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Total Production Techniques & Forecast

Answer the following questions

1. Consider the total production (and sales) of ice cream in Canada (in millions of liters) for the period 1995 until 2007 (from left to right):

341, 331, 317, 315, 321, 278, 298, 311, 302, 302, 335, 320, 285

Fit a model to ice cream production data using each of the following techniques and forecast the 2008 production in each case. Also, plot the two moving average forecasts and the actual, the two exponential smoothing forecasts and the actual, and the linear trend and the actual (three graphs altogether).

• Two-year moving average.
• Four-year moving average.
• Exponential smoothing with smoothing constant = 0.2.
• Exponential smoothing with smoothing constant = 0.4.
• Linear trend (regression).
• Just by observing the plots, which of the above techniques would you use to forecast the ice cream production and why? (Hint: The plot overall closest to actual demand will be most accurate).
• Alternatively, compute the MAD for each forecasting technique and determine the most accurate technique.

2. The number of Toyota Corollas produced in the Cambridge, Ontario, plant during each month of January 2008 to December 2009 period was as follows:

Assume that the cars are sold in the same month they are produced. Identify an appropriate forecasting technique, briefly state the reason(s) you chose it, and forecast Corolla demand in January 2010.

3. Fleet managers have a large pool of cars and trucks to maintain.13 One approach to the vehicle maintenance is to use periodic oil analysis: the oil from the engine and transmission are subjected periodically to a test. These tests can sometimes signal an impending failure (for example, iron particles in the oil), and preventive maintenance is then performed (at a relatively low cost), eliminating the risk of failure (failure would result in a relatively high cost). However, oil analysis costs money and it is not perfect—it can indicate that a unit is defective when in fact it is not, and it can indicate that a unit is nondefective when in fact it is. As a possible substitute for oil analysis, the company could simply change the oil periodically, thereby reducing the probability of failure. The fleet manager for the Southern Company, an electrical utility based in Atlanta (parent of Georgia Power and Light), has four alternatives: (1) do nothing, (2) use oil analysis only, (3) replace oil only, or (4) replace oil and do oil analysis. For option (1) the probability of failure is 0.1, and the cost of failure is $1,200. For option (2), the probability of failure remains at 0.1. If the unit is about to fail, the oil analysis will indicate this with probability 0.7; if the unit is not about to fail, the oil analysis will indicate this with probability 0.8. The oil analysis itself costs $20, and if it indicates that failure is about to occur, the oil will be changed at the cost of $14.80 and preventive maintenance will be performed. The cost of preventive maintenance to restore a unit that is about to fail is $500, whereas the cost of maintenance for a unit that is not about to fail is $250. For options (3) and (4), probability of failure decreases from 0.1 to 0.04. Analyze this decision problem.
4. One of the products of Edwards Lifesciences (EL) is artificial heart valves made from the heart valves of pigs.8 Different sizes of valves are required. However, the size of a pig’s heart valve cannot be ascertained before the heart is purchased and opened. Therefore, EL has a mismatch problem: shortages of some sizes and excess of others. A program was established to document the size distribution of valves supplied by each supplier, and purchases were made from those suppliers with the needed sizes. Linear programming was used to determine the set of the suppliers that collectively satisfied EL’s demand. Suppose EL purchases pig valves from three suppliers. The cost and size mix of the valves purchased from each supplier are given in the table below. Each month EL places one order with each supplier. Suppose next month, 250 large, 300 medium, and 100 small valves are needed. Formulate an LP that can be used to minimize the cost of acquiring the needed valves and use Excel’s Solver to solve it.
5. A manager is attempting to put together an aggregate production plan for the coming nine months. She has obtained forecasts of aggregate demand for the planning horizon. The plan must deal with highly seasonal demand; demand is relatively high in months 3 and 4, and again in month 8, as can be seen below:

The company has 20 permanent employees, each of whom can produce 10 units of output per month at a cost of $6 per unit. Inventory holding cost is $5 per unit per month, and back-order cost is $10 per unit per month. The manager is considering a plan that would involve hiring two people to start working in month 1, one on a temporary basis who would work until the end of month 5. The hiring of these two would cost $500. Beginning inventory is 0.

Start with 20 permanent workers. Prepare a minimum cost plan that may use some combination of hiring ($250 per worker), subcontracting ($8 per unit, maximum of 20 units per month, must use for at least three consecutive months), and overtime ($9 per unit, maximum of 25 units per month). The ending inventory in month 9 should be zero with no back orders at the end.

Compute the comprehensive cost analysis. (Hint: Use max. overtime and subcontracting in months 2–4.)

6. A manufacturer of exercise equipment purchases pulleys from a supplier who lists these prices: less than 1,000, $5 each; 1,000 to 3,999, $4.95 each; 4,000 to 5,999, $4.90 each; and 6,000 or more, $4.85 each. Ordering cost is $50 per order, annual holding cost is 20 percent of purchase cost, and annual usage is 4,900 pulleys.

Determine the order quantity that will minimize total cost.

7. MT makes small camping and snowmobile trailers. The demand for camping trailers occurs between January and June (mostly in April and May). MT makes camping trailers from January to June, shuts down in July and then makes snowmobile trailers from August to November. Suppose now is the end of December. For simplicity, we consider every two months as a period. The forecasts for camping trailers during each of the next three periods (six months) are:

MT employs 40 permanent workers who are paid an average of $20 per hour (including fringe benefits) and work approximately 320 hours a period (2 months). They make approximately 1,000 camping trailers per period during regular time. They can also work up to 50 percent more as overtime (i.e., up to 12 hours a day vs. the regular 8 hours a day) and will be paid 1.5 times the regular wage rate. Alternatively, MT can hire up to 40 additional temporary workers to work during a second shift. Hiring cost is $3,000 per temporary worker. Assume temporary workers’ wage rate and productivity are the same as permanent workers. Also assume that temporary workers work only during regular time (no overtime) and are kept for whole periods (i.e., for 2 months or 4 months). Inventory holding cost per camping trailer per period is $180 and is charged to average inventory level during each period. Currently there are no camping trailers on hand, and the desired inventory at the end of period 3 is zero (although a small positive number is also acceptable). MT wishes to meet the total demand, but shortage during a period (except last) is acceptable, in which case the shortage is assumed to be backordered at the cost of $600 per camping trailer per period.

1. Calculate all the relevant unit costs.
2. Suppose MT uses permanent workers during regular time and overtime. Determine the minimum cost plan in this case. Hint: Use overtime in each period.
3. Suppose MT hires temporary workers but decides not to use permanent workers during overtime (just regular time). Determine the minimum cost plan in this case. Hint: Hire 15 temps for two periods and 9 temps for 1 period starting in period 2.
4. Would overtime production by permanent workers and regular time production by temporary workers simultaneously result in a lower total cost? Do a tradeoff analysis. What is the overall minimum cost plan?

 Information concerning the product structure, lead times, and quantities on hand for an electric golf cart is shown in the following table. Use this information to do each of the following:

1. 1. Draw the product structure tree.
   2. Draw the assembly time chart.
   3. Develop the material requirements plan that will provide 200 golf carts at the start of week 8, assuming lot-for-lot ordering.