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