SKEDSOFT

Introduction:

Replacement model is the part of operation research which is not include in linear programming, used to minimise the production time and maximise the profit.

Group Replacement of Items

·         A Group replacement policy consists of two steps.

·         Firstly, it consists of individual replacement at the time of failure of any item in the system and there is group replacement of existing live units at some suitable time.

·         Here the individual replacement at the time of failure ensures running of the system, whereas group replacement after some time interval will reduce the probability of failure of the system.

·         The application of such type of policy has to take into consideration the following points:

a)      The rate of individual replacement during the period and

b)      The total cost incurred due to individual and group replacement during the period chosen.

·         This policy is favors the group replacement, when the total cost is minimum and the period of replacement are known as optimal period of replacement.

·         The information required to formulate this policy is:

a)      Probability of failure

b)      Losses due to these failures

c)       Cost of individual replacement

d)      Cost of group replacement

Group replacement definition:

“The group replacement policy states that: Group replacement should be made at the end of ‘i’ th period, if the cost of individual replacement for ‘i’ th period is greater than average cost per period by the end of the period‘t’ and one should not adopt a group replacement policy if the cost of individual replacement at the end of (t - 1) th period is not less than the average cost per period through time (t – 1)”.

Example:

A system consists of 10000 electric bulbs. When any bulb fails, it is replaced immediately and the cost of replacing a bulb individually is Re.1/- only. If all the bulbs are replaced at the same time, the cost per bulb will be Rs. 0.35. The percent surviving i.e. S (t) at the end of month ‘t’ and P (t) the probability of failure during the month ‘t’ are as given below. Find the optimum replacement policy.

Solution

The problem is to be solved in two stages:

·         Policy of individual replacement

·         Policy of group replacement

As per the given data, no bulb will survive for more than 6 months. That is a bulb, which has survived for 5 months, is sure to fail during the sixth month. Though we replace the failed bulb immediately, it is assumed that the bulb fails during the month will be replaced just at the end of the month.