Managing Capacity and Demand

Learning Objectives Describe the strategies for matching supply and demand for services. Recommend an overbooking strategy. Use Linear Programming to prepare a weekly workshift schedule. Prepare a work schedule for part-time employees. Use yield management.

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

Partitioning Demand at a Health Clinic Smoothing Demand by Appointment Scheduling Day Appointments Monday 84 Tuesday 89 Wednesday 124 Thursday 129 Friday 114

Discriminatory Fee Schedule 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 Decision Matrix 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

Scheduling Part-time Bank Tellers Decreasing part-time teller demand histogram Tellers required 5 4 4 0 1 2 3 4 5 6 7 Tellers required 3 3 0 1 2 3 4 5 2 2 1 Two Full-time Tellers 1 1 5 2 Fri. Mon. Wed. Thurs Tues. Mon. Tues. Wed. Thurs. Fri. 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

Daily Scheduling of Telephone Operator Workshifts Topline profile Scheduler program assigns tours so that the number of operators present each half hour adds up to the number required Tour 12 2 4 6 8 10 12 2 4 6 8 10 12 12 2 4 6 8 10 12 2 4 6 8 10 12

Weekly Workshift Scheduling with Days-off 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

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

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

Demand Control Chart for a Hotel Expected Reservation Accumulation 2 standard deviation control limits

Yield Management Using the Critical Fractile Model Where x = seats reserved for full-fare passengers d = demand for full-fare tickets p = proportion of economizing (discount) passengers Cu = lost revenue associated with reserving one too few seats at full fare (underestimating demand). The lost opportunity is the difference between the fares (F-D) assuming a passenger, willing to pay full-fare (F), purchased a seat at the discount (D) price. Co = cost of reserving one to many seats for sale at full-fare (overestimating demand). Assume the empty full-fare seat would have been sold at the discount price. However, Co takes on two values, depending on the buying behavior of the passenger who would have purchased the seat if not reserved for full-fare. if an economizing passenger if a full fare passenger (marginal gain) Expected value of Co = pD-(1-p)(F-D) = pF - (F-D)

Topics for Discussion What organizational problems can arise from the use of part-time employees? How can computer-based reservation systems increase service capacity utilization? What possible dangers are associated with developing complementary services? Will the widespread use of yield management eventually erode the concept of fixed prices? What possible negative effects can yield management have on customer relations?