Decision Sciences
A transportation problem with n origins and m destinations will have how many origins?
(n)(m)
In the integer programming model it is desired to have the Variable x1 be exactly twice the value of the variable x2, the constraint would be written as x1-2x2=0.
...
In 0-1 Integer programming, what does 0 and 1 stand for?
1 if assigned= success. 0 if assigned= otherwise.
When integers are used to represent yes or no decisions, typically the following values are
1, 0.
In a linear programming formulation of an assignment problem with 3 jobs to be done by 3 person available to these jobs, how many constraints will it have?
6
Lattic points?
???
When a transportation model is formulated into a spreadsheet, which of the following is required?
A parameter table and a solution table.
The 0-1 variable is in the fixed cost models correspond to
A process for which a fixed cost occurs.
There are three basic types of integer linear programming models:
A total integer model, a 0-1 integer model, and a mixed integer model.
Zero integer programming can be used for
Capital budgeting, facility location, and fixed charge/
Decision variables in a linear programming moel are equivalent to what in a transportation problem?
Cells in a transportation table.
What is not a type a type of a integer programming model?
Continuous
C1j is
Distribution cost/Unit between source I and destination J.
An 0-1 variable can be used to determine:
Either/or constraints, mutually exclusive items, and set up costs.
A rounded down integer solution can never result in a less than optimal solution. True/False?
False!
Transportation problems do or do not ALWAYS involve shipping goods from one location to another?
False.
Mutually exclusive constraint:
In order for the sum of x1 and x2 to be less than or equal to one, either of the variables can have a value of one, or both variable can equal zero.
Rounding up method leads to a what solution?
Infeasible.
A linear programming model in which some of the decision variables are restricted to integer variables is called
Mixed integer programming model.
The three methods for obtaining an initial solution arw
Northwest corner method, Short cut method, and the Approximation Method (VAM Method)
Binary values can be what?
Only 0 or 1
Non basic means-
Other than zero in which the objective coefficient has to improve by.
There are 5 different types of solution methods:
Rounding off, graphical solution, branch and bound method (2 variable), Gowary method, and Excel.
Constraints in a linear programming model would be equivalent to what in the transportation model?
Rows and columns of the transportation model.
What is a requirement of the transportation model?
Shipping unit costs per unit are constant, goods to be shipped are the same, and there is one route between each source and destination.
Which is not a requirement of the transportation model?
Supply and demand must be equal./
The key characteristics of the balanced transportation problem are:
Supply equals demand.
Unit shipping distance is not used needed with what model?
The transportation mode.
If a transportation problem has a dummy customer, then:
There are dummy arcs from the dummy supply node, no goods are supplied from the dummy supply node, and demand exceeds supply.
A multiple choice constraint
When a model forces a choice between two things with a solution that would include x1=1 or x2=1 but both would not equal one (nor would both equal zero).
Co-requisite constraint:
Wherein if one facility is "constructed", the other one will also be constructed and vice versa. Written as x2=x1
Assignment problems are cost minimization problems that CAN BE solved as
a profit maximization problem.
A transportation problem is
a special case of linear programming that deals with the distribution of goods and services from multiple services to multiple destinations in order to minimize distribution costs.
In a transportation problem represented as a network, an arc between a source and destination represents
a valid shipping route in the real world.
George Dantziq created the ____ method using
algebra.
In a mixed integer linear programming model, some but not
all of decision variables are restricted to integer values.
The assignment problem is a transportation problem where
all supply and demand values are equal to one.
0-1 Integer Programming is when
all variables have variables of 0 or 1.
Pure-Integer Programming is when
all variables must have integer programming, some but not a programming.
What is the other term for if there are unused variables available
also called slack.
In a mixed integer model, some of the decision variables (not all)
are required to have integer solutions.
Left hand side is also called
cell reference.
Decision Variables are also called
changing variable cells.
Right hand side is also called a
constraint.
An integer condition that some or all of the
decision variables be integer.
Problems involving integer variables are much more
difficult to solve than linear programming problems.
In an assignment problem,
each person is assigned to his/her own best job.
