the transportation models
TRANSCRIPT
The Transportation Models
Transportation model is one of the class of linear programming models, so named because of the linear relationships among variables in transportation model, transportation cost are treated as a direct linear function of the number of units shipped.
Transportation models can be used to determine how to allocate the supplies available from various factories to the warehouses that stock or demand those goods, in such a way that total shipping cost (time, distance) is minimized.
The shipping (supply) points can be factories, warehouses, department or any other place from which goods are sent.
The destination (demand) can be factories, warehouses, departments or other place that receive goods.
Major assumptions for the transportation model
1. The items to be shipped are homogeneous.2. Shipping cost per unit is the same regardless of the number of units shipped.3. There is only one route or mode of transportation being used between each source and each destination.
The information needed to use the model
1. A list of the origins and each one’s capacity or supply quantity per period2. A list of the destinations and each one’s demand per period3. The unit cost of shipping items from each origin to each destination.
The transportation model starts with the development of a feasible solution, which is then sequentially tested and improved until an optimal solution is obtained.
Major Steps
1.Obtaining an initial solution2.Testing the solution for optimality3.Improving sub optimal solution
Approaches
1. Intuitive Lowest cost approach2. North West Corner stepping stone method3. Modified Transportation Approach
With the intuitive approach, cell allocations are made according to cell cost, beginning with the lowest cost. The procedure involves these steps:
Intuitive Lowest-Cost Method
Intuitive Lowest-Cost Method
1. Identify the cell with the lowest cost2. Allocate as many units as possible to that cell
without exceeding supply or demand; then cross out the row or column (or both) that is exhausted by this assignment
3. Find the cell with the lowest cost from the remaining cells
4. Repeat steps 2 and 3 until all units have been allocated
Intuitive Lowest-Cost Method
To
From Albuquerque Boston Cleveland
Des Moines $5 $4 $3
Evansville $8 $4 $3
Fort Lauderdale $9 $7 $5
Intuitive Lowest-Cost Method
Albuquerque(300 unitsrequired)
Des Moines(100 unitscapacity)
Evansville(300 unitscapacity)
Fort Lauderdale(300 unitscapacity)
Cleveland(200 unitsrequired)
Boston(200 unitsrequired)
Figure C.1
Transportation Matrix
From
ToAlbuquerque Boston Cleveland
Des Moines
Evansville
Fort Lauderdale
Factory capacity
Warehouse requirement
300
300
300 200 200
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
Cost of shipping 1 unit from FortLauderdale factory to Boston warehouse
Des Moinescapacityconstraint
Cell representing a possible source-to-destination shipping assignment (Evansville to Cleveland)
Total demandand total supply
Clevelandwarehouse demand
Figure C.2
Intuitive Lowest-Cost MethodTo (A)
Albuquerque(B)
Boston(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse requirement 300 200 200
Factory capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
First, $3 is the lowest cost cell so ship 100 units from Des Moines to Cleveland and cross off the first row as Des Moines is satisfied
Figure C.4
Intuitive Lowest-Cost MethodTo (A)
Albuquerque(B)
Boston(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse requirement 300 200 200
Factory capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
Second, $3 is again the lowest cost cell so ship 100 units from Evansville to Cleveland and cross off column C as Cleveland is satisfied
Figure C.4
Intuitive Lowest-Cost MethodTo (A)
Albuquerque(B)
Boston(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse requirement 300 200 200
Factory capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
200
Third, $4 is the lowest cost cell so ship 200 units from Evansville to Boston and cross off column B and row E as Evansville and Boston are satisfied
Figure C.4
Intuitive Lowest-Cost MethodTo (A)
Albuquerque(B)
Boston(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse requirement 300 200 200
Factory capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
200
300
Finally, ship 300 units from Albuquerque to Fort Lauderdale as this is the only remaining cell to complete the allocations
Figure C.4
Intuitive Lowest-Cost MethodTo (A)
Albuquerque(B)
Boston(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse requirement 300 200 200
Factory capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
200
300
Total Cost = $3(100) + $3(100) + $4(200) + $9(300)= $4,100
Figure C.4
Intuitive Lowest-Cost MethodTo (A)
Albuquerque(B)
Boston(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse requirement 300 200 200
Factory capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
200
300
Total Cost = $3(100) + $3(100) + $4(200) + $9(300)= $4,100
Figure C.4
This is a feasible solution, and an improvement over the previous solution,
but not necessarily the lowest cost alternative