Equipment Replacement Problem (variation on Shortest Route) Assume Farmer Dale n
ID: 407926 • Letter: E
Question
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
Explanation / Answer
Answer:
There are four rental plans and the farmer can select any one of them:
Decision variable are:
X1 is if he selects only one month plan
X2 if he selects One month and two month
X3 if he selects one month and three month plan
X4 if he selects four month plan
X5 if he selects two two-months plan.
Constraints:
Non negativity constraints:
X1, X2, X3 X4 and X5 >=0
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