Equipment Replacement Problem (variation on Shortest Route)

Assume Farmer Dale needs to rent a BEFCO for the four month planting season from Buck & Knobby Equipment Rental. A BEFCO can be rented based on a one-month, two-month, three-month or four months plans. The costs vary depending on the length of the rental and the particular month due to demand fluctuations. The table below summarizes the possibilities based on last year’s rental costs.

One Month plans Two Months Plans

Month 1 Cost $1800          Months 1 & 2             Cost       $3,000

Month 2 Cost $1500          Months 2 & 3             Cost       $4,200 

Month 3 Cost $2400          Months 3 & 4             Cost $4,800        

Month 4 Cost $2800

Three Month Plans                  Four Month Plan

Months 1-3   Cost $6,000 Months 1-4          Cost      $8,400 

Months 2-4   Cost $6,300

Farmer Dale needs one BEFCO for all four months.

He could rent any combination.

For instance he could rent a one month plan each month (1800 + 1500 + 2400 + 2800).

Or he could rent a one month plan ($1800), two month plan ($4,200) and another one month plan ($2800)

Or he could rent a three month plan ($6000) and a month plan ($2800).

Any possibility can work

Do not solve.

Formulate the LP model to minimize rental costs and ensure that Farmer Dale has BEFCO rented for each month. (Diagram as a shortest route problem to get from node 0(month 1) to node 4 (month 4)).

Objective function: _________________________________________________

ST