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Linear Programming-Ice Cream Blending
Data Processing Application
CONTENTS
Introduction . . . . . . . . . 1
Problem Profile and Economics 2
Model Formulation - Single Vat. 2
Input Data Requirements . . . . . . 3
Example Problem . . . . . . . . . . . . 3
Cost Constraint (Objective Function) . . . . 7
Recipe Specification Constraints . . . . 7
Yield Constraint . . . . . . . . . . . . . . . 8
Availability Constraints . . . . . . 9
Model Formulation - Multiple Vat. 9
Capacity Constraint 11
Output Reports. . . . . . 12
Basis Variables Report 13
Check Report . . . . . . . . . . . 14
DO. D/J Report . . 14
Cost Range- Report 16
Summary . . . . . . 17
Copies of this and other IBM publications can be obtained through IBM branch
offices. Address comments concerning the contents of this publication to
IBM, Technical Publications Department, 112 East Post Road, White Plains, N. Y. 10601
INTRODUCTION
This manual explores the application of linear programming (LP) in ice
cream blending. Linear programming is becoming more and more
important as a decision-making tool in a variety of industries - notably,
alloy blending, feed mixing, cotton blending, and food blending. For
some time it has been standard in the petroleum industry, where it is
used in all phases of refinery scheduling and control as well as in
refinery expansion studies.
Whenever a process involves the blending of a variety of materials
within specification constraints, the application of linear programming
techniques enables the producer to determine rapidly the optimal, or
least-cost, blend. The usefulness of LP increases as the number of
materials and the complexity of the industrial process increase.
The production of ice cream involves precisely the sort of complex
blending and control problem that LP is designed to solve, and the
purpose of this manual is to demonstrate the application of this solution
method to ice cream blending. This is accomplished through use of a
typical pro~uction problem that illustrates the principles and advantages
of LP in a specific situation.
An LP model is developed that can, with minor modifications, be solved
by any IBM linear programming system. Among its more immediate
and obvious benefits, as will be shown, linear programming helps the
producer to:
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