eRide is an electric bicycle manufacturer in Australia. The plant currently employs 20 workers who operate for 20 days a month for 9 hours in each day. Workers are paid $10 per hour for normal working hours and $20 per hour for overtime. Overtime is limited to a maximum of 20 hours per month per employee. One worker can assemble a bicycle every 15 minutes. Component costs for each scooter is $90. Carrying inventory from one month to the next incurs a cost of $5 per bicycle per month. Assume the starting inventory is 4,000 units and eRide wants to end the year with minimum 3,000 units of inventory. Hiring cost is $250 and lay off cost is $350. Cost of stock out/backlog is $10 per unit per month.

Assume you are the plant manager at eRide that have been tasked to provide aggregate production plan for the coming year. Below table shows the forecasted monthly demand.

Month Demand

January 11,500

February 12,500

March 15,500

April 16,500

May 17,500

June 18,700

July 19,600

August 17,500

September 15,400

October 13,500

November 12,500

December 11,500

a. Assuming no subcontracting is available, solve the aggregate planning to find the optimal production schedule. Find the minimum cost involved.

b. Assuming no overtime is available and that a subcontractor is offering to produce the bicycles at a cost of $93 per unit (including the component costs). Solve the aggregate planning problem to determine how eRide should use the third party.