291 Quiz 2
Steps in solving the transportation problem
1) Arrange the problem in table form 2) Balance table (if necessary) 3)Find an initial feasible solution 4) Test the optimality 5)If, yes, problem is solved; no generate improved solution
Characteristics and assumptions of transportation problem
1)The Supply: A limited quantity of one commodity is available at certain sources 2)The Demand: There is a demand for commodity at several destinations such as warehouses, distribution centers, or stores. 3) The Quantities: The quantities of supply at each source ad the demand or requirements at each destination are constant 4)The Shipping Cost: The per unit cost of transportation the commodity from each source to each destination are assumed to be constant 5)It is assumed that no shipments are allowed between sources or between destinations 6) All supply and demand quantities are given whole numbers (integers)
When does transportation problem arise?
The transportation problem arises frequently in planning for the distribution of goods and services from several supply location to several demand locations
what is said to exist when total demand equals total supply in a transportation problem
a balanced problem
multiply for decision variables
add for constraints
Each cell in a transportation table is
analogous to a decision variable that indicates the amount allocated from a source to a destination
The linear programming model for a transportation problem has
constraints for supply at each source and demand at each destination
The problem is to
determine how many units should be shipped from each source to each destination at the minimum total cost
Transportation models
do not start at the origin where all decision variables equal zero; they must be given an initial feasible solution
in a transportation problem each destination must be supplied by one and only one source
f
transportation models can be used for which of the following decisions
facility location
The transportation model
is formulated for a class of problems with the following unique characteristics: 1) A product is transported from a number of sources to a number of destinations at the minimum possible cost; and 2) each source is able to supply a fixed number of units of the product, and each destination has a fixed demand for the product.
In a transportation problem
items are allocated from sources to destinations at a minimum cost
If total supply exceeds total demand,
no modification in the LP formulation necessary
In a balanced transportation model
supply equals demand, all constraints are equalities
In an unbalanced transportation model,
supply is greater than demand or demand is greater than supply
a typical transportation problem may ask the question "how many x should be shipped to point E from source A"
t
in a transportation problem a single source may supply something to all destinations
t
the objective of a transportation problem solution is to schedule shipments from sources to destinations while minimizing total transportation and production costs
t
Use of the transportation solution technique requires that
the problem be balanced; that is total supply MUST equal the total demand.
If total supply is less than total demand,
the transportation problem will not have a feasible solution; In this case, we modify the model by adding a dummy origin with supply equal to the difference between the total demand and total supply
what is the use of inventory?
to separate production and distribution processes, to provide a buffer against the fluctuations in demand, and supply the demand that is anticipated to be higher next season
when using a general LP model for transportation problems, if there are 4 sources and 3 destinations, which of the following statements are true
when using a general LP model for transportation problems, if there are 4 sources and 3 destinations, which of the following statements are true there are typically 12 decision variables and 7 constraints