GE Capital is in the business of providing loans to small to medium companies. However, GE Capital’s top management beli

[answerhappygod]

GE Capital is in the business of providing loans to small to
medium companies. However, GE Capital’s top
management believes the company is losing significant amounts of
cash from delinquent accounts, and
they have assigned John Barlow, a senior financial manager, to
analyze the problem. After some research,
John finds that GE Capital currently has 50,000 accounts. Of these,
40,000 are paid up (the company refers
to these as “0-due”), 4000 are one month overdue (1-due), 4000 are
two months overdue (2-due), and
2000 are 3 months overdue (3-due). After an account is more than
three months overdue, it is written off
as bad debt.
Each month an account is overdue, GE Capital has three contact
options: it can phone the company; it can
send a letter to the company; or it can make no contact. Although
phone calls and letters are fairly routine,
they do take some time. It takes approximately 20 minutes for a
letter and 40 minutes for a phone call.
(Much of this time is for the contact person to assemble
information on the account.) Each month, 5000
hours are available from the employees who make the contacts. GE
Capital’s policy is to never contact
companies with 0-due accounts.
John has discovered that the average amount of a monthly payment is
$10,000. Therefore, for example,
if a 2-due account remains 2-due by next month, this means that one
month of payment, $10,000, has
been received. However, if this 2-due account becomes 0-due by next
month, this means that 3 months
of payments, $30,000, have been received. However, if this account
becomes 3-due by next month, no
payment is received.
On the basis of thousands of accounts, delinquency movement
matrices (DMMs) have been estimated.
These are listed in the file Case_Study_Data.xlsx . For example,
the top-left 60% entry in the first DMM
indicates that 60% of all 1-due accounts that receive a letter
become 0-due. The 10% and 30% values in
this same row indicate that 10% of all 1-due accounts remain 1-due
after receiving a letter, and 30% of all
1-due accounts become 2-due after receiving a letter. The bottom
row of each DMM simply means that
bad debt remains bad debt; it is never recovered.
John’s goal is to allocate his contact employees over the next four
months to maximize the expected
collection revenue received during this period. As John’s
assistant, you have been asked to do the
following:
1. You should develop a linear programing model to find the optimal
strategy. This strategy should
specify the number of each type of account (0-due, 1-due, 2-due,
3-due) that should receive each
contact type (letter, phone call, no contact) in each month. You
should also describe the optimal
strategy in a brief memo, and this memo should mention how much
more revenue can be
obtained with this optimal strategy than from a strategy of no
contacts at all.
2. John wonders whether it would be worth increasing the contact
hours available each month,
either by hiring new contact employees or by reallocating current
employees. Before he makes
detailed decisions on this, he wants you to discover how much these
extra hours would be worth.