UNIT 2: Linear Programming applied to OM problems
Common applications:
► Many management decisions involve trying to make the most effective use of
limited resources.
• Aggregate sales and operations planning. Mid-term production planning at
minimum cost.
• Service/manufacturing productivity analysis. Efficiency degree of resources
consumed with respect to best working unit.
• Product planning. Optimum mixture of products considering they require
different materials and costs.
• Product routing. Optimum path to manufacture a product.
• Vehicle/crew scheduling. Best route to use resources such as airplanes, buses,
trucks,…
• Process control. Minimization of waste material.
• Inventory control. Optimum combination of products in a warehousing network.
Linear programming model
► All LP problems have 4 properties in common:
1. All problems seek to maximize or minimize some quantity (the objective
function). In operations normally we maximize profit or minimize costs.
2. Restrictions or constraints that limit the degree to which we can pursue
our objective are present.
3. There must be alternative courses of action from which to choose.
4. The objective and constraints in problems must be expressed in terms of
linear equations or inequalities.
Linear programming essential conditions
► We assume conditions of certainty exist and numbers in the objective and
constraints are known with certainty and do not change during the period being
studied.
► We assume proportionality or linearity exists in the objective and constraints.
Requirement of the linear model.
► We assume homogeneity of products produced (i.e., products must the identical)
and all hours of labor used are assumed equally productive.
The same quality products for example, to have a stability in our products.
► We assume divisibility in that solutions need not be whole numbers. Divisibility
assumes products and resources are divisible.
Formulating LP problems
► Formulating a linear program involves developing a mathematical model to
represent the managerial problem.
► The steps in formulating a linear program are:
1. Completely understand the managerial problem being faced.
2. Identify the objective and the constraints.
3. Define the decision variables.
4. Use the decision variables to write mathematical expressions for the
objective function and the constraints.
Formulating objective function
• Cj is a constant that describes the rate of contribution to costs or profit of (Xj)
units being produced
• Z is the total cost or profit from the given number of units being produced
Formulating constraints
Maximize (or Minimize) Z = C1X1 + C2X2 + … + CnXn
