OPERATIONS RESEARCH
Chapter 4
Job Sequencing and Replacement
Theory
Prof. Bibhas C. Giri
Department of Mathematics
Jadavpur University
Kolkata, India
Email:
, MODULE - 3: Introduction to
Replacement Theory and Determination of
Optimal Replacement Time
3.1 Introduction
The replacement theory is concerned with the situations that arise when some items
such as machines, electric light bulbs, computer, etc. need replacement due to their
decreased efficiency, failure or break-down. Such decreased efficiency or complete
breakdown may either be gradual or all of a sudden. The replacement problem arises
primarily because of the following reasons:
• The old item works badly or requires expensive maintenance.
• The old item has failed due to accident or otherwise and does not work at all, or
the old item is expected to fail shortly.
• A better or more efficient design of machine or equipment has become available
in the market.
Failure of item is of two types: (i) Gradual failure, and (ii) Sudden failure. Here the
term ‘failure’ will be considered in the context of replacement decisions.
3.1.1 Gradual failure
Gradual failure is progressive in nature, i.e., as the life of an item increases, its opera-
tional efficiency also deteriorates. This results in:
2
Chapter 4
Job Sequencing and Replacement
Theory
Prof. Bibhas C. Giri
Department of Mathematics
Jadavpur University
Kolkata, India
Email:
, MODULE - 3: Introduction to
Replacement Theory and Determination of
Optimal Replacement Time
3.1 Introduction
The replacement theory is concerned with the situations that arise when some items
such as machines, electric light bulbs, computer, etc. need replacement due to their
decreased efficiency, failure or break-down. Such decreased efficiency or complete
breakdown may either be gradual or all of a sudden. The replacement problem arises
primarily because of the following reasons:
• The old item works badly or requires expensive maintenance.
• The old item has failed due to accident or otherwise and does not work at all, or
the old item is expected to fail shortly.
• A better or more efficient design of machine or equipment has become available
in the market.
Failure of item is of two types: (i) Gradual failure, and (ii) Sudden failure. Here the
term ‘failure’ will be considered in the context of replacement decisions.
3.1.1 Gradual failure
Gradual failure is progressive in nature, i.e., as the life of an item increases, its opera-
tional efficiency also deteriorates. This results in:
2
