Transportation, Transshipment and Assignment Models and Assignment Models.
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Transcript of Transportation, Transshipment and Assignment Models and Assignment Models.
TransportationTransportation, Transshipment, Transshipment
and and Assignment ModelsAssignment Models
Learning ObjectivesLearning Objectives
• Structure special LP network flow models.• Set up and solve transportation models • Extend basic transportation model to include
transshipment points.• Set up and solve facility location and other application
problems as transportation models.• Set up and solve assignment models
OverviewOverview
Part of a larger class of linear programming problems are known as network flow models.
They possess special mathematical features that enabled the development of very efficient, unique solution methods.
Transportation ModelTransportation Model
Transportation problem deals with the distribution of goods from several points of supply to a number of points of demand. They arise when a cost-effective pattern is needed to ship items from origins that have limited supply to destinations that have demand for the goods.
Resources to be optimally allocated usually involve a given capacity of goods at each source and a given requirement for the goods at each destination.
Most common objective of the transportation problem is to schedule shipments from sources to destinations so that total production and transportation costs are minimized
Transshipment ModelTransshipment Model
An extension of transportation problems is called transshipment problem in which a point can have shipments that both arrive as well as leave.
Example would be a warehouse where shipments arrive from factories and then leave for retail outlets
It may be possible for a firm to achieve cost savings (economies of scale) by consolidating shipments from several factories at a warehouse and then sending them together to retail outlets.
Assignment ModelAssignment Model
Assignment problem refers to a class of LP problems that involve determining most efficient assignment of:
People to projects,
Salespeople to territories,
Contracts to bidders,
Jobs to machines, and so on
Objective is to minimize total cost or total time of performing tasks at hand, although a maximization objective is also possible.
Transportation ModelTransportation Model
Problem definition
– There are m sources. Source i has a supply capacity of Si.
– There are n destinations.The demand at destination j is D j.
– Objective:
To minimize the total shipping cost of supplying the
destinations with the required demand from the available supplies at the sources.
Transportation ModelTransportation Model
The Transportation ModelThe Transportation ModelCharacteristicsCharacteristics
A product is to be transported from a number of sources to a number of destinations at the minimum possible cost.
Each source is able to supply a fixed number of units of the product, and each destination has a fixed demand for the product.
The linear programming model has constraints for supply at each source and demand at each destination.
All constraints are equalities in a balanced transportation model where supply equals demand.
Constraints contain inequalities in unbalanced models where supply is not equal to demand.
Transportation ModelTransportation Model- - Example 1Example 1
Executive Furniture Corporation
Transportation ModelTransportation Model Example 1Example 1
Executive Furniture Corporation
Transportation Costs Per Desk
Transportation ModelTransportation Model Example 1Example 1
Objective: minimize total shipping costs =
5 XDA + 4 XDB + 3 XDC + 3 XEA + 2 XEB +
1 XEC + 9 XFA + 7 XFB + 5 XFC
Executive Furniture Corporation:LP Transportation Model Formulation
Where: Xij = number of desks shipped from factory i to warehouse j
i = D (for Des Moines),
E (for Evansville), or
F (for Fort Lauderdale).
j = A (for Albuquerque),
B (for Boston), or
C (for Cleveland).
Transportation ModelTransportation Model Example 1Example 1
Net flow at Des Moines = (Total flow in) - (Total flow out)
= (0) - (XDA + XDB + XDC)
Net flow at Des Moines =
-XDA - XDB - XDC = -100 (Des Moines capacity) and
-XEA - XEB - XEC = -300(Evansville capacity)
-XFA - XFB - XFC = -300 (Fort Lauderdale capacity)
Multiply each constraint by -1 and rewrite as:
XDA + XDB + XDC = 100 (Des Moines capacity)
XEA + XEB + XEC = 300 (Evansville capacity)
XFA + XFB + XFC = 300 (Fort Lauderdale capacity)
Executive Furniture Corporation: Supply Constraints
Transportation ModelTransportation Model Example 1Example 1
Executive Furniture Corporation: Demand Constraints Net flow at Albuquerque = (Total flow in) - (Total flow out)
= (XDA + XEA + XFA) - (0)
Net flow at Albuquerque =
XDA + XEA + XFA = 300 (Albuquerque demand) and
XDB + XEB + XFB = 200 (Boston demand)
XDC + XEC + XFC = 200 (Cleveland demand)
Transportation Model Transportation Model Example 1:Example 1:The Optimum SolutionThe Optimum Solution
SHIP:
100 desks from Des Moines to Albuquerque,
200 desks from Evansville to Albuquerque,
100 desks from Evansville to Boston,
100 desks from Fort Lauderdale to Boston,
and 200 desks from Fort Lauderdale to Cleveland.
