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(Book: 3.5 problem 7) Each hour from 10 A.M. to 7P.M., Big Bank receives checks and must process them. Its goal is to process all the checks the same day they are received. The bank has 13 check-processing machines, each of which can process up to 500 checks per hour. It takes one worker to operate each machine. Bank One hires both full-time and part-time workers. Full-time workers work 10 A.M.-6 P.M., 11 A.M.- 7 P.M., Noon-8 P.M. and are paid $ 160 per day. Part-time workers work either 2 P.M.-7 P.M. or 3 P.M.-8 P.M. and are paid $75 per day. The number of checks received each hour is given in the Table below. In the interest of maintaining continuity, Big Bank requires it must have at least three full-time workers under contract. Set up the LP and solve to determine the minimal cost schedule that processes all checks by 8P.M. For simplicity we allow fractional numbers of employees. The minimum labor cost subject to the conditions is Time checks 10AM 5000 11AM 4000 Noon 3000 1PM 4000 2PM 2500 3PM 3000 4PM 4000 5PM 4500 6PM 3500 7PM 3000 This one needs a hint: the decision variables need to be at a minimum a variable for how many full-time employees start at each permitted starting time and similarly for part-time employees. This will already give your cost (objective) function. But, to more easily express the many constraints, it is helpful (and perfectly allowed) to introduce many other decision variable. For example, let Pi denote the number of checks that get processed in the hour starting at time i. Also let Ii (for inventory) denote the number of checks that have arrived up to and including time i that have not yet been processed. We don't need I10 but notice that I11 = 5000 - P10 would be one of the constraints, and for all i, Pi ≤ 6500 is a constraint. Another constraint is that the number of checks processed depends on how many employees are working.

(Book: 3.5 problem 7) Each hour from 10 A.M. to 7P.M., Big Bank receives checks and must process them. Its goal is to process all the checks the same day they are received. The bank has 13 check-processing machines, each of which can process up to 500 checks per hour. It takes one worker to operate each machine. Bank One hires both full-time and part-time workers. Full-time workers work 10 A.M.-6 P.M., 11 A.M.- 7 P.M., Noon-8 P.M. and are paid $ 160 per day. Part-time workers work either 2 P.M.-7 P.M. or 3 P.M.-8 P.M. and are paid $75 per day. The number of checks received each hour is given in the Table below. In the interest of maintaining continuity, Big Bank requires it must have at least three full-time workers under contract. Set up the LP and solve to determine the minimal cost schedule that processes all checks by 8P.M. For simplicity we allow fractional numbers of employees. The minimum labor cost subject to the conditions is Time checks 10AM 5000 11AM 4000 Noon 3000 1PM 4000 2PM 2500 3PM 3000 4PM 4000 5PM 4500 6PM 3500 7PM 3000 This one needs a hint: the decision variables need to be at a minimum a variable for how many full-time employees start at each permitted starting time and similarly for part-time employees. This will already give your cost (objective) function. But, to more easily express the many constraints, it is helpful (and perfectly allowed) to introduce many other decision variable. For example, let Pi denote the number of checks that get processed in the hour starting at time i. Also let Ii (for inventory) denote the number of checks that have arrived up to and including time i that have not yet been processed. We don't need I10 but notice that I11 = 5000 - P10 would be one of the constraints, and for all i, Pi ≤ 6500 is a constraint. Another constraint is that the number of checks processed depends on how many employees are working.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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(Book: 3.5 problem 7) Each hour from 10 A.M. to 7P.M., Big Bank receives checks and must process them. Its goal is to process all the checks the same day they are received. The bank has 13 check-processing machines, each of which can process up to 500 checks per hour. It takes one worker to operate each machine. Bank One hires both full-time and part-time workers. Full-time workers work 10 A.M.-6 P.M., 11 A.M.- 7 P.M., Noon-8 P.M. and are paid $ 160 per day. Part-time workers work either 2 P.M.-7 P.M. or 3 P.M.-8 P.M. and are paid $75 per day. The number of checks received each hour is given in the Table below. In the interest of maintaining continuity, Big Bank requires it must have at least three full-time workers under contract. Set up the LP and solve to determine the minimal cost schedule that processes all checks by 8P.M. For simplicity we allow fractional numbers of employees. The minimum labor cost subject to the conditions is Time checks 10AM 5000 11AM 4000 Noon 3000 1PM 4000 2PM 2500 3PM 3000 4PM 4000 5PM 4500 6PM 3500 7PM 3000 This one needs a hint: the decision variables need to be at a minimum a variable for how many full-time employees start at each permitted starting time and similarly for part-time employees. This will already give your cost (objective) function. But, to more easily express the many constraints, it is helpful (and perfectly allowed) to introduce many other decision variable. For example, let Pi denote the number of checks that get processed in the hour starting at time i. Also let Ii (for inventory) denote the number of checks that have arrived up to and including time i that have not yet been processed. We don't need I10 but notice that I11 = 5000 - P10 would be one of the constraints, and for all i, Pi ≤ 6500 is a constraint. Another constraint is that the number of checks processed depends on how many employees are working.
Transcribed Image Text:(Book: 3.5 problem 7) Each hour from 10 A.M. to 7P.M., Big Bank receives checks and must process them. Its goal is to process all the checks the same day they are received. The bank has 13 check-processing machines, each of which can process up to 500 checks per hour. It takes one worker to operate each machine. Bank One hires both full-time and part-time workers. Full-time workers work 10 A.M.-6 P.M., 11 A.M.- 7 P.M., Noon-8 P.M. and are paid $ 160 per day. Part-time workers work either 2 P.M.-7 P.M. or 3 P.M.-8 P.M. and are paid $75 per day. The number of checks received each hour is given in the Table below. In the interest of maintaining continuity, Big Bank requires it must have at least three full-time workers under contract. Set up the LP and solve to determine the minimal cost schedule that processes all checks by 8P.M. For simplicity we allow fractional numbers of employees. The minimum labor cost subject to the conditions is Time checks 10AM 5000 11AM 4000 Noon 3000 1PM 4000 2PM 2500 3PM 3000 4PM 4000 5PM 4500 6PM 3500 7PM 3000 This one needs a hint: the decision variables need to be at a minimum a variable for how many full-time employees start at each permitted starting time and similarly for part-time employees. This will already give your cost (objective) function. But, to more easily express the many constraints, it is helpful (and perfectly allowed) to introduce many other decision variable. For example, let Pi denote the number of checks that get processed in the hour starting at time i. Also let Ii (for inventory) denote the number of checks that have arrived up to and including time i that have not yet been processed. We don't need I10 but notice that I11 = 5000 - P10 would be one of the constraints, and for all i, Pi ≤ 6500 is a constraint. Another constraint is that the number of checks processed depends on how many employees are working.
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