CH 12 Managing Capacity and Demand

Strategies for Matching Supply and Demand for Services Partitioning demand Developing complementary services Establishing price incentives reservation systems Promoting off-peak Yield management SUPPLY Cross- training employees Increasing customer participation Sharing capacity Scheduling work shifts Creating adjustable Using part-time

Segmenting Demand at a Health Clinic 60 70 80 90 100 110 120 130 140 1 2 3 4 5 Day of week Percentage of average daily physician visits Smoothing Demand by Appointment Scheduling Day Appointments Monday 84 Tuesday 89 Wednesday 124 Thursday 129 Friday 114

Discriminatory Pricing for Camping Experience No. of Daily type Days and weeks of camping season days fee 1 Saturdays and Sundays of weeks 10 to 15, plus 14 $6.00 Dominion Day and civic holidays 2 Saturdays and Sundays of weeks 3 to 9 and 15 to 19, 23 2.50 plus Victoria Day 3 Fridays of weeks 3 to 15, plus all other days of weeks 43 0.50 9 to 15 that are not in experience type 1 or 2 4 Rest of camping season 78 free EXISTING REVENUE VS PROJECTED REVENUE FROM DISCRIMINATORY PRICING Existing flat fee of $2.50 Discriminatory fee Experience Campsites Campsites type occupied Revenue occupied (est.) Revenue 1 5.891 $14,727 5,000 $30,000 2 8,978 22,445 8,500 21,250 3 6,129 15,322 15,500 7.750 4 4,979 12,447 …. …. Total 25,977 $ 64,941 29,000 $59,000

Hotel Overbooking Loss Table Number of Reservations Overbooked No- Prob- shows ability 0 1 2 3 4 5 6 7 8 9 0 .07 0 100 200 300 400 500 600 700 800 900 1 .19 40 0 100 200 300 400 500 600 700 800 2 .22 80 40 0 100 200 300 400 500 600 700 3 .16 120 80 40 0 100 200 300 400 500 600 4 .12 160 120 80 40 0 100 200 300 400 500 5 .10 200 160 120 80 40 0 100 200 300 400 6 .07 240 200 160 120 80 40 0 100 200 300 7 .04 280 240 200 160 120 80 40 0 100 200 8 .02 320 280 240 200 160 120 80 40 0 100 9 .01 360 320 280 240 200 160 120 80 40 0 Expected loss, $ 121.60 91.40 87.80 115.00 164.60 231.00 311.40 401.60 497.40 560.00

LP Model for Weekly Workshift Schedule with Two Days-off Constraint Schedule matrix, x = day off Operator Su M Tu W Th F Sa 1 x x … … … … ... 2 … x x … … … … 3 … ... x x … … … 4 … ... x x … … … 5 … … … … x x … 6 … … … … x x … 7 … … … … x x … 8 x … … … … … x Total 6 6 5 6 5 5 7 Required 3 6 5 6 5 5 5 Excess 3 0 0 0 0 0 2

Scheduling Part-time Bank Tellers Decreasing part-time teller demand histogram Tellers required Mon. Tues. Wed. Thurs. Fri. Two Full-time Tellers 5 4 1 3 2 Fri. Mon. Wed. Thurs Tues. 0 1 2 3 4 5 Tellers required 0 1 2 3 4 5 6 7 DAILY PART-TIME WORK SCHEDULE, X=workday Teller Mon. Tues. Wed. Thurs. Fri. 1 x …. x …. x 2 x …. …. x x 3,4 x …. …. …. x 5 …. …. x …. x

Ideal Characteristics for Yield Management Relatively Fixed Capacity Ability to Segment Markets Perishable Inventory Product Sold in Advance Fluctuating Demand Low Marginal Sales Cost and High Capacity Change Cost

Seasonal Allocation of Rooms by Service Class for Resort Hotel First class Standard Budget 20% 20% 20% 30% 50% 30% 50% 60% Percentage of capacity allocated to different service classes 50% 30% 30% 10% Peak Shoulder Off-peak Shoulder (30%) (20%) (40%) (10%) Summer Fall Winter Spring Percentage of capacity allocated to different seasons

Surfside Hotel No-Show Experience Probability Reservations Overbooked Cumulative d P(d) x P(d〈 x) 0.07 0.00 1 0.19 2 0.22 0.26 3 0.16 0.48 4 0.12 0.64 5 0.10 0.76 6 0.86 7 0.04 0.93 8 0.02 0.97 9 0.01 0.99 Opportunity loss of no-show : $ 40 Overbooking loss of guest “walked” : $ 100 The expected number of no-show is calculated as 0*(0.07) + 1*(0.19) + 2*(0.22) + … + 8*(0.02) + 9*(0.01) = 3.04 Expected opportunity loss per day = 3.04 x $ 40 = $ 121.60

E (revenue of next booking) ≥ E (cost of next booking) Marginal Cost Approach E (revenue of next booking) ≥ E (cost of next booking) Revenue of filling a room ⅹ Probability of more no-shows than overbooked rooms ≥ Cost of dissatisfied customer ⅹ Probability of fewer of the same number of no- Shows than overbooked rooms Cu ⅹ P (Overbookings ＜ No-shows) ≥ Co ⅹ P (Overbookings ≥ No-shows) Cu ⅹ P( x ＜ d ) ≥ Co ⅹ P( x ≥ d ) Cu ⅹ {1 - P( x ＞ d )} ≥ Co ⅹ P( x ＞ d ) Cu ⅹ P( x ＞ d ) + P( x ＞ d ) ≤ Cu P( x ＞ d ) ≤ o Cu Co + Cu Where Cu = the $40 room contribution that is lost when a reservation is not honored (i.e., the number of no-shows is underestimated) Co = the $100 opportunity loss associated with not having a room available for an overbooked guest (i.e., the number of no-shows is overestimated) d = the number of no-shows based on past experience x = the number of rooms overbooked $40 $40 + $100 P( x ＞d ) ≤ ≤ 0.286