Total shipping cost is $3,000.
Grain Elevator Supply Mill Demand
1. Kansas City 150 A. Chicago 200
2. Omaha 175 B. St. Louis 100
3. Des Moines 275 C. Cincinnati 300
Total 600 tons Total 600 tons
Transport Cost from Grain Elevator to Mill ($/ton)
Grain Elevator A. Chicago B. St. Louis C. Cincinnati 1. Kansas City 2. Omaha 3. Des Moines
$ 6 7 4
$ 8 11 5
$10 11 12
Transportation Model ExampleTransportation Model Example 2 2Problem Definition and DataProblem Definition and Data
Problem: How many tons of wheat to transport from each grain elevator to each mill on a monthly basis in order to minimize the total cost of transportation?
Data:
Transportation Model ExampleTransportation Model Example 2 2Model Formulation Model Formulation
Minimize Z = $6x1A + 8x1B + 10x1C + 7x2A + 11x2B + 11x2C + 4x3A + 5x3B + 12x3C
subject to:x1A + x1B + x1C = 150
x2A + x2B + x2C = 175 x3A + x3B + x3C = 275 x1A + x2A + x3A = 200 x1B + x2B + x3B = 100 x1C + x2C + x3C = 300 xij 0
xij = tons of wheat from each grain elevator, i, i = 1, 2, 3, to each mill j, j = A,B,C
Transportation Model ExampleTransportation Model Example 2 2Model Formulation Model Formulation
Transportation ModelTransportation Model- Example 3- Example 3
• Carlton Pharmaceuticals supplies drugs and other medical supplies.
• It has three plants in: Cleveland, Detroit, Greensboro.
• It has four distribution centers in: Boston, Richmond, Atlanta, St. Louis.
• Management at Carlton would like to ship cases of a certain vaccine as economically as possible.
Carlton Pharmateuticals
• Data– Unit shipping cost, supply, and demand
• Assumptions– Unit shipping cost is constant.– All the shipping occurs simultaneously.– The only transportation considered is between
sources and destinations.– Total supply equals total demand.
To From Boston Richmond Atlanta St. Louis Supply Cleveland $35 30 40 32 1200 Detroit 37 40 42 25 1000 Greensboro 40 15 20 28 800 Demand 1100 400 750 750
NETWORK
REPRESENTATION
Boston
Richmond
Atlanta
St.Louis
Destinations
Sources
Cleveland
Detroit
Greensboro
S1=1200
S2=1000
S3= 800
D1=1100
D2=400
D3=750
D4=750
37
40
42
32
35
40
30
25
4015
20
28
• The Mathematical Model
– The structure of the model is:
Minimize <Total Shipping Cost>
ST
[Amount shipped from a source] = [Supply at that source]
[Amount received at a destination] = [Demand at that destination]
– Decision variablesXij = amount shipped from source i to destination j.
