Stateline Shipping and Transport Company The transportation model will be set up by assigning a variable to each site. The plants Danville, Selma, and Columbus are 1, 2 and 3 respectively. This makes the waste disposal sites at White Water, Los Canos, Duras variables A, B and C, respectively.
Decision variables: 1. Ship from 1: x1A, x1B, x1C 2. Ship from 2; x2A, x2B, x2C, 3. Ship from 3: x3A, x3B, x3C,
The objective function is:
Min. cost Z= 14x1A+9x1B+10x1C+17x2A+16x2B+19x2C+7x3A+14x3B+12x3C
There will be one constraint for each location regardless of how many variables.
Plant constraints:
Output from plant 1: x1A + x1B + x1C =26
Output from plant 2: x2A + x2B + x2C = 53
Output from plant 3: x3A + x3B + x3C = 29
Waste disposal site constraints:
Intake at site A: x1A + x2A + x3A ≤65
Intake at site B: x1B + x2B + x3B ≤80
Intake at site C: x1C + x2C + x3C ≤105
Once the data solver is set up the model comes up with this solution:
Ship all Danville and Selma waste to Los Canos and all Columbus Waste to White Water to get a shipping cost of $1285.00

3. The transshipment model will follow the same logic as the transportation when setting up the variables. There will be a variable for each shipment from plant to plant, plant to waste disposal site and waste disposal site to waste disposal site. I started out
Decision variables: 1. Ship from 1: x12, x13, x1A, x1B, x1C 2. Ship from 2; x21, x23, x2A, x2B, x2C, 3. Ship from 3: x31, x32, x3A, x3B, x3C, 4. Ship from A: xAB, xAC, 5. Ship from B: xBA, xBC, 6. Ship from C: xCA, xCB
Once the decision variables are found, the objective function can be determine by attaching the shipping costs to each variable and adding them together. The objective will look like this when done.
Objective function:
Z = 10x12 +12x13 +14x1a +9x1b +10x1c +10x21 +3x23 +17x2a +16x2b +19x2c +12x31 +3x32 +7x3a +14x3b +12x3c +12xab +10xac +12xba +15xbc +10xca +15xcb
There will be one constraint for each location regardless of how many variables. These constraints will be set using two rules.
* For each plant the output of waste added together minus the intake of waste must equal the amount of waste for each plant. With that rule you get the following three constraints: x12 + x13 + x1a +x1b +x1c -x21-x31 = 26 x21 + x23 + x2a +x2b +x2c -x12-x32 = 53 x31 + x32 + x3a + x3b + x3c - x13- x23 = 29
*For each waste disposal site the intake of waste added together minus the output of waste must be less than or equal to the amount of waste for each plant. With that rule you get the following three constraints: x1A + x2A + x3A + xBA + xCA – xAB – xAC ≤65 x1B + x2B + x3B + xAB + xCB – xBA – xBC ≤ 80 x1c + x2c + x3c + xAc + xBc – xcA – xCb ≤ 105 once this information is entered into the transshipment model, the data solver can be used to get the answer, which is $1052.00.
According to the transshipment model, the least expensive way to ship all waste:
Ship all 26 gallons of waste from Danville to Los Canos
Ship all 53 gallons of waste from Selma to Columbus
Ship 12 gallons of Columbus waste plus the 53 gallons from Selma to White water and the remaining 17 gallons of Columbus waste to Duras.

Since the company will save $233.00 a week by using the transshipment method it is a viable option for her to pursue.