EM 505 – DECISION MODELS
Spring 2021, METU
Case Study 1
Due date: May 21, 2021
Fortune Electronics has just signed a contract to supply searchlights to the U.S army. During the next
four months, the firm must meet the following delivery schedule:
February
150 units
March
160 units
April
225 units
May
180 units
Fortune’s factory in Texas can produce searchlights at a cost of $20 per unit (labor cost is not included).
To produce a searchlight 10 hours of labor are required and there are 10 workers available at the plant
at the beginning of February. Each worker can work 160 hours per month in regular hours with a rate
of $1.5 per hour, and 80 hours in overtime per month with a rate of $2.5. It is possible to hire new
workers or to layoff some of the existing workers at the beginning of a month. A one-time additional
cost for hiring and layoff of a worker is $400 and $1000, respectively. Assume that it is possible to have
non-integer number of workers.
It is also possible to subcontract some of the searchlights to another factory at a cost of $50 each, but
the subcontractor has a production capacity of 10 units.
Searchlights can be carried in inventory to meet the demand of a future month, but this costs $5 per unit
per month, but the storage has a capacity of 20 units. Backordering is also allowed with a cost of $7.5
per unit per month.
Formulate a linear programming model to represent Fortune’s problem and find the optimal decisions.
Use Excel Solver to find the solution. Answer the following questions and interpret the results.
a. How much should the subcontractor lower its price to become competitive in period 4?
b. How much lower does the inventory carrying cost need to be in order inventory be carried in
period 3?
c. How much should the hiring cost go down in each period so that workers would be hired?
d. At what layoff cost would the company consider laying off workers?
e. If Fortune’s could negotiate to lower the demand in some period, which period would they do
so?
f. How much lower does the backordering cost need to be in order backordering be favorable in
each period?