Sweetland Sugar &Co. produces cane sugar in its three plants in Tampa, Mobile, a

Question

Sweetland Sugar &Co. produces cane sugar in its three plants in Tampa, Mobile, and Houston It has four distribution centers in Charlotte, Kansas City, Indianapolis, and Flagstaff. These distribution centers serve five major markets, New York, Chicago, St. Louis, Las Vegas, and Seattle. The capacities of each plant, demands of each market and the transportation costs of sending a ton sugar from a plant to distribution center and from a distribution center to a market are given in the tables below. The company seeks to develop a plan to minimize the transportation costs.

a) Determine the objective function and constraints.

b) Find the minimum cost and the amounts of sugar sent from each plant to distribution centers and from each distribution center to markets using Excel Solver.

From

Plants

To Distribution Center

Supply

(Tons)

Charlotte

Kansas City

Indianapolis

Flagstaff

Tampa

$13

$17

$18

$25

20,000

Mobile

$16

$15

$15

$22

18,000

Houston

$18

$13

$17

$18

25,000

From

Distribution

Centers

To Markets

New York

Chicago

St. Louis

Las Vegas

Seattle

Charlotte

$16

$13

$12

$22

$25

Kansas City

$20

$11

$6

$15

$18

Indianapolis

$10

$8

$8

$17

$19

Flagstaff

$25

$18

$15

$8

$15

Demand

(tons)

15,000

12,000

9,000

14,000

13,000

From

Plants

To Distribution Center

Supply

(Tons)

Charlotte

Kansas City

Indianapolis

Flagstaff

Tampa

$13

$17

$18

$25

20,000

Mobile

$16

$15

$15

$22

18,000

Houston

$18

$13

$17

$18

25,000

Explanation / Answer

As mentioned in the question, the objective is to have minimum total cost of transportation to meet the demands at the demand centers.

Let us define Decision Variables Xij as the nember of units transported from ith place to the jth place and Cij is the corresponding unit cost of transportatation from ith place to jth place.

Therefore Objective is to Minimize Sigma (i,j) CijXij

Constraints are in terms of availability of units at the ith place and demands at the jth place.

Formulation as per transportation problem format is as follows:

Formulation and solution using excel solver is as follows:

Solution using excel solver

Answer b

From To Distribution Center & Markets Supply Plants&Centers Charlotte Kansas City Indianapolis Flagstaff New York Chicago St. Louis Las Vegas Seattle (Tons) Tampa $13 $17 $18 $25 20,000 Mobile $16 $15 $15 $22 18,000 Houston $18 $13 $17 $18 25,000 Charlotte $16 $13 $12 $22 $25 Kansas City $20 $11 $6 $15 $18 Indianapolis $10 $8 $8 $17 $19 Flagstaff $25 $18 $15 $8 $15 Demand 15,000 12,000 9,000 14,000 13,000

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