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SCOTSBURN DAIRY

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 litres capacities), homogenized, cooled, and stored in one of 8 storage tanks.

In the second stage, the mix is fed into one of three lines where flavour(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 litres. The plant manager has received the following aggregate demand forecasts (in units, i.e., 10,000 litres) for the next 12 months:

JanFebMarAprMayJunJulAugSepOctNovDec

140160190180180220240210170170160130

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 changeovers.

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 litres 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 litres per hour).

The plant manager uses the following labour schemes: 40 hours a week (1 shift; 10 hours a day for 4 days Monday - Thursday), 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 Monday - Thursday).

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

Scotsburn has on-site warehouse space for 6500 pallets of products. Each pallet's load differ by tub size. For example, 550 two-litre tubs can be placed on a pallet. For simplicity, we will use as a measure of on-site warehouse capacity (i.e. 6500 (550 * 2). =7150,000 litres or 715 units).

The production cost of the 40-hour a week labour scheme (requiring 3 freezer operators, nine freezer packers, one freezer bypass, five palletizers, one quality control lab supervisor, one lab technician, two wash staff, four mixers, one production supervisor, one maintenance manager, and four maintenance workers) (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 employment.

Value of one litre of product is $1, cost of capital is 11 percent per year, each pallet holds 1100 litres and warehousing cost is $20 per pallets per month. From these, inventory holding cost per unit (10,000 litres) per month is 0.11($1)(10,000)/12 + 20(10,000/1100) = $273. Planning for shortage/backorder is highly undesirable. Assume a cost of $1,000 per unit per month back ordered.

Question

What is the minimum cost aggregate production plan for Scotsburn diary? (Hint use second shift in May and June, supplemented overtime in several months)

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