During the next three months, Shoemakers, Inc. must meet(on time) the following demands for shoes: month 1, 1,000pairs; month 2, 1,500 pairs; month 3, 1,800 pairs. It takes 1hour of labor to produce a pair of shoes. During each of thenext three months, the following number of regular-time laborhours are available: month 1, 1,000 hours; month 2, 1,200hours; month 3, 1,200 hours. Each month, the company canrequire workers to put in up to 400 hours of overtime. Workersare paid only for the hours they work, and a worker receives$4 per hour for regular-time work and $6 per hour for overtimework. At the end of each month, a holding cost of $1.50 perpair of shoes is incurred. Formulate an MCNFP that can beused to minimize the total cost incurred in meeting thedemands of the next three months. A formulation requiresdrawing the appropriate network and determining the cij’s, bi’s,and arc capacities. How would you modify your answer ifdemand could be backlogged (all demand must still be met bythe end of month 3) at a cost of $20/pair/month?
During the next three months, Shoemakers, Inc. must meet
(on time) the following demands for shoes: month 1, 1,000
pairs; month 2, 1,500 pairs; month 3, 1,800 pairs. It takes 1
hour of labor to produce a pair of shoes. During each of the
next three months, the following number of regular-time labor
hours are available: month 1, 1,000 hours; month 2, 1,200
hours; month 3, 1,200 hours. Each month, the company can
require workers to put in up to 400 hours of overtime. Workersare paid only for the hours they work, and a worker receives
$4 per hour for regular-time work and $6 per hour for overtime
work. At the end of each month, a holding cost of $1.50 per
pair of shoes is incurred. Formulate an MCNFP that can be
used to minimize the total cost incurred in meeting the
demands of the next three months. A formulation requires
drawing the appropriate network and determining the cij’s, bi
’s,
and arc capacities. How would you modify your answer if
demand could be backlogged (all demand must still be met by
the end of month 3) at a cost of $20/pair/month?
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