Question

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door — you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. The landlord wants to create an integer programming model to determine which project should be done by the contractor and by himself to maximize the rent. a) Define the decision variables. b) Write the O.F. c) Construct all the constraints d) Solve the formulated model using excel.

Answer 1

a) Define the decision variables

The aim is

• to chose which work should be done among the four- wood floor, Kitchen tile, Back door   Garage door
• to chose who should do it – landlord or the professional

so that rent is maximized

Variables are assigned as follows

X1= landlord works on wood floors

X2= Hired professional works on wood floors

X3= landlord works on kitchen tile

X4= Hired professional works on kitchen tile

X5= landlord works on back door

X6= Hired professional works on back (safety) door

X7=landlord works on garage door

X8= Hired professional works on garage door

Xi=1 or 0 : 1= if the option is selected;0=if the option is not selected

b) Write the O.F

Objective- maximize rent

Objective function

Maximize,

Z=100(X1+X2)+80(X3+X4)+20(X5+X6)+15(X7+X8)

c) Construct all the constraints

1. x1,x2,x3,x4,x5,x6,x7,x8 ?Binary(1,0)

1. Only one of the two options (landlord/professions) can be selected , if selected

e.g. Both landlord and professional cannot be selected at the same time for a wood floors iof landlord is elected the it is X1=1, then X2 must be 0, so that sum (x1+x2)=1 or if the wood floor is not required then both x1 and x2 can be 0 i.e. x1=x2=0

(X1+X2) ?1

(X3+X4) ?1

(X5+X6) ?1

(X7+X8) ?1

note- time and budget constrsinst haev not been mentioned in the case

d) Solve the formulated model using excel.

Additional

if time and cost constraints are provided

eg .

• the work shoudl be completed within 4 weeks
• the budget is $3000

two additional constraints are added