where: i=1 (Cleveland), 2 (Detroit), 3 (Greensboro) j=1 (Boston), 2 (Richmond), 3 (Atlanta), 4(St.Louis)
Boston
Richmond
Atlanta
St.Louis
D1=1100
D2=400
D3=750
D4=750
The supply constraints
Cleveland S1=1200
X11
X12
X13
X14
Supply from Cleveland X11+X12+X13+X14 = 1200
DetroitS2=1000
X21
X22
X23
X24
Supply from Detroit X21+X22+X23+X24 = 1000
GreensboroS3= 800
X31
X32
X33
X34
Supply from Greensboro X31+X32+X33+X34 = 800
• The complete mathematical model
Minimize 35X11+30X12+40X13+ 32X14 +37X21+40X22+42X23+25X24+ 40X31+15X32+20X33+38X34
ST
Supply constrraints:X11+ X12+ X13+ X14 1200
X21+ X22+ X23+ X24 1000X31+ X32+ X33+ X34 800
Demand constraints: X11+ X21+ X31 1000
X12+ X22+ X32 400X13+ X23+ X33 750
X14+ X24+ X34 750
All Xij are nonnegative
===
====
Excel Optimal SolutionExcel Optimal Solution
CARLTON PHARMACEUTICALS
UNIT COSTSBOSTON RICHMOND ATLANTA ST.LOUIS SUPPLIES
CLEVELAND 35.00$ 30.00$ 40.00$ 32.00$ 1200DETROIT 37.00$ 40.00$ 42.00$ 25.00$ 1000GREENSBORO 40.00$ 15.00$ 20.00$ 28.00$ 800
DEMANDS 1100 400 750 750
SHIPMENTS (CASES)BOSTON RICHMOND ATLANTA ST.LOUIS TOTAL
CLEVELAND 850 350 0 0 1200DETROIT 250 0 0 750 1000GREENSBORO 0 50 750 0 800
TOTAL 1100 400 750 750 TOTAL COST = 84000
Range of optimality
WINQSB Sensitivity AnalysisWINQSB Sensitivity Analysis
If this path is used, the total cost will increase by $5 per unit shipped along it
Range of feasibility
Shadow prices for warehouses - the cost incurred from having 1 extra case of vaccine demanded at the warehouse
Shadow prices for plants - the cost savings realized for each extra case of vaccine available at the plant
Interpreting sensitivity analysis resultsInterpreting sensitivity analysis results
– Reduced costs
• The amount of transportation cost reduction per unit that
makes a given route economically attractive.
• If the route is forced to be used under the current cost structure, for each item shipped along it, the total cost increases by an amount equal to the reduced cost.
– Shadow prices
• For the plants, shadow prices convey the cost savings realized for each extra case of vaccine available at plant.
• For the warehouses, shadow prices convey the cost incurred from having an extra case demanded at the warehouse.
Transportation ModelTransportation Model- Example 4- Example 4
Montpelier Ski Company: Using a Transportation model for production scheduling
– Montpelier is planning its production of skis for the months of July, August, and September.
– Production capacity and unit production cost will change from month to month.
– The company can use both regular time and overtime to produce skis.
– Production levels should meet both demand forecasts and end-of-quarter inventory requirement.
– Management would like to schedule production to minimize its costs for the quarter.
• Data:
– Initial inventory = 200 pairs
– Ending inventory required =1200 pairs
– Production capacity for the next quarter is shown on the table
– Holding cost rate is 3% per month per ski.
– Production capacity, and forecasted demand for this quarter (in pairs of skis), and production cost per unit (by months)
Forecasted Production Production Costs Month Demand Capacity Regular Time OvertimeJuly 400 1000 25 30August 600 800 26 32September 1000 400 29 37
• Analysis of demand:
– Net demand to satisfy in July = 400 - 200 = 200 pairs
– Net demand in August = 600
– Net demand in September = 1000 + 1200 = 2200 pairs
• Analysis of Supplies:
– Production capacities are thought of as supplies.
– There are two sets of “supplies”:
• Set 1- Regular time supply (production capacity)
• Set 2 - Overtime supply
Initial inventory
Forecasted demand In house inventory• Analysis of Unit costs
Unit cost = [Unit production cost] +
[Unit holding cost per month][the number of months stays in inventory]
Example: A unit produced in July in Regular time and sold in September costs 25+ (3%)(25)(2 months) = $26.50
Network representation
252525.7525.7526.5026.50 00 3030
30.9030.9031.8031.80
00+M+M
2626
26.7826.78
00
+M+M
3232
32.9632.96
00
+M+M
+M+M
2929
00
+M+M
+M+M
3737
00
ProductionMonth/period
Monthsold
JulyR/T
July O/T
Aug.R/T
Aug.O/T
Sept.R/T
Sept.O/T
July
Aug.
Sept.
Dummy
1000
500
800
400
400
200
200
600
300
2200
Demand
Prod
uctio
n Ca
pacit
y
July R/T
Source: July production in R/TDestination: July‘s demand.
Source: Aug. production in O/TDestination: Sept.’s demand
32+(.03)(32)=$32.96Unit cost= $25 (production)Unit cost =Production+one month holding cost
• Summary of the optimal solution
– In July produce at capacity (1000 pairs in R/T, and 500 pairs in
O/T). Store 1500-200 = 1300 at the end of July.
– In August, produce 800 pairs in R/T, and 300 in O/T. Store
additional 800 + 300 - 600 = 500 pairs.
