# Service Management

## Quiz 11 :Managing Capacity and Demand

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The sheriff has been asked by the county commissioners to increase weekend patrols in the lake region during the summer months. The sheriff has proposed the following weekly schedule, shifting deputies from weekday assignments to weekends: Develop a weekly workshift schedule of duty tours, providing 2 consecutive days off per week for each officer. Formulate the problem as an integer linear programming model to minimize the number of officers needed, and solve using Excel Solver.
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For the forecast period (i.e., July - December), determine the number of new trainees who must be hired at the beginning of each month so that total personnel costs for the flight attendant staff and training program are minimized. Formulate the problem as a linear programming model and solve.
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Sequoia Airlines faces the problem of planning the optimal use of its resources during the next six months.  It must hire new employees and develop them through three stages of training, first as trainees, then as junior flight attendants, and finally as full flight attendants.  Moreover, Sequoia must meet staff requirements for all flights during the training period.  This problem is analyzed using total personnel cost as the selection criterion.
Other resources in addition to the available personnel create constraints that must be considered when hiring and training new employees.  We will solve the problem by using linear programming and then follow up with an analysis of the objective function and the constraints and assumptions on which they are based.  We will also offer an interpretation of the results.
Because cost is the only criterion we will use to solve this problem, the objective function is straightforward.  One assumption is noteworthy:  we assume that once an experienced attendant becomes an instructor, he or she continues to receive the instructor's salary even when there is a surplus of instructors who act as attendants.  The objective function, therefore, becomes the sum of the number of employees in each class during each period multiplied by the appropriate wage.
Minimize:

We must also deal with several resource constraints.  First, we must meet the requirement for hours of in-flight attendant service.  We assume that a surplus instructor works the same number of hours as an experienced attendant does.
Next, we must satisfy the constraint that requires the total number of hours for junior attendants to be less than or equal to 25 percent of the total attendant hours in each month.
Also, there must be one instructor for every five trainees.
The remaining constraints deal with the relationships between the status of employees during the current and prior periods.  In this case we make assumptions that pertain to the initial staffing levels for the positions of junior attendant, full attendant, and instructor.
We see a total of 42 constraints in the following computer model.
Min 1050J1+ 1050J2+ 1050J3+ 1050J4+ 1050J5+ 1050J6+ 1400F1+ 1400F2+ …Subject to(1) 140J1+ 125F1+ 125S1 = 14000(2) 140J2+ 125F2+ 125S2 = 16000(3) 140J3+ 125F3+ 125S3 = 13000(4) 140J4+ 125F4+ 125S4 = 12000(5) 140J5+ 125F5+ 125S5 = 18000(6) 140J6+ 125F6+ 125S6 = 20000(7) 105Jl-31.25Fl-31.25S1 = 0(8) 105J2-31.25F2-31.25S2 = 0(9) 105J3-31.25F3-31.25S3 = 0(10) 105J4-31.25F4-31.25S4 = 0(11) 105J5-31.25F5-31.25S5 = 0(12) 105J6-31.25F6-31.25S6 = 0(13) 1I1-.2T1 = 0(14) 112-.2T2 = 0(15) 113-.2T3 = 0(16) 114-.2T4 = 0(17) 115-.2T5 = 0(18) 116-.2T6 = 0(19) 1J1 = 8(20) 1F1 = 119(21) 111 = 6(22) -111+ 1Sl+.2T1 = 0(23) -112+ 1S2+.2T2 = 0(24) -113+ 1S3+.2T3 = 0(25) -114+ 1S4+.2T4 = 0(26) -115+ 1S5+.2T5 = 0(27) -116+ 1S6+.iT6 = 0(28) 1J2-.8T1 = 0(29) 1J3-.8T2 = 0(30) 1J4-.8T3 = 0(31) 1J5-.8T4 = 0(32) 1J6-.8T5 = 0(33) -.95J1-.92F1+ 1F2 = 0(34) -.95J2-.92F2+ 1F3 = 0(35) -.95J3-.92F3+ 1F4 = 0(36) -.95J4-.92F4+ 1F5 = 0(37) -.95J5-.92F5+ 1F6 = 0(38) -.005F1-.95I1+ 112 = 0(39) -.005F2-.9512+ 113 = 0(40) -.005F3-.9513+ 114 = 0(41) -.005F4-.9514+ 115 = 0(42) -.005F5-.9515+ 116 = 0

