is a scientific approach to decision making that seeks to best design and operate a system, usually under conditions requiring the allocation of scarce resources.”

• - aka Management Science

- discipline of applying appropriate analytical methods to help make better decisions. It is the use of mathematical models, statistics, and algorithm to aid in decision making.

(a)  

The most significant type of OR model that assumes that all the relevant variables, parameters, and constraints as well as the objectives are quantifiable.

(a)  

OR models are designed to “optimize” a given objective function subject to a set of constraints.

is generally taken to signify the MAXIMIZATION or MINIMIZATION of the objective function.

(a)  

which are the unknowns to be determined by the solution to the model.

(a)  

represent the physical limitations of the system

(a)  

the identification of a set of variable values which are feasible (satisfy all the constraints) and which lead to the optimal value of the objective function.

(a)  

is a quantitative technique that involves a sequence of steps that will lead to optimum solution to a class of problem. It is planning by the use of linear relationship of the variables involved.

It makes use of certain mathematical techniques to get the best possible solution to a problem involving limited resources.

(a)  

consists of a set of variables, a linear objective function indicating the contribution of each variable to the desired outcome, and a set of linear constraints describing the limits on the values of the variables

(a)  

is the process of translating a real-world problem into a linear program.

(a)  

is an algebraic expression introduced by the word “Maximize” or “Minimize”.

This is the objective of what we are trying to achieve in solving the problem.

(a)  

are introduced by the words “subject to”. These restrict the available alternatives.

The algebraic sentences in the constraints are expressed in equations or inequalities.

(a)  

are conditions which are to be expressed in mathematical sentences from the condition of the problem.

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are those constraint that are implied

(a)  

negativity values of decision variables are unacceptable.

(a)  

values of parameters are known and constant.

(a)  

non-integer values of decision variables are acceptable.

The values of decision variables can be fractions.

(a)  

is a method of finding optimal solutions to two-variable problems

(a)  

do not affect the feasible region

(a)  

when no feasible solution exists (there is no feasible region).

(a)  

when there is more than one optimal solution.

(a)  

when nothing prevents solution from becoming infinitely large

(a)  

It can handle a problem with any number of variables (two or more variables)

It is an algebraic procedure for solving LP problems.

Starting with initial solution, the procedure evaluates corner points of the feasible region that the objective function improves at each iteration.

(a)  

all constraints are equations and all variables are nonnegative

(a)  

any basic solution where all variables are nonnegative

matches a vertices in domain of LP model's feasible solution

(a)  

a chosen set of variables where variables equal to 0.

regular variables

(a)  

Simplex method was first published by an American mathematician in 1947

(a)  

the remaining variables that satisfy the system of equations at the standard form

slack variables

(a)  

version of the Simplex Algorithm that first finds a BFS by adding "artificial" variables to the problem

If an LP has any ≥ or = constraints, a starting BFS may not be readily apparent.

(a)  

assessing the impact of potential changes to the parameters (the numerical values) of a LP model.

Such changes may occur due to forces beyond a manager’s control;

or a manager may be contemplating making the changes, say, to increase profits or reduced costs.

(a)  

the range of possible values of the objective function coefficient over which the optimal values of the decision variables will not change.

(a)  

an estimate of how much the objective function will change if we make (force) the zero (non basic) variable to be non-zero (basic).

(a)  

is a marginal value that indicates the amount by which the value of the objective function would change if there were a one-unit change in the RHS value of that constraint.

(a)  

In this range, the value of the shadow price remains constant.

Hence, as long as a change in RHS value of constraint is within its range of feasibility, the shadow price will remain the same.

(a)  

Every linear programming problem is associated with another linear programming problem called its (a)   .

is a special type of LP where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations

(a)  

a method for computing a basic feasible solution of a transportation problem where the basic variables are selected from the North – West corner.

(a)  

method for computing a basic feasible solution of a transportation problem where the basic variables are chosen according to the unit cost of transportation

(a)  

an iterative procedure for computing a basic feasible solution of the transportation problem.

This method is more likely to be closer to the optimal solution.

(a)  

analysis of each unused (empty) cell to determine the potential for reducing total cost of the solution in transportation problem

(a)  

This is accomplished by transferring one unit into an empty cell and noting its impact on costs.

Requires that every unused cell be evaluated for potential improvement

(a)  

Cell evaluation by borrowing one unit from a full cell to assess the impact of shifting units into the empty cell

crossing a shallow pond by stepping from stone to stone.

To maintain the balance of supply and demand for every row and column, a shift of one unit into an empty cell requires a series of shifts from other occupied cells.

(a)  

the problem with equal quantity of demand and supply

(a)   Transportation Problem

A case in which supply and demand are not equal.

- This condition can be remedied by adding a dummy.

A dummy is something we pretend to exists, although in reality it does not.

(a)  

exists when there are too few completed cells to allow all necessary paths to be constructed.

It can occur in an initial solution or in subsequent solutions, so it is necessary to test for degeneracy after each iteration using R + C - 1.

(a)  

is a special type of transportation model where the resources are allocated to destinations on a one-to-one basis to minimize the total cost.

(a)  

A simple assignment method for one-to-one matching is called the (a)   to identify the lowest cost solution.

Assumes that every machine is capable of handling every job, and that the costs or values associated with each assignment combination are known and fixed.

works only if the matrix is a cost matrix.

(a)  

A (a)   assignment problem can be converted to a minimization problem by creating a lost opportunity matrix.

to establish the timing of the use of equipment, facilities, and human activities in an organization.

The objective is to achieve tradeoffs among conflicting goals, which include efficient staff utilization, equipment, and facilities, and minimization of customer waiting time, inventories, and process times.

(a)  

gives rise to two basic issues for schedulers: loading, how to distribute the workload among work centers, and sequencing, what job processing sequence to use

(a)  

refers to the assignment of jobs to processing (work) centers and to various machines in the work centers.

(a)  

are used as visual aid for loading and scheduling purposes. from Henry Gantt in early 1900s.

to organize and clarify the actual or intended use of resources in a time framework.

(a)  

assign jobs to work centers without regard to the capacity of the work center.

One possible result of this is the formation of queues in some work centers.

(a)  

projects actual job starting and stopping times at each work center, taking into account the capacities of each work center and the processing times of jobs, so that capacity is not exceeded.

Have to be updated often, perhaps daily, due to processing delays at work centers and the addition of new jobs or cancellation of current jobs

(a)  

scheduling ahead from a point in time

(a)  

means sscheduling backward from a due date.

(a)