New England Feed Supply

On April 14, 1996, Jeff Smith, formulation analyst for New England Feed Supply Inc. (NEFS), was evaluating next week’s requirements for three animal feed mixes produced by the Burlington plant. A shortage of one ingredient, meat meal, meant that NEFS would find it difficult to meet the orders on hand. Smith needed to determine which, if any, of the mixture formulae should be altered, and in what way; alternately, he could elect to buy additional meat meal on the spot market, at a significantly higher price.

The Company

New England Feed Supply was an animal feed blending company with twelve plants located in major center throughout New England. The principal ingredients were purchased from farmers and brokers each month, and mixed into a number of standards animal feed products which were sold to feedlots, individual farmers, and large corporate farms. NEFS mixed products to meet orders, and kept no product inventory. Since ingredients were purchased at different times and prices, the cost of each ingredient in inventory was recorded as the total price paid for an ingredient divided by the number of tons in stock.

Each product mix sold had a standard nutritional content that met or exceeded the requirements set by the National Research Council. Ingredient costs were more than 80 per cent of the total product cost with the result that the determination of least cost formulae was critical if the company was to retain competitive and profitable.

Formulation

Customer orders for various types of animal feed were taken directly by the producing plants. The formulation department, located at head office, advised each plant on appropriate feed formulations. From the standard feed formulae supplied by the formulation department, each plant would then determine the amounts of the ingredients required for the following week, and forward these requirements to head office by Wednesday morning. Since the delivery of ordered products for the customer’s livestock, it was company policy that an order, once taken, must be filled. Shortages (or back orders) were not acceptable.

NEFS faced a relatively steady and predictable demand for each of its products. This, and the fact that each plant offered between 150 and 200 different product mixes, necessitated that the plants follow standard mix formulae on a day-to-day basis, even though minor changes in market prices or ingredient costs could occur. Occasionally, however, shortages of raw ingredients required the formulation department to recalculate the feed formulae. The alternative to recalculating formulae was to buy additional units of the short ingredient on the spot market at a price significantly higher than that normally paid.

The Burlington Plant

The Burlington plant mixed and sold three products which potentially used meat meal as an ingredient: 15 percent Pig Grower, 40 percent Pig Supplement, and 17 percent Cage Layer (the percentage values identify the amount of protein in the product). In preparing these products, the company had to ensure that the minimum nutritional standards set by the NRC were met, The NRC standards for these products are given in Exhibit 1. For example, one ton of 15 percent Pig Grower required zero units of ME: Poultry, 3000 units of ME: Swine, 15 units of Protein, etc. Exhibit 1 also indicates the demand, in tons, that the firm faced for the coming week.

The necessary nutrients could be formulated into each of the three end products by combining appropriate quantities of the raw ingredients. The ingredients used included corn, barley, soyameal, meat meal, lime, and dical. A ton of each ingredient contained a certain amount of each nutrient, e.g., a ton of corn contained 3,500 units of the ME: Poultry nutrient. The nutrient contents, together with the current cost of each ingredient, are given in Exhibit 2.

The basic feed formulation problem faced by Smith, then, was to determine a combination of the raw ingredients that satisfied the nutrient requirements for each product, at minimum cost.

In deciding on a mixture for each end product, Mr. Smith needed to ensure that the combination of ingredients that were selected to make up a ton of a product did not, in fact, weigh more than one ton. If the combined ingredients weighed less than one ton, the weight difference could be made up by adding non-nutritive filler at essentially no cost.

Jeff Smith’s Problem

The company’s head office had received an order for 168 tons of meat meal from the Burlington plant to the following week. This was the amount of meat meal the plant needed to fulfill its orders, using the standard mixing formulae then in effect. As there were only 80 tons in stock, Smith has been advised of the shortage.

In evaluating the current formulae for the three mixes sold in the Burlington plant, Smith noted that each required meat meal. He was well aware that the availability of meat meal was determined by the month’s purchase contracts, and that the meat meal on hand had a weighted average cost of $339.00 per ton. Any additional requirements would have to be bid for on the spot market. The spot market was managed by independent commodity brokers who could supply on short notice, but at a significantly higher price.

The constraints of a maximum availability of 80 tons of meat meal could be taken into consideration and the formular recalculated, or a spot market bid could be made. The immediate problem was to determine an appropriate bid, if one was to be made on the next day’s market, or to determine new mix formulae with the meat meal limitation taken into account. The result of whatever action was taken would have to be sent back to the plant by Friday morning.

Their other ingredient were not in short supply, even if the formulae changed somewhat, since inventories had been built up for the summer season.

Exhibit 1

Demand and required nutrients for each product – Burlington Plant

Product	15% Pig Grower	40% Pig Supplement	17% Cage Layer
Demand for coming week (tons)	400	120	600
Units of nutrients required per ton
ME: Poultry ME: Swine Protein Calcium Phosphates Lysine Methionine Meth & Cystine Tryptophane	0 3000 15 0.75 0.60 0.61 0.20 0.30 0.10	0 2500 40 5.50 2.50 2.00 0.45 0.80 0.25	2675 0 17 3.80 0.70 0.68 0.28 0.48 0.15

Exhibit 2

Nutrient makeup and cost of ingredients

Ingredient	Corn	Barley	Soyameal	Meat Meal	Lime	Dical
Cost per ton ($):	127	145	314	339	25	405
Nutrient Makeup (units of nutrient per ton of ingredient):
ME: Poultry ME: Swine Protein Calcium Phosphates Lysine Methionine Meth & Cystine Tryptophane	3500 3325 8.70 0.02 0.28 0.20 0.20 0.33 0.09	2865 2870 10.00 0.06 0.33 0.35 0.15 0.32 0.12	2530 3485 48.4 0.30 0.69 3.20 0.70 1.44 0.63	1984 2540 50.9 9.70 4.02 2.82 0.62 1.24 0.31	- - - 39 - - - - -	- - - 16.75 21.0 - - - -

• Formulate the mix problem for each product separately. What are the minimum cost solutions?
• Would the formulation differ if all three products were included together?
• Solve the combined problem. Then add the 80-ton meat meal constraint and solve again.
• Determine a spot market bid (price and quantity) (or bids) for meat meal.
• What would Smith's options be if he could purchase as much meat meal as needed at $365 per ton?
• Does the optimization provide any information that would be helpful in planning ingredient purchases?
• How might the feed formulator incorporate ingredient inventories into the formulation problem?

Discussion questions to address once you have used Solver for the assigned problems above.