Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 3, Problem 56RP

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LP to minimize the cost:

  • Assume the following for shifts,
    • Consider the time from midnight to 6 A.M. as shift “1”.
    • Consider the time from 6 A.M. to noon as shift “2”.
    • Consider the time from noon to 6 P.M. as shift “3”.
    • Consider the time from 6 P.M. to midnight as shift “4”.
  • Let “X1” be the number of employees who works both shifts “1” and “2”.
  • Let “X2” be the number of employees who works both shifts “2” and “3”.
  • Let “X3” be the number of employees who works both shifts “3” and “4”.
  • Let “X4” be the number of employees who works both shifts “4” and “1”.
  • Let “Cm” be the number of customers left after end of shift “m”.
  • Let “Sm” be the number of customers served during shift “m”.
  • The Linear Programming (LP) to minimize the sum of impatience costs of bank’s worker and customer, is as follows,

Minz=120(X1+X2+X3+X4)+5(C1+C2+C3+C4)

  • The above function subject to the following conditions,
    • C1=100S1” denotes the number of customers, who are left after end of shift “1”

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Introduction to mathematical programming

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