1. BA250 MANAGEMENT SCIENCE EXAMPLE PROBLEMS

2. Example 1 Labor Scheduling
Arlington Bank of Commerce and Industry is a busy bank that has requirements for between 10 and 18 tellers depending on the time of day. Lunchtime, from noon to 2 P.M., is usually heaviest. The table below indicates the workers needed at various hours that the bank is open.
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3. Example 1 Labor Scheduling
The bank now employs 12 full-time tellers, but many people are on its roster of available part-time employees. A part-time employee must put in exactly 4 hours per day but can start anytime between 9 A.M. and 1 P.M. Fulltimers, on the other hand, work from 9 A.M. to 5 P.M. but are allowed 1 hour for lunch. (Half the full-timers eat at 11 A.M., the other half at noon.)
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

4. Example 1 Labor Scheduling
By corporate policy, the bank limits part-time hours to a maximum of 50% of the day’s total requirement. Part-timers earn $6 per hour (or $24 per day) on average, whereas full-timers earn $75 per day in salary and benefits on average. The bank would like to set a schedule that would minimize its total man-power costs. It will release 1 or more of its full-time tellers if it is profitable to do so.
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

5. Example 1 Labor Scheduling
Time Number of Time Number of
Period Tellers Required Period Tellers Required
9 AM - 10 AM 10 1 PM - 2 PM 18
10 AM - 11 AM 12 2 PM - 3 PM 17
11 AM - Noon 14 3 PM - 4 PM 15
Noon - 1 PM 16 4 PM - 5 PM 10
F = Full-time tellers
P1 = Part-time tellers starting at 9 AM (leaving at 1 PM)
P2 = Part-time tellers starting at 10 AM (leaving at 2 PM)
P3 = Part-time tellers starting at 11 AM (leaving at 3 PM)
P4 = Part-time tellers starting at noon (leaving at 4 PM)
P5 = Part-time tellers starting at 1 PM (leaving at 5 PM)

6. Example2: MARKET SURVEY
Market Survey, Inc. (MSI), is a marketing firm that specializes in evaluating consumer research to new products, services, and advertising campaigns. A client firm has requested assistance from MSI in ascertaining consumer reaction to a recently marketing product for household use. During meetings with the client it was agreed that door-to-door personal interviews would be used to obtain information from both households with children and households without children. In addition, it was agreed that both day and evening interviews would be necessary in order to allow for a variety of household work schedules. Specifically, the clients contract called for MSI to conduct 1000 interviews with the following quota guidelines:
At least 400 households with children would be interviewed.
At least 400 households without children would be interviewed.
The total number of households interviewed during the evening would be at least as great as the number of households interviewed during the day.
At least 40% of the interviews for households with children would be conducted during the evening.
At least 60% of the interviews for households without children would be conducted during the evening.
Since the interviews of households with children take additional interviewer time, and since evening interviewers are paid more than daytime interviewers, the cost of an interview varies with the type of interview. Based on previous research studies, estimates of the interview costs are as follows:
INTERVIEW COST
HOUSEHOLD DAY EVENING
Children $20 $25
No children $18 $20
What is the household, time-of-day interview plan that will satisfy the contract requirements at a minimum total interviewing cost?

7. Example 3: Production Scheduling
Chip Hoose is the owner of Hoose Custom Wheels. Chip has just received orders for 1,000 standard wheels and 1,250 deluxe wheels next month and for 800 standard and 1,500 deluxe the following month. All orders must be filled.
The cost of making standard wheels is $10 and deluxe wheels is $16. Overtime rates are 50% higher. There are 1,000 hours of regular time and 500 hours of overtime available each month. It takes 0.5 hour to make a standard wheel and 0.6 hour to make a deluxe wheel. The cost of storing a wheel from one month to the next is $2.

8. Develop an LP model to determine the regular-time, overtime production and inventory quantities in each month for standard and deluxe wheels so that total production and inventory costs can be minimized.