold as discounted-priced. So, the expected revenue img g. Given the protection level, compute the expected revenue as follows: Protection level, Q = 50 img The corresponding loss function from the loss function table, img Expected lost sales, img So, img img So, the expected revenue is img .

Revenue management is concerned with maximizing the revenue by making optimal choice of capacity and pricing strategy given the supply or demand is fairly constant. In case of overbooking strategy, the overbooking is done for regular-price reservations. Overbooking is deployed only when the customer reservation is not deterministic in nature and as a result, a portion of the customer do not show up for their reserved seats. a. Compute the optimum overbooking limit using the following formula: img Where, img is the price of the regular-fare rooms. For optimal overbooking limit, the probability of demand being less than or equal to reserved quantity equals the critical ratio. In other words, img Or, img From the given Poisson table, F (13) = 0.3171 0.270 So, the optimal overbooking limit is img b. The booked number of rooms is 160. So, if 9 or more no-shows happens, the hotel will not be able to completely accommodate the demand. From the Poisson table, F (9) = 0.0552. So, there is a img chance that the demand cannot be fulfilled. c. The booked number of rooms is 165. So, if 15 or fewer no-shows happen, the hotel will be fully occupied and not able to completely accommodate the demand. From the Poisson table, F (15) = 0.5170. So, the probability that the Inn is fully occupied is img d. The overbooking limit is img . Corresponding to this value, the loss function is img So, img So, the expected cost of bumping = img Therefore, the expected cost of bumping is img .

Revenue management is concerned with maximizing the revenue by making optimal choice of capacity and pricing strategy given the supply or demand is fairly constant. In case of protection level/ booking limit is a capacity control tool. In this case, generally, two types of reservations are used to cater two types of customer arrivals. The arrival occurs in a staggered manner i.e. the low fare or discounted price offers are given the first priority is arrival. The concept from a newsvendor model from single period inventory model is borrowed in computing the optimal choice of capacity reserved for the full-priced offers. a. Compute the optimal quantity sold in advance as follows: High price, img Regular price, img img For optimal reserved capacity of high price, the probability of high-price demand being less than or equal to reserved quantity equals the critical ratio. In other words, img Or, img Compute the cumulative probability from the given discrete distribution of number of slots using the Excel formulation as follows: img Result img With the given high-price demand cumulative distribution as shown above, F(13) = 0.60 So, the optimal level of high-priced booking is 13. So, the optimal quantity that is to be sold in advance img b. Compute the optimal quantity sold in advance after altering the critical ratio based on the given salvage value of the slots. High price, img Regular price, img img For optimal reserved capacity of high price, the probability of high-price demand being less than or equal to reserved quantity equals the critical ratio. In other words, img Or, img With the given high-price demand cumulative distribution, F(15) = 0.60 So, the optimal level of high-priced booking is 15. So, the optimal quantity that is to be sold in advance img c. Given the number of slots booked in advance equal to 10, compute the probability of stock left-over for the stand-by customers as follows: So, high-price booking img . There will be stand-by customers if 14 or less slots are booked. From the cumulative distribution table, F(14) = 0.70 So, the probability of stock left-over for the stand-by customers is img d. Compute the optimum overbooking limit using the following formula: Cost of underage, img Cost of underage, img img For optimal overbooking limit, the probability of demand being less than or equal to reserved quantity equals the critical ratio. In other words, img Or, img From the given Poisson table for the mean of 9, F(6) = 0.2068 0.1304 So, the optimal overbooking limit is 6 slots. So, the number of slots to be booked img e. Compute the optimum overbooking limit using the following formula: Cost of underage, img Cost of underage, img img For optimal overbooking limit, the probability of demand being less than or equal to reserved quantity equals the critical ratio. In other words, img Or, img From the given Poisson table for the mean of 4.5, F(6) = 0.0611 0.0476 So, the optimal overbooking limit is 1 slot only. So, the number of slots to be booked img Therefore, the optimal overbooking quantity is img .