Goal Programming
Applications for Services
References:
‘Operations
Research
’
byWinston
‘
Operations Research Models And Methods
’
byPaul A. JensenAndJonathanF. Bard

Introduction
•
Many service operations management decisions involve trying to make the most
effective use of an organization's resources.
•
Resources typically include
•
labor,
•
money,
•
storage space/capacity, or
•
materials.
•
These resources may be used to produce services such as
•
schedules for shipping and production,
•
advertising policies,
•
investment decisions, or
•
hospital meal plans.
•
Linear programming (LP)
and
Goal programming (GP)
are widely used
mathematical techniques designed to help operations managers in planning and
decision making relative to the tradeoffs necessary to allocate resources.

Overview of Linear Programming
All LP problems have four properties in common.
1.
All problems seek to
maximize
or
minimize
some quantity.
2.
The presence of restrictions, or
constraints
,
limits the
degree to which we can pursue our objective.
3.
There must be
alternative courses
of action
to choose from.
4.
The objective and constraints in linear programming
problems must be expressed in terms of
linear
equations or
inequalities.

Applications of Linear Programming
•
Ingredient Blending Applications: The diet problem
•
Shift Scheduling Problem
•
Workforce Planning Problem
•
Transportation Problem
•
Employee Scheduling Applications: An Assignment
Problem
•
Labor Planning
•
Marketing Applications: Media Selection
•
…

Goal Programming
•
Linear programming models allow for only one objective, and all
constraints must be met absolutely.
•
In real life, virtually all problems have several objectives in different
units of measure. This makes construction of a consolidated single
objective difficult.
•
For example, an emergency ambulance system could have the
following objectives:
1.
Maintain an average response time of approximately 4 minutes.
2.
Ensure that 90 percent of all calls receive aid in less than 10 minutes.
3.
Try not to exceed a budget of $100,000 per year.
4.
Allocate calls to ambulance crews in an equitable manner.

Goal Programming
•
is a variation of LP that permits multiple and conflicting goals with
different dimensions.
•
Multiple goals are
rank-ordered
and treated as
preemptive priorities.
•
The solution approach:
•
higher-ranked goals are not sacrificed to achieve lower-ranked goals.
•
is equivalent to solving a series of nested LP problems in which higher-
ranked goals become constraints on lower-ranked goals.
•
While LP optimizes a single objective, goal programming
minimizes deviations from goals
.
•
This solution approach is known as
satisfying
,
because not all
goals necessarily will be met. Instead, the goals will be achieved
as closely as possible
.

Goal Programming
Goal Types
Three possible types of goals:
1.