MODELING OF OPERATIONS
Chapter 1
Management science: a scientific approach to solving management problems. It
can be used in a variety of organizations to solve many different types of problems.
Furthermore, it encompasses a logical approach to problem solving. Steps of
scientific method to problem solving:
1. Observation (can often be identified by a management scientist: a person
skilled in the application of management science techniques)
2. Definition of the problem
3. Model construction (a model is an abstract mathematical representation of a
problem situation), mostly in the form of a set of mathematical records. A
variable is a symbol used to represent an item that can take on any value.
Parameters are known, constant values that are often coefficients of
variables in equations. Data are pieces of information from the problem
environment. A functional relationship includes variables, parameters and
equations.
4. Model solution
5. Implementation (the actual use of a model once it has been developed)
Break-even analysis is a modelling technique to determine the number of units to
sell or produce that will result in zero profit. Fixed costs are independent of volume
and remain constant. Variable costs depend on the number of items produced.
Total cost = total fixed cost + total variable cost
TC
= cf
+
vcv
Profit is the difference between total revenue (volume multiplied by price) and total
cost.
The break-even point is the volume (v) that equals total revenue with total cost
where profit is zero. Break-even formula =
0 = v(p-cv)-cf
Sensitivity analysis: sees how sensitive a management model is to changes. In
general, an increase in price lowers the break-even point, all other things held
constant. An increase in variable costs will increase the break-even point, all other
things held constant. Also, an increase in fixed costs will do this.
Management science techniques
-
Linear mathematical programming
Probabilistic techniques
Network techniques
Other techniques
A deterministic technique assumes certainty in the solution
Chapter 2
Objectives of a business frequently are to maximize profit or minimize cost. Linear
programming is a model that consists of linear relationships representing a firm’s
decisions, given an objective and resource constraints.
Decision variables are mathematical symbols that represent level of activity. The
objective function is a linear relationship that reflects the objective of an operation.
A model constraint is a linear relationship that represents a restriction on decision
making. A linear programming model consists of decision variables, an objective
function and constraints.
A solution is feasible when it does not violate any of the constraints. An infeasible
problem violates at least one of the constraints.
When solving it using a graph  the optimal solution point is the last point the
objective function touches as it leaves the feasible solution area.
Multiple optimal solutions can occur when the objective function is parallel to a
constraint line. A slack variable represents unused resources.
A surplus variable is substracted from a => constraint to convert it to an equation.
A surplus variable represents an excess above a constraint requirement level.
Chapter 3
Simplex method: a procedure involving a set of mathematical steps to solve linear
programming problems
Marginal value: the money amount one would be willing to pay for one additional
resource unit
Sensitivity analysis: the analysis of the effect of parameter changes on the optimal
solution
The sensitivity range for an objective coefficient is the range of values over which
the current optimal solution point will remain optimal
Shadow price: the estimated price of a good or service for which no market price
exists
Chapter 4
Linear programming model formulation steps
Step 1: define the decision variables
Step 2: define the objective function
Step 3: define the constraints
Standard form requires all variables to be left of the inequality and numeric values
to the right. Also requires that fractional relationships between variables be
eliminated.
In a “balanced” transportation model, supply equals demand such that all
constraints are equalities; in an “unbalanced” transportation model supply does not
equal demand, and one set of constraints is <=.
Chapter 5
Three basic types of integer linear programming models:
-
In a total integer model, all the decision variables are required to have integer
solution values
In a 0-1 integer model, all the decision variables have integer values of zero
or one
In a mixed integer model, some of the decision variables (but not all)
Rounding noon-integer solution values up to the nearest integer value can result in
an infeasible solution. A feasible solution is ensured by rounding down non-integer
solution values. A rounded-down integer solution can result in a less-than optimal
solution (sub-optimal solution). The traditional approach for solving integer
programming problems is the branch and bound method. It is a mathematical
solution approach that can be applied to a number of different problems. The
branch and bound method is based on the principle that the total set of feasible
solutions can be portioned into smaller subsets of solutions. These smaller subsets
can then be evaluated systematically until the best solution is found.