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Assume that you are the assistant to the manager for operations at the FAA. Use the techniques of workshift scheduling to develop an analysis of the total workforce requirements and days-off schedule.
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Reconsider Example 11.3 (Blackjack Airline). After initial success with the Los Angeles-to-Las Vegas route, Blackjack Airline's demand for full-fare tickets has increased to an average of 75, with the standard deviation remaining at 15. This early experience has allowed Blackjack to make a better estimate of the percentage of discount-seeking passengers, which appears to be 80 percent. Consequently, Blackjack has decided to raise all ticket prices by $10. Under these new conditions, how many full-fare seats should Blackjack reserve? Essay Answer: Tags Choose question tag Reconsider Example 11.2 (Hospital Emergency Room) to determine if additional nurses will be required to staff the revised daily shift requirements shown below: Develop a weekly workshift schedule providing 2 consecutive days off per week for each nurse. Formulate the problem as an integer linear programming model to minimize the number of nurses needed, and solve using Excel Solver. If more nurses are required than the existing staff of eight, suggest an alternative to hiring full-time nurses. Essay Answer: Tags Choose question tag What additional suggestions could you make to the manager of operations to minimize the workforce requirements level and days-off scheduling difficulty ? Essay Answer: Tags Choose question tag An airline serving Denver's International Airport and Steamboat Springs, Colorado, is considering overbooking its flights to avoid flying with empty seats. For example, the ticket agent is thinking of taking seven reservations for an airplane that has only six seats. During the past month, the no-show experience has been The operating costs associated with each flight are pilot,$150; first officer, $100; fuel,$30; and landing fee, $20. What would be your recommendation for overbooking if a one-way ticket sells for$80 and the cost of not honoring a reservation is a free lift ticket worth $50 plus a seat on the next flight? What is the expected profit per flight for your overbooking choice? Essay Answer: Tags Choose question tag A commuter airline overbooks all its flights by one passenger (i.e., the ticket agent will take seven reservations for an airplane that only has six seats). The no-show experience for the past 20 days is shown below: Using the critical fractile find the maximum implied overbooking opportunity loss C o if the revenue C u from a passenger is$20.
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Reconsider Example 11.1 (Surfside Hotel), because rising costs now have resulted in a $100 opportunity loss from a no-show. Assume that the no-show experience has not significantly changed and that the resulting loss when a guest is overbooked still is$100. Should Surfside revise its no-show policy?
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Will the widespread use of yield management eventually erode the concept of fixed prices for any service?
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An outpatient clinic has kept a record of walk-in patients during the past year. The table below shows the expected number of walk-ins by day of the week: The clinic has a staff of five physicians, and each can examine 15 patients a day on average. a. What is the maximum number of appointments that should be scheduled for each day if it is desirable to smooth out the demand for the week? b. Why would you recommend against scheduling appointments at their maximum level? c. If most walk-ins arrive in the morning, when should the appointments be made to avoid excessive waiting?
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Do you feel that this would result in a larger or smaller degree of difficulty in meeting the four general constraints? Why ?
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2. On the basis of your primary analysis, discuss the potential implications for workforce requirements and days-off scheduling if assumptions (a) and (b) above are relaxed so that analysis can be based on the hourly demand without the constraints of a preset number of shifts and no overlapping of shifts. In other words, discuss the effects of analyzing hourly demand requirements on the basis of each ATC position essentially having its own shift, which can overlap with any other ATC shift to meet that demand.
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Crazy Joe operates a canoe rental service on the Guadalupe River. He currently leases 15 canoes from a dealer in a nearby city at a cost of $10 per day. On weekends, when the water is high, he picks up the canoes and drives to a launching point on the river, where he rents canoes to white-water enthusiasts for$30 per day. Lately, canoeists have complained about the unavailability of canoes, so Crazy Joe has recorded the demand for canoes and found the experience below for the past 20 days: Recommend an appropriate number of canoes to lease.
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What organizational problems can arise from the use of part-time employees ?
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Illustrate how a particular service has implemented successfully strategies for managing both demand and capacity.
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Town and Country has experienced a substantial increase in business volume because of recent fare wars between the major air carriers. Town and Country operates a single office at a major international airport, with a fleet of 60 compact and 30 midsize cars. Recent developments have prompted management to rethink the company's reservation policy. The table below contains data on the rental experience of Town and Country: The daily demand appears to follow a normal distribution; however, it has been observed that midsize-car customers do not choose to rent a compact when no midsize car is available. The discount rate is available to persons who are willing to reserve a car at least 14 days in advance and agree to pick up that car within 2 hours after their flight arrives. Otherwise, a nonrefundable deposit against their credit card will be forfeited. The current reservation policy is that 40 compact cars are held for customers who are willing to pay the full rate and 25 midsize cars are held for full rate-paying customers. a. Using yield management, determine the optimal number of compact and midsize cars to be held for customers paying the full rate. b. Given your optimal reservation policy determined here, would you consider a fleet expansion?
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How can computer-based reservation systems increase service capacity utilization ?
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