Midwest Grain Elevator performs storage and handling services for buyers and sellers of grain on a service fee basis. To achieve maximum profit Midwest must maximize the amount of grain it handles. In order to accomplish this objective, Midwest must build customer loyalty on the part of both buyers and sellers of grain. Thus, Midwest's preferred policy is to encourage repeat business by satisfying buyers' orders at minimum cost. This policy benefits sellers as well as by increasing the number of orders for high quality grain that can be filled.
Currently Midwest is storing 507,900 bushels of corn for Saw Mill River Feed & Grain Company. This corn has been classified into 26 different types, which differ by moisture content, weight per bushel, amount of damage, and amount of foreign material.
Saw Mill has limited quantities of each of the 26 types of corn. The ability to meet an order is obviously restricted by this supply. The quantities and cost of each type of corn is detailed in the table shown below.
Corn Type Supply Cost
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1 15000 1.50
2 30000 1.45
3 45000 1.44
4 25000 1.45
5 40000 1.42
6 20000 1.38
7 30000 1.37
8 75000 1.37
9 15000 1.39
10 50000 1.39
11 16000 1.27
12 20000 1.28
13 10000 1.17
14 12000 1.22
15 6000 1.12
16 2000 1.18
17 5000 1.42
18 4000 1.42
19 5000 1.42
20 6000 1.36
21 1300 1.29
22 29000 1.29
23 1900 1.42
24 33000 1.40
25 6700 1.22
26 5000 1.30
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Saw Mill has now received an order for 6 different grades of
corn totaling 272,000 bushels which it intends to fill from the
grain stored with Midwest.
The Saw Mill must meet the stated demand for each of the 6 grades.
Exceeding demand would be ill-advised, since there is no guarantee
that the next order filled will require the same characteristics.
The demand for each type of grade is shown in the table below.
Corn Grade Demand
Corn Grade Demand
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Gr1 40000
Gr2 32000
Gr3 50000
Gr4 20000
Gr5 30000
Gr6 100000
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Midwest's handling fee will be based on supplying the 272,000
bushels of corn, regardless of the manner in which the various corns
are blended to meet the specifications. However, in keeping with
the policy of providing quality service to other buyers and sellers,
the problem Midwest faces is that of determining the least cost
blend of available grains that will satisfy the specified criteria
of the current order.
Each of the 6 grades of corn demanded must meet specified criteria for moisture content,
minimum weight per bushel, percentage damaged, and percentage of foreign material,
which are detailed in the table below.
Corn Grade Characteristics
Grade MaxMoisture MinWeight MaxDamage MaxForeign
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Gr1 13.0 56.0 2.0 2.0
Gr2 15.5 54.0 5.0 3.0
Gr3 15.0 56.0 2.0 4.0
Gr4 16.0 54.0 9.0 4.0
Gr5 23.0 54.0 10.0 6.0
Gr6 20.0 54.0 9.0 4.0
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For each of the 6 grades the four quality requirements are as follows:
The quality characteristics for each of the 26 corn types is given in the table below.
Corn Type Moisture Weight Damage Foreign
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1 11.0 58.0 3.0 1.0
2 12.0 57.0 2.0 1.5
3 15.0 57.0 2.0 1.0
4 12.0 58.0 3.0 3.0
5 13.0 56.0 4.0 2.0
6 15.0 54.0 4.0 2.0
7 15.0 55.0 5.0 3.0
8 18.0 57.0 5.0 1.0
9 14.0 58.0 2.0 4.0
10 15.0 55.0 3.0 2.0
11 17.0 53.0 7.0 5.0
12 15.0 55.0 8.0 3.0
13 22.0 56.0 8.0 5.0
14 18.0 54.0 13.0 5.0
15 17.0 55.0 20.0 8.0
16 13.5 57.0 30.0 2.0
17 13.5 57.0 3.0 2.0
18 13.5 57.5 3.0 2.0
19 13.5 57.0 5.0 3.0
20 15.0 56.5 10.0 4.0
21 13.5 58.0 15.0 4.0
22 13.0 57.0 15.0 5.0
23 13.0 58.0 3.0 2.0
24 13.0 56.0 5.0 3.0
25 14.0 56.0 20.0 5.0
26 15.0 56.5 10.0 4.0
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The objective for this problem is to determine the number of bushels used in the blending for each of the 26 types of corn so the the total cost of the 6 desired grades of corn is minimized.
Submitted by Prof. Ramesh Sharda, Operations Research Dept., Oklahoma State University