Case Problem Truck Leasing Strategy

Case Problem
Truck Leasing Strategy
By: Alex Somerville
November 8, 2014

In this problem, Bob Reep the owner and president of Reep Construction, needs to figure out a way to accommodate a short term leasing plan for trucks within budget to complete this project. In order to appropriately illustrate and solve Reep’s problem, I will be using the concept of a sensitivity analysis. This analysis will show how changes in this problem will affect the overall optimal solution. The following sensitivity analysis will detail the optimal leasing plan, the costs associated with the leasing plan, and the cost Reep construction would incur by maintaining its current policy of no layoffs.
1. Decision Variables

Let Xij = # of trucks from a short term lease in month i for period of j month(s). Yi = # of trucks from a long term lease used in month i.

Objective Function

Monthly Costs for Short-Term Leased Trucks Monthly fuel costs - 20 * $100 = $2000 Note: the table shown below include $2000/mo fuel cost.

Decision Variables Cos­t­­­­________________
X11, X21, X31, X41 $4000 + $2000 = $6000
X12, X22, X32 2 ($3700 + $2000) = $11,400
X13, X23 3 ($3225 + $2000) = $15,675
X14 4 ($3040 + $2000) = $20,160

Monthly Costs for Long-Term Leased Trucks
Reep Construction no layoffs and commitment to long term lease = $2000 monthly fuel cost

LINEAR PROGRAMMING PROBLEM

MIN 6000X11 + 11400X12 + 15675X13 + 20160X14 + 6000X21 + 11400X22 + 15675X23 + 6000X31 + 11400X32 + 6000X41 + 2000Y1 + 2000Y2 + 2000Y3 + 2000Y4

S.T.

1) 1X11+1X12+1X13+1X14+1Y1=10 2) 1X12+1X13+1X14+1X21+1X22+1X23+1Y2=12 3) 1X13+1X14+1X22+1X23+1X31+1X32+1Y3=14 4) 1X14+1X23+1X32+1X41+1Y4=8 5) 1Y1≤1 6) 1Y2≤2 7) 1Y3≤3 8) 1Y4≤1

OPTIMAL SOLUTION

Objective Function Value = 203660.000

Variable Value Reduced Costs -------------- --------------- ------------------