All the constraint coefficients in a transportation model are
equal to one.
The initial solution is the
feasible ble solution.
In a transportation problem, items are allocated
from sources to destinations at minimum costs.
The linear programming model for a transportation problem
has constraints for supply at each source and demand at each destination.
Constraint is when the right hand side shows
how much variables are left.
Binding constraints are
if all available constraints are used.
non binding constraints are
if there are unused variable available.
With the rounding method you will never know
if your answer is the optimal solution.
When testing for optimality using the stepping stone method, it helps calculate an
index.
In a total integer model, all the decision variables are required to have
integer solution values.
In a total integer model, all the decision variables are required to have
integer values of zero or one.
Transportation, transshipment and assignment problems are part of linear programming models
known as network flow problems.
Non-negativity is also called
make unconstrain variable.
Added integer requirements to a linear programming problem
makes the feasible solution smaller.
A transportation problem with n origins and m destinations will have how many constraints
n+m
To visualize a transportation problem, a
network representation can be used.
Reduced cost is
non basic.
In a balanced transportation model, supply does
not equal demand at all constraints, and they are inequalities.
An index is just a
number. Any number that can be zero.
The steps in obtaining a solution of a transportation problem is
obtaining an initial solution, test solution for optimality, and improve sub optimal solution.
In a transportation problem, nodes represent:
plants that produce products, warehouses that hold goods, and customers that require goods.
The sources in a transportation problem are
production facilities.
A feasible solution is not ensure by
rounding down integer solution values
After solving a linear programming problem, one has fractional values for the decision variable. The problem demands that the solution be integer. The process of moving each fractional value to the nearest value to the nearest integer is
rounding.
The objective function is also called
set objective (target)
When it is binding, you will have
shadow price.
The objective of the transportation problem is to
ship goods from supply to demand at the least cost.
The transportation problem can be solved by the
simplex method.
Integer programming models are linear programming models with the added complication that
some or all of the decision variables are restricted to integer values.
In using rounding of a linear programming model to obtain an integer solution, the solution that is produced is
sometimes optimal and feasible.
The integer requirements of the Excel Solver are specified by
specifying INT option for appropriate changing cells.
If the transportation problem has a dummy customer, then:
supply equals demand, there is a dummy arc connecting the dummy customer, and no goods are sent to the dummy customer.
Conditional constraints:
the "Construction" of one facility is conditional upon the construction of another. X2<x1
Computer solutions are based off of the
the branch and bound method.
C1 in a transportation problem is
the destination.
The transportation problem assumes that the shipping costs are NOT directly dependent on
the distance that the goals are shipped.
In an assignment problem, dummy people or jobs are created when
the number of people and jobs is equal.
A transportation problem where demand and supply are not equal,
the problem can be solved.
In an assignment problem where the number of jobs does not equal the number of people-
the problem can be solved. FO SHO!
In a transportation problem, the arcs represent
the routes the goods follow.
The primary determinants of computational difficulty for an 0-1 programming model is
the special structure of the model.
The two methods for testing optimality arw
the stepping stone method, modified Distribution Method (MODI).
In an unbalanced transportation problem, a suppy node actually represents:
there is a shortage of goods.
A method of prohibiting a shipping route in a transportation problem is
to assign a shipping cost M to this route.
In a transportation problem , shipments from a dummy origin are used
to signify demand.
The distributions place are
to somewhere else.
Sometimes one or more of the routes of the
transportation model are prohibited.
The assignment problem is NOT a special form of the __
transportation problem where all supply and demand values equal zero.
The branch and bound method has
two variables.
In an assignment problem, if the number of persons is not the same as the number of jobs, then the problem is
unbalanced.
The transportation problem requires a
unit cost for every source and destination point.
In a transportation problem with a maximization objective on which there is a prohibited route, the method often used to prohibit such a route is
use a negative m cost to the route.
Divisibility is
when a solution can be divisible/fraction of values. Fractional.
A minis tic model is when it is
with certainty.
In a capital budgeting example, a firm wants to select no more than three projects from a set of five projects. Which of the following constraints will ensure this?
y1+y2+y3+y4+y5<3