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					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

             DEMAND                                              SUPPLY
            STRATEGIES                                         STRATEGIES


                     Partitioning                                       Increasing
                      demand                                             customer
   Developing                                                          participation
                                                   Sharing
 complementary
                                                   capacity
    services
                     Establishing
                                                                       Scheduling
                        price
  Developing                                        Cross-             work shifts
                      incentives
  reservation                                      training
   systems                                        employees
                         Promoting                                       Creating
                          off-peak                                      adjustable
                                                    Using
                          demand                                         capacity
                                                   part-time
                                                  employees

                                        Yield
                                     management
Partitioning Demand at a
Health Clinic

                               140
Percentage of average dail y




                               130                                 Smoothing Demand by Appointment
                               120                                 Scheduling
      physi ci an vi sits




                               110                                 Day                 Appointments
                               100
                                                                   Monday                   84
                               90
                                                                   Tuesday                   89
                               80                                  Wednesday               124
                               70                                  Thursday                129
                                                                   Friday                   114
                               60
                                     1   2        3        4   5
                                             Day of week
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
         7  5 6
 Tellers required




                                                                                                                    Decreasing part-time teller demand histogram




                                                                                                           Tellers required
                                                                                                         0 1 2 3 4 5
                                                                                                                                 5
2 3 4




                                                                                                                                 4      4
                                                                                                                                 3      3
                                                                                                                                 2      2        1
                           Two Full-time Tellers                                                                                 1      1        5      2
         1




                                                                                                                                Fri.   Mon.     Wed.   Thurs   Tues.
         0




                    Mon.      Tues.         Wed.            Thurs.           Fri.
                              Object ive   funct io n:
                              Minim i ze                 x1 +   x2 +x3 +x4 +x5 +x6 +x7

                              Co nst raint s:
                                  Sunday                        x2 +x3 +x4 +x5 +x6          b1
                                  Mo nday                           x3 +x4 +x5 +x6 +x7      b2




                     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


        2500
                                                                                              30
                                                                                                        Topline profile




                                                                        Number of operators
        2000                                                                                  25

                                                                                              20
        1500
Calls




                                                                                                                          Scheduler program assigns
                                                                                              15                          tours so that the number of
        1000
                                                                                                                          operators present each half
                                                                                                                          hour adds up to the number
                                                                                              10                          required
        500
                                                                                              5                                           Tour

          0
               12   2   4   6   8   10   12   2   4   6   8   10   12
                                                                                              012   2      4    6   8     10    12    2     4    6   8   10   12
                                     Time
                                                                                                                               Time
Weekly Workshift Scheduling
with Days-off
             Objective function:
              Minimize      x1 + x2 + x3 + x4 + x5 + x6 + x7

             Constraints:
             Sunday              x2 + x3 + x4 + x5 + x6         3
             Monday                  x3 + x4 + x5 + x6 + x7     6
             Tuesday        x1         + x4 + x5 + x6 + x7      5
             Wednesday      x1 + x2           + x5 + x6 + x7    6
             Thursday       x1 + x2 + x3            + x6 + x7   5
             Friday         x1 + x2 + x3 + x4            + x7   5
             Saturday       x1 + x2 + x3 + x4 + x5              5
                             xi  0 and integer


                                   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
Percentage of capacity allocated
  to different service classes




                                                                   20%              20%            20%
                                   First class      30%

                                                                                     30%
                                                                    50%                            50%
                                    Standard
                                                    60%

                                                                                     50%            30%
                                      Budget                        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
                  300
                                               Expected Reservation Accumulation

                  250
                                                              2 standard deviation control limits

                  200
  Reservati ons




                  150

                  100

                  50

                   0
                        1

                            6

                                11

                                     16

                                          21

                                               26

                                                    31

                                                         36

                                                              41

                                                                   46

                                                                        51

                                                                              56

                                                                                   61

                                                                                        66

                                                                                             71

                                                                                                  76

                                                                                                       81

                                                                                                            86
                                                         Days before arrival
Yield Management Using the
Critical Fractile Model
                       Cu      ( F  D)
         P(d  x )          
                     Cu  Co      p F
   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.
          D                  if an economizing passenger
   Co  
         ( F  D)       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?

				
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