The North West Corner Rule
The North West corner rule is a technique used to compute a basic and feasible solution for a transportation problem. In this technique, the basic variables are chosen from the North West corner, or as it would appear in a table, the top left corner.
The economic problem at this point is to distribute the available bushels of olives to the different retail outlet destinations in a manner that keeps the transportation cost at a minimum.
The number of retail outlets (n) = 7
The number of distribution centers (m) = 6
The number of basic variables = m + n – 1 = 6 + 7 – 1 = 13 – 1 = 12
The total transportation cost incurred is calculated by multiplying the Xij in every occupied cell with its corresponding Cij and then adding them together.
= (38.43 * 150) + (37.25 * 150) + (29.55 * 100) + (38.87 * 100) + (39.52 * 250) + (35.98 * 150) + (36.45 * 175) + (38.27 * 250) + (39.33 * 75) + (46.33 * 75) + (28.00 * 125) + (25.90 * 300)
= 5764.5 + 5587.5 + 2955 + 3887 + 9880 + 5397 + 6378.75 + 9567.5 + 2949.75 + 3474.75 + 3500 + 7770
= 67111.75dollars
The Least Cost Method
The cell with the least transport const is G1.
Total transportation cost =
(24.08*300) + (29.55 * 25) + (29.37 * 50) + (25.40 * 125) + (35.98 * 250) + (36.97 * 150) + (28.01 * 150) + (29.70 * 350) + (28.88 * 200) + (31.44 * 225) + (34.88 * 75)
= 7224 + 738.75 + 1468.5 + 3175 + 8995 + 5545.5 + 4201.5 + 10395 + 5776 + 7074 + 2616
= 57209.25dollars
Summary of the findings
Using the North West corner rule, the total cost of transportation is 67111.75dollars.
Using the Least Cost rule, the total cost of transportation is 57209.25dollars
The difference in cost between the two methods is 9902.5 dollars.
I hereby recommend that the operations manager uses the least cost methods
Operators required 156
Shift cost
Shift1 = 30 * 4 = 120 * 14 = 1680
Shift2 = 30 * 2 = 60 * 10 = 600
Shift2 = 20 * 2 = 40 * 2 = 80
Shift3 = 20 * 4 = 80 * 8 = 640
Shift4 = 20 * 4 = 80 * 6 = 480
Shift5 = 20 * 4 = 80 * 10 = 800
Shift6 = 20 * 4 = 80 * 16 = 1280
Shift7 = 20 * 2 = 40 * 4 = 160
Shift7 = 30 * 2 = 60 * 4 = 240
Shift8 = 30 * 4 = 120 * 10 = 1200
Shift9 = 30 * 2 = 60 *10 = 600
Total daily cost is 7760
Definition of variables
X1 is the number of operators assigned to shift 1
X2 is the number of operators assigned to shift 2
X3 is the number of operators assigned to shift 3
X4 is the number of operators assigned to shift 4
X5 is the number of operators assigned to shift 5
X6 is the number of operators assigned to shift 6
X7 is the number of operators assigned to shift 7
X8 is the number of operators assigned to shift 8
X9 is the number of operators assigned to shift 9
Objective function
The minimum cost is (120 * 1) + (100 * 2) + (80 * 3) + (80 * 4) + (80 * 5) + (80 * 6) + (100 * 7) + (120 * 8) + (60 * 9)
Constraints
X1 ≥ 14
X1 + X2 ≥24
X2 + X3 ≥18
X3 + X4 ≥14
X4 + X5 ≥16
X5 + X6 ≥26
X6 + X7 ≥20
X7 + X8 ≥14
X9 ≥10