– In September, produce 400 pairs (clearly in R/T). With 1000
pairs
retail demand, there will be
(1300 + 500) + 400 - 1000 = 1200 pairs available for shipment
Inventory + Production -
Demand
Unbalanced Transportation ProblemsUnbalanced Transportation Problems
• If supplies are not equal to demands, an unbalanced transportation model exists.
• In an unbalanced transportation model, supply or demand constraints need to be modified.
• There are two possible scenarios:
(1)Total supply exceeds total requirement.
(2)Total supply is less than total requirement.
Total Supply Exceeds Total RequirementTotal Supply Exceeds Total Requirement
Total flow out of Des Moines ( XDA + XDB + XDC) should be
permitted to be smaller than total supply (100).
The constraint should be written as
-XDA - XDB - XDC >= -100 (Des Moines capacity)
-XEA - XEB - XEC >= -300 (Evansville capacity)
-XFA - XFB - XFC >= -300 (Fort Lauderdale capacity)
XDA + XDB + XDC <= 100
XEA + XEB + XEC <= 100
XFA + XFB + XFC <= 100
Total Supply Less Than Total RequirementTotal Supply Less Than Total Requirement
Total flow in to Albuquerque (that is, XDA + XEA + XFA) should
be permitted to be smaller than total demand (namely, 300).
This warehouse should be written as:
XDA + XEA + XFA <= 300 (Albuquerque demand)
XDB + XEB + XFB <= 200 (Boston demand)
XDC + XEC + XFC <= 200 (Cleveland demand)
Develop the linear programming model and solve using Excel:
Construction site Plant A B C Supply (tons)
1 2 3
$ 8 15
3
$ 5 10 9
$ 6 12 10
120 80 80
Demand (tons) 150 70 100
Transportation Transportation Example Example 5: Formulation5: Formulation
Minimize Z = $8x1A + 5x1B + 6x1C + 15x2A + 10x2B + 12x2C + 3x3A + 9x3B + 10x3C
subject to:x1A + x1B + x1C = 120 x2A + x2B + x2C = 80
x3A + x3B + x3C = 80x1A + x2A + x3A 150 x1B + x2B + x3B 70
x1C + x2C + x3C 100 xij 0
Transportation Transportation Example Example 5: Formulation 5: Formulation
Transportation Model-Example 6Transportation Model-Example 6 Hardgrave Machine Company - New Factory Location
• Produces computer components at its plants in Cincinnati, Kansas City, and Pittsburgh.
• Plants not able to keep up with demand for orders at four warehouses in Detroit, Houston, New York, and Los Angeles.
• Firm has decided to build a new plant to expand its productive capacity.
• Two sites being considered:
– Seattle, Washington and
– Birmingham, Alabama.
• Both cities attractive in terms: labor supply, municipal services, and ease of factory financing.
Transportation Model-Example 6Transportation Model-Example 6Hardgrave Machine Company: Demand Supply Data and Production Costs
Transportation Model-Example 6Transportation Model-Example 6Hardgrave Machine Company: Shipping Costs
Transshipment ModelTransshipment Model
Transshipment ModelTransshipment Model
In a Transshipment Problem flows can occur both out of and into the
same node in three ways:
1. If total flow into a node is less than total flow out from node,
node represents a net creator of goods (a supply point).
- Flow balance equation will have a negative right hand
side (RHS) value.
2. If total flow into a node exceeds total flow out from node,
node represents a net consumer of goods, (a demand point).
- Flow balance equation will have a positive RHS value.
3. If total flow into a node is equal to total flow out from node,
node represents a pure transshipment point.
- Flow balance equation will have a zero RHS value.
It is an extension of the transportation model.
Intermediate transshipment points are added between the sources and destinations.
Items may be transported from:
Sources through transshipment points to destinations
One source to another
One transshipment point to another
One destination to another
Directly from sources to to destinations
Some combination of these
The Transshipment ModelThe Transshipment ModelCharacteristicsCharacteristics
Executive Furniture Corporation – RevisitedExecutive Furniture Corporation – Revisited
Assume it is possible for Executive Furniture to ship desks from Evansville factory to its three warehouses at very low unit shipping costs.
Consider shipping all desks produced at other two factories (Des Moines and Fort Lauderdale) to Evansville.
Consider using a new shipping company to move desks from Evansville to all its warehouses.
Executive Furniture Corporation - RevisitedExecutive Furniture Corporation - Revisited
• Revised unit shipping costs are shown here.
