The Columbia Manufacturing Company’s sales manager has produced the following sales forecast for next year and the production manager has provided additional information listed below.
Product Family Q1 Q2 Q3 Q4
A 250 350 500 125
B 150 225 360 75
Product Family A:
• Two direct labor hours per unit of product
• Setup cost equals $700 if the product is produced in a quarter
• Setup time equals eight direct labor hours
• Inventory carrying cost per quarter equals $1.50 per one direct labor hour of work left in
inventory at the end of the quarter
• Materials cost equals $70 per direct labor hour of production
• Beginning inventory is zero units
Product Family B:
• One direct labor hour per unit of product
• Setup cost equals $600 if the product is produced in a quarter
• Setup time equals ten direct labor hours
• Inventory carrying cost per quarter equals $1 per one direct labor hour of work left in inventory at
the end of the quarter
• Materials cost equals $50 per direct labor hour of production
• Beginning inventory is zero units
Additional Factors:
• Hiring cost per employee equals $1,500
• Firing cost per employee equals $500
• Overtime cost per direct labor hour equals $15
• Regular time cost per direct labor hour equals $10
• The maximum number of regular time hours to be worked per employee per quarter equals 520
• Employees may not work more than 25% of the regular time hours on overtime each quarter
• The company currently has 2 manufacturing workers at the beginning of quarter 1.
Formulate and solve a mixed-integer program to generate a production plan that minimizes the total cost over
the next year