The forecasted demands for the next 10 months are given below.
Month Demand Working Days
Jan 16000 21
Feb 18000 22
March 18000 20
April 30000 22
May 28000 21
June 20000 20
July 15000 22
Aug 25000 20
Sep 20000 21
Oct 26000 23
Hiring 600 Per person
Firing 9000 Per person
Overtime 20 Per unit
Regular Production 15 Per unit
Subcontract 24 Per unit
Inventory 2 Per unit
There are currently 60 workers employed regularly for 8 hours/day. Maximum overtime allowed is 3 hours per day. The start month of planning horizon is January. According to data last December, 60 workers assembled approximately 9,600 finished goods with no over time, no idle time and no subcontract within 20 working days. The ending inventory last December is 2,000 units and the company wants to have 1,500 units inventory at the end of the planning horizon (October). No shortage is allowed for each month. Determine the workforce level for each month and the total cost of the following plans. Also, write down the linear programming model for each plan:
a. Minimum constant workforce with no overtime, no idle time and no subcontract.
b. Zero inventory approach with no overtime, no idle time and no subcontract. Note: Zero inventory approach means that we want there is no inventory left in each month.
c. Optional overtime (no more than 3 hours per day), no idle time and optional subcontract (no more than 3000 unit per month). Workforce level can be changed no more than twice during the planning horizon. (You don’t have to solve this problem, just write down your linear programming model)


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