• Note Evansville factory shows up in both the “From” and “To” entries.
LP Model for theTransshipment Problem Two new additional decision variables for new shipping
routes are to be added.
XDE= number of desks shipped from Des Moines to Evansville
XFE = number of desks shipped from Fort Lauderdale to Evansville
Objective Function: minimize total shipping costs =
5XDA + 4XDB + 3XDC + 2XDE + 3XEA + 2XEB +
+1XEC + 9XFA + 7XFB + 5XFC + 3XFE
Executive Furniture CoExecutive Furniture Corporation Revisitedrporation Revisited
Executive Furniture CoExecutive Furniture Corporation Revisitedrporation Revisited
• Relevant flow balance equations written as:
(0) - (XDA + XDB + XDC + XDE) = -100 (Des Moines capacity)
(0) - (XFA + XFB + XFC + XFE) = -300 (Fort Lauderdale capacity)
• Supplies have been expressed as negative numbers in the RHS.
Net flow at Evansville = (Total flow in) - (Total flow out)
= (XDE + XFE) - (XEA + XEB + XEC)
• Net flow equals total number of desks produced (the supply) at Evansville.
Net flow at Evansville = (XDE + XFE) - (XEA + XEB + XEC) = -300
• No change in demand constraints for warehouse requirements:
XDA + XEA + XFA = 300 (Albuquerque demand)
XDB + XEB + XFB = 200 (Boston demand)
XDC + XEC + XFC = 200 (Cleveland demand)
LP Model for theTransshipment Problem
Extension of the transportation model in which intermediate transshipment points are added between sources and destinations. An example of a transshipment point is a distribution center or warehouse located between plants and stores
Data:
Stores Warehouses 6. Chicago 7. St. Louis 8. Cincinnati 3. Kansas 4. Omaha 5. Des Moines
$6 7
4
8 11 5
10 11 12
Transshipment Model ExampleTransshipment Model Example 2 2Problem Definition and Data Problem Definition and Data
Grain Elevator Farm 3. Kansas City 4. Omaha 5. Des Moines 1. Nebrasca 2. Colorado
$16 15
10 14
12 17
Transshipment Model ExampleTransshipment Model Example 2 2Problem Definition and Data Problem Definition and Data
Minimize Z = $16x13 + 10x14 + 12x15 + 15x23 + 14x24 + 17x25 + 6x36 + 8x37 + 10x38 + 7x46 + 11x47 +
11x48 + 4x56 + 5x57 + x58
subject to: x13 + x14 + x15 = 300x23+ x24 + x25 = 300x36 + x46 + x56 = 200x37+ x47 + x57 = 100x38 + x48 + x58 = 300x13 + x23 - x36 - x37 - x38 = 0x14 + x24 - x46 - x47 - x48 = 0x15 + x25 - x56 - x57 - x58 = 0xij 0
Transshipment Model ExampleTransshipment Model Example 2 2Model FormulationModel Formulation
Assignment ModelAssignment Model
The Assignment ModelThe Assignment Model
Problem definition– m workers are to be assigned to m jobs
– A unit cost (or profit) Cij is associated with worker i performing job j.
– Minimize the total cost (or maximize the total profit) of assigning workers to jobs so that each worker is assigned a job, and each job is performed.
It is a special form of linear programming models similar to the transportation model.
Supply at each source and demand at each destination is limited to one unit.
In a balanced model supply equals demand.
In an unbalanced model supply is not equal to demand.
The Assignment ModelThe Assignment ModelCharacteristicsCharacteristics
– The number of workers is equal to the number of jobs.
– Given a balanced problem, each worker is assigned exactly once, and each job is performed by exactly one worker.
– For an unbalanced problem “dummy” workers (in case there are more jobs than workers), or “dummy” jobs (in case there are more workers than jobs) are added to balance the problem.
The Assignment ModelThe Assignment Model Assumptions Assumptions
Fix-It Shop Example
Received three new rush projects to repair: (1) a radio, (2) a toaster oven, and (3) a broken coffee table. Three workers (each has different talents and abilities).Estimated costs to assign each worker to each of the three projects.
Assignment ModelAssignment Model Example 1 Example 1
Assignment Model Assignment Model Example 1 Example 1 Fix-It Shop
• Rows denote people or objects to be assigned, and columns denote tasks or jobs assigned.
• Numbers in table are costs associated with each particular assignment.
