Question 4 - Aggregate capacity management (8 marks) A manufacturing company is setting up a production plan for its products to achieve the following demand forecast over four seasons; starting with Autumn: 12,000 units, followed by Winter: 10,000 units, Spring: 9,000 units, and finally Summer: 11,000 units. The company operates for 60 days per season and for 8 hours per day. At the beginning of Autumn, the company already has 40 workers and 1,000 units of inventory. Each employee takes 2 hours to produce one unit of the product and all employees work at their full capacity within the normal operating hours. The operating costs that are applicable in this company are as follows. The standard (straight time) labour cost is $30 per hour, and the overtime labour cost is $45 per hour. The cost for hiring a new employee is $1,000 and it costs $1,200 to lay off an employee. The backorder cost is $15 per unit-season, and the inventory holding cost is $5 per unit-season. a) Construct a complete production plan for the four seasons to produce the lowest total production costs under the following restrictions. The company is allowed to use overtime during the Winter and Spring seasons only, at a maximum of 3,000 hours per season. Note that overtime can only be used to reduce backorders during these two seasons. No hiring or laying off employees is allowed in all seasons, except in Summer, but the company must not have backorders or ending inventory at the end of Summer. Show and explain the calculations of any backorder and inventory units, the overtime hours, and the number of employees that the company should hire or layoff (4 marks). If you use overtime, explain clearly how you determine the amount of overtime, and the seasons during which you use overtime. Similarly, show how you determine the number of workers that you hire or lay off in Summer if you need to do so (1 mark). 4 b) The company is now required to deliver the exact demand of each season. In addition, it is also required to produce and keep safety stock at the amount of 20% of the demand for each season. This means that backorders, overtime, and ending inventory (other than safety stock) are not allowed in all seasons. In order to meet these requirements, the company is now allowed to change the number of workers employed in each season, and the workers do not have to work at their full capacity although they will still be paid at the full amount based on the available working hours in the season. Construct a complete production plan for this scenario over the four seasons, and show the associated costs (including the cost for keeping the safety stock) as well as the percentage of production capacity utilisation of the workers (3 marks).