Scotsburn Dairy's (SD) plant in Truro, Nova Scotia, makes over 300 types and sizes of ice cream and frozen yoghurt. The process is in two stages. First, a type of mix such as premium white is made in one of two large pasteurizing vats (5,400 and 7,500 liters), homogenized, cooled, and stored in one of 8 storage tanks. In the second stage, the mix is fed into one of three lines where flavor(s)/fruit(s) are added, and the mix is packaged in containers (tubs) of various sizes. All three lines feed into the spiral freezer and the tubs are stored in the on-site warehouse. For simplicity, we assume that all the products can be aggregated, and the volume of the product represents its production speed and cost. Furthermore, we assume that a unit is 10,000 liters. The plant manager has received the following aggregate demand forecasts (in units, i.e., 10,000 liters) for the next 12 months:

Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
140	160	190	180	180	220	240	210	170	170	160	130

A major consideration is product changeover/setup time. These are significant as a mix is changed and as a tub size is changed. The manager estimates that out of 4.3 weeks per month, on average 1 week is spent for changeover time.

Although production speed of a line in the second stage varies by product (and not as a linear function of products? tub size), the spiral freezer's speed is based on volume of ice cream going through it (10,000 liters per hour). For some products, the line is a bottleneck but for most products the spiral freezer is. For simplicity, we assume that the production capacity of the plant is determined by the capacity of the spiral freezer (1 unit or 10,000 liters per hour).

The plant manager uses the following labor schemes: 40 hours a week (1 shift; 10 hours a day for 4 days), 50 hours a week (40 + 10 hours of overtime on Fridays), and 80 hours a week (2 shifts; 10 hours a day for 4 days each).

The initial inventory is 210 units (i.e., 2,100,000 liters). The manager would like to have safety stocks at the end of each month greater or equal to the forecast demand next month. Also, the ending inventory next Dec should be at least 170 units.

The production cost of the 40-hour a week labor scheme (requiring 32 workers with various skills) is $78,408 per month. Overtime production cost is approximately 1.5 times regular time production. A temp worker's production cost is approximately the same as a permanent worker's.

The average hiring cost of 32 temp workers required to run the plant is $500, charged to the first month of production.

The inventory holding cost per unit (10,000 liters) per month is $273. Planning for shortage/backorder is highly undesirable. Assume a cost of $1,000 per unit per month backordered.

1) Show that regular production per month is 132 units.

2) Show that overtime production per month is 33 units.

3) Show that regular labor cost is $594 per unit.

4) Show that Hire cost/unit is $121.

5) Using tradeoff analysis show that using temp workers that results in carrying inventory two months ahead is more costly that using permanent workers during overtime two months ahead.