Assignment Assignment Model Example 1Model Example 1
• Owner's objective is to assign three projects to workers in a way that result is lowest total cost.
Fix-It Shop: Assignment Alternatives and Costs
Assignment Assignment Model Example 1 Model Example 1
• Owner's objective is to assign three projects to workers in a way that results in lowest total cost.
Fix-It Shop
Assignment ModelAssignment Model Example 1 Example 1
Formulate LP model -
Xij = “Flow” on arc from node denoting worker i to node denoting
project j.
Solution value will equal 1 if worker i is assigned to project j :
i = A (for Adams), B (for Brown), or C (for Cooper)
j = 1 (for project 1), 2 (for project 2), or 3 (for project 3)
Objective Function: minimize total assignment cost =
11XA1 + 14XA2 + 6XA3 + 8XB1 + 10XB2 + 11XB3 +
+ 9XC1 + 12XC2 + 7XC3
Fix-It Shop
Assignment Model Example 1 Assignment Model Example 1 Fix-It Shop
Constraints expressed using standard flow balance equations are as
follows:
-XA1 - XA2 - XA3 = -1 (Adams availability)
-XB1 - XB2 - XB3 = -1 (Brown availability)
-XC1 - XC2 - XC3 = -1 (Cooper availability)
XA1 + XB1 + XC1 = 1 (Project 1 requirement)
XA2 + XB2 + XC2 = 1 (Project 2 requirement)
XA3 + XB3 + XC3 = 1 (Project 3 requirement)
Assignment Model- Example 2 Assignment Model- Example 2
Ballston Electronics• Five different electrical devices produced on five
production lines, are needed to be inspected.• The travel time of finished goods to inspection areas
depends on both the production line and the inspection area.
• Management wishes to designate a separate inspection area to inspect the products such that the total travel time is minimized.
• Data: Travel time in minutes from assembly lines to inspection areas.
Inspection AreaA B C D E
1 10 4 6 10 12Assembly 2 11 7 7 9 14 Lines 3 13 8 12 14 15
4 14 16 13 17 175 19 17 11 20 19
Inspection AreaA B C D E
1 10 4 6 10 12Assembly 2 11 7 7 9 14 Lines 3 13 8 12 14 15
4 14 16 13 17 175 19 17 11 20 19
Assignment Model- Example 2Assignment Model- Example 2
Assignment Model Example 2: Network RepresentationAssignment Model Example 2: Network Representation(3 of 3)(3 of 3)
1
2
3
4
5
Assembly Line Inspection AreasA
B
C
D
E
S1=1
S2=1
S3=1
S4=1
S5=1
D1=1
D2=1
D3=1
D4=1
D5=1
• Computer solutions– A complete enumeration is not efficient even
for moderately large problems (with m=8, m! > 40,000 is the number of assignments to enumerate).
– The Hungarian method provides an efficient solution procedure.
• Special cases– A worker is unable to perform a particular job.– A worker can be assigned to more than one job.– A maximization assignment problem.
Assignment Model ExampleAssignment Model Example 3 3 Problem Definition and DataProblem Definition and Data
Problem: Assign four teams of officials to four games in a way that will minimize total distance traveled by the officials. Supply is always one team of officials, demand is for only one team of officials at each game.
Data:
Minimize Z = 210xAR + 90xAA + 180xAD + 160xAC + 100xBR + 70xBA + 130xBD + 200xBC + 175xCR + 105xCA +
140xCD + 170xCC + 80xDR + 65xDA + 105xDD + 120xDC
subject to: xAR + xAA + xAD + xAC = 1 xij 0xBR + xBA + xBD + xBC = 1xCR + xCA + xCD + xCC = 1xDR + xDA + xDD + xDC = 1xAR + xBR + xCR + xDR = 1xAA + xBA + xCA + xDA = 1xAD + xBD + xCD + xDD = 1xAC + xBC + xCC + xDC = 1
Assignment Model ExampleAssignment Model Example 3 3 Model FormulationModel Formulation
SummarySummary
Three Three network flow modelsnetwork flow models have been have been presented:presented:
1.1. Transportation modelTransportation model deals with distribution of goods from several supplier to a number of demand points.
2.2. Transshipment modelTransshipment model includes points that permit goods to flow both in and out of them.
3.3. Assignment modelAssignment model deals with determining the most efficient assignment of issues such as people to projects.