Professor Jonathan Eckstein

Operations Management, 33:623:386:01/02

School of Business – New Brunswick

Rutgers University

Review Material for First Midterm ExamFall 2001Supplementary Problem

10: Processing Flax Oil

Your firm is in the business of processing flax oil, a popular health food ingredient. Like many agricultural products, the price and demand for flax oil, along with your processing costs, vary seasonally. The following table shows, for the coming six months, your unit costs for purchasing “raw” (unprocessed) oil, your unit cost for processing it, and the amount of processed oil you have committed to deliver to your customers.

Unit Costs (per Gallon)
/
Demand
Month / Raw Oil / Processing / (Gallons)
1 / $ 4.50 / $ 2.50 / 4000
2 / $ 4.85 / $ 2.75 / 4200
3 / $ 5.85 / $ 2.80 / 4500
4 / $ 6.15 / $ 3.45 / 5600
5 / $ 6.20 / $ 3.60 / 5500
6 / $ 5.95 / $ 3.25 / 4600

You must deliver exactly the specified amount of processed oil each month. The conversion efficiency of your process is 80%, meaning that, for each gallon of raw oil processed, you obtain 0.8 gallons of processed oil (the remaining 20% waste is donated to local farmers for use in compost). You can process up to 6500 gallons of raw oil per month.

Both raw oil and processed oil can be held in inventory. The total amount of oil stored each month cannot exceed 7000 gallons, and (for technical reasons) at least 45% of the amount stored must be raw oil. It costs $0.20 to hold a gallon of raw oil in inventory for a month, and $0.50 for a gallon of processed oil. All these constraints and costs apply to inventories as measured at the end of each month. At the beginning of month one, you have 1000 gallons of raw oil and 500 gallons of processed oil on hand.

You would like to meet your commitments to your customers at the smallest possible total cost over the next six months. To this end, you are using the spreadsheet on the following page. The shaded cells contain formulas; cell D16 contains the formula =G10, and cell E16 contains the formula =G11. The sheet contains an optimal solution, formatted to display rounded to the nearest whole number.

(a)  Which cells hold the uncontrollable inputs for the model?

(b)  What formula should be in cell D17, to compute the amount of raw oil left in inventory at the end of month one? Make sure your answer will yield correct results for the following months when copied to cells D18:D22.

(c)  What formula should be in cell E17, to compute the amount of processed oil left in inventory at the end of month one? Make sure your answer will yield correct results for the following months when copied to cells E18:E22.

(d)  What formula should be in cell F17, to compute the total amount of oil left in inventory at the end of month one? Make sure your answer will yield correct results for the following months when copied to cells F18:F22.

(e)  What formula should be in cell G17, to compute the minimum amount of raw oil needed to meet the 45% storage requirement for the end of month one? Make sure your answer will yield correct results for the following months when copied to cells G18:G22.

(f)  What formulas should be in cells C25 through C29, to compute all the costs of the six month production plan?

(g)  What is the target cell? Should it be maximized or minimized? What are the changing cells? What are all the constraints that should be used in the solver? Should you “assume linear model”? Should you “assume nonnegative”?

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