I need resolution for two operation research exercises. Here are:
You don’t need to send me a full formatted doc report, just the main notes and perhaps some afterwards doubts by email.
A problem of equipment maintenance
A company operates a device that uses a replaceable device of fast wear
but expensive. The needs of this device vary daily depending on the type of
product and equipment operated in accordance with the following table.
days 2AF 3af 4AF 5AF 6af Sat Sun
need 24 12 14 20 18 14 22
The needs of this device can be satisfied as follows
• through new devices at a cost of € 12 each;
• through devices reused at a cost of € 6 each;
• through a service of cleaning and maintenance at a cost of € 3 each.
The reuse of the devices means a device sent to this service at the end of
one days i, will be ready to be reused the next day, i + 1, or the day i + 2. The service
cleaning and maintenance needs at least two days to be made. Thus a
Device sent to this service at the end of a day i only will be ready on day i +3, or
the following days.
The company intends to make the planning of the purchase, reuse and maintenance of these devices
over a week to minimize the total cost.
(a) Formulate this problem, taking into account that can be formulated as a problem
transport, and solve it using an appropriate software (Xpress or another). Properly interpret the results
(b) Suppose that on Monday and on Tuesday service is available for cleaning and maintenance
at a cost of € 1 for each device, but slower, ie a device sent to
this service at the end of a day i (2AF or 3af) only will be ready on day i + 4, or
days. Restate the problem and interpret and new solution.
(c) Suppose now that the devices ready to be reused shall not incur
a storage cost of 50 cents per day. Restate the problem and interpret
and new solution.
A problem of replacing equipment
A company needs to plan the substitution of a certain equipment in the next 4
years. It is company policy that the equipment at the age of 6 years must be replaced. The
cost of new equipment and 100 000 €. Over the years the performance of equipment
will be degraded and in need of maintenance. The company determined a way to quantify the
performance was translated into a value that indicates the profit that 'it is possible to obtain
with the equipment in operation. The old equipment replaced and sold, allowing
the company regain some value of investment. Consider that at the end of the 4 years
equipment and sold. In the following we find out the problem. For each value
t the age of the equipment are shown in 3-values, &#8467; (t), c (t), r (t).
age t 0 1 2 3 4 5
&#8467; (t) (x € 1000) 20 19 18.5 17.2 15.5 14 --
c (t) (× 1000 €) 0.2 0.6 1.2 1.5 1.7 1.8 --
r (t) (× 1000 €) - 80 60 50 30 10 5
The value &#8467; (t) tells us the profit on the equipment up to the age corresponds to
equipment performance translated into a cash value (profit). The value c (t) tells us
cost of maintenance of equipment with age t. The value r (t) shows us the value retrieved
with the sale of equipment with age t. Determine an optimal policy and substitutability
the equipment that currently has 3 years.
(a) Formulate the problem as a dynamic programming problem: identify the stages
the decision variables and the states set ¸ ca and the recursive equations.
(b) Solve the problem using the equations established.
(c) What will be the optimum solution if the equipment 2 years? E 1 year? And if it is new?
Interpret the results.