Reep Construction recently won a contract for the excavation and site preparatio

Question

Reep Construction recently won a contract for the excavation and site preparation of a new rest area on the Pennsylvania Turnpike. In preparing his bid for the job, Bob Reep, founder and president of Reep Construction, estimated that it would take four months to perform the work and that 10, 12, 14, and 8 trucks would be needed in months 1 through 4, respectively. The firm currently has 20 trucks of the type needed to perform the work on the new project. These trucks were obtained last year when Bob signed a long-term lease with PennState Leasing. Although most of these trucks are currently being used on existing jobs, Bob estimates that one truck will be available for use on the new project in month 1, two trucks will be available in month 2, three trucks will be available in month 3, and one truck will be available in month 4. Thus, to complete the project, Bob will have to lease additional trucks. The long-term leasing contract with PennState charges a monthly cost of $600 per truck. Reep Construction pays its truck drivers $20 an hour, and daily fuel costs are approximately $100 per truck. All maintenance costs are paid by PennState Leasing. For planning purposes, Bob estimates that each truck used on the new project will be operating eight hours a day, five days a week for approximately four weeks each month.

Bob does not believe that current business conditions justify committing the firm to additional long-term leases. In discussing the short-term leasing possibilities with PennState Leasing, Bob learned that he can obtain short-term leases of one to four months. Short-term leases differ from long-term leases in that the short-term leasing plans include the cost of both a truck and a driver. Maintenance costs for short-term leases also are paid by PennState Leasing. The following costs for each of the four months cover the lease of a truck and driver:

Bob Reep would like to acquire a lease that minimizes the cost of meeting the monthly trucking requirements for his new project, but he also takes great pride in the fact that his company has never laid off employees. Bob is committed to maintaining his no-layoff policy; that is, he will use his own drivers even if costs are higher. Managerial Report (original questions) Perform an analysis of Reep Construction's leasing problem and prepare a report for Bob Reep that summarizes your findings. Be sure to include information on and analysis of the following items:

1. The optimal leasing plan

2. The costs associated with the optimal leasing plan

3. The cost for Reep Construction to maintain its current policy of no layoffs

Addendum to Case 8-3 – Truck Leasing Strategy There are some minor problems with the way this case was written that makes it confusing and difficult to solve. To address these shortcomings, I’ve (1) revised the assignment questions, and (2) listed a couple of tips that should help you get started. Revised Assignment questions:

1. If Reep Construction requires that the leasing plan must use the 1, 2, 3 and 1 trucks available from previous long-term lease agreements for months 1 to 4, respectively, and that Reep will not accept a surplus of trucks for any month of the four-month project, determine the optimal leasing plan. That is, identify the number of short-term leases, by month and length of lease, that Reep should obtain for each month to minimize their lease costs, while ensuring that the number of available trucks is equal to the company’s needs for each month of the four-month project. We shall refer to this solution as the “original formulation”.

2. What are the costs associated with this optimal lease plan?

3. Identify and interpret the “reduced cost” for the decision variables and “shadow price” for the constraints in your original formulation.

4. What is the total project cost that Reep will experience for this contract?

5. Raylan, a Sr. Data Analyst at Reep, argued that if your “original formulation” includes sunk costs of previous long-term leases, then to get a better picture of Reep’s total leasing costs for this project you should allow, but not require the use of trucks available under previous long-term leases. Following Raylan’s suggestions, which we shall call the “revised formulation”, what is the optimal leasing plan and associated costs?

Explanation / Answer

Optimal Solution Month 1 2 3 4 Total Truck Requirement 10 12 14 8 No of trucks taken on 4 month Lease 8 No of trucks taken on 3 month lease 2 No of trucks taken on 2 month lease 2 No of trucks taken on 1 month lease 2 Costs Associated with Optimal Leasing Plan Month 1 2 3 4 Total Truck Requirement 10 12 14 8 Trucks taken in month 1 on 4 month lease 8 8 8 8 Trucks taken in month 1 on 3 month lease 2 2 2 0 Trucks taken in month 2 on 2 month lease 0 2 2 0 Trucks taken in month 3 on 1 month lease 0 0 2 0 Monthly cost of trucks on 4 month lease 24320 24320 24320 24320 Monthly cost of trucks on 3 month lease 6450 6450 6450 0 Monthly cost of trucks on 2 month lease 0 7400 7400 0 Monthly cost of trucks on 1 month lease 0 0 8000 0 Total Monthly cost under optimal solution 30770 38170 46170 24320 Average cost per truck 3077.00 3180.83 3297.86 3040.00 Cost for Reep Construction to maintain its current policy of no layoffs Month 1 2 3 4 Total Truck Requirement 10 12 14 8 Trucks used from long term leases 1 2 3 1 Trucks to be taken on short term lease 9 10 11 7 Trucks taken in month 1 on 4 month lease 7 7 7 7 Trucks taken in month 1 on 3 month lease 2 2 2 0 Trucks taken in month 2 on 2 month lease 0 1 1 0 Trucks taken in month 3 on 1 month lease 0 0 1 0 Monthly cost of trucks on long term lease 5800 11600 17400 5800 Monthly cost of trucks on 4 month lease 21280 21280 21280 21280 Monthly cost of trucks on 3 month lease 6450 6450 6450 0 Monthly cost of trucks on 2 month lease 0 3700 3700 0 Monthly cost of trucks on 1 month lease 0 0 4000 0 Total Monthly cost under original formulation 33530 43030 52830 27080 Cost per truck under original formulation 3353.00 3585.83 3773.57 3385.00 Calculation of reduced costs Month 1 2 3 4 Cost of the contract if all the trucks on long term lease 58000 69600 81200 46400 monthly costs under original formulation 33530 43030 52830 27080 Reduced Costs 24470 26570 28370 19320 Per truck reduced cost 2447.00 2214.17 2026.43 2415.00 Modified original formulation after adjusting for sunk costs Month 1 2 3 4 Total Truck Requirement 10 12 14 8 Trucks used from long term leases (already available) 1 2 3 1 Trucks to be taken on short term lease 9 10 11 7 Trucks taken in month 1 on 4 month lease 7 7 7 7 Trucks taken in month 1 on 3 month lease 2 2 2 0 Trucks taken in month 2 on 2 month lease 0 1 1 0 Trucks taken in month 3 on 1 month lease 0 0 1 0 Monthly cost of trucks on long term lease (Sunk Cost) 5800 11600 17400 5800 Monthly cost of trucks on 4 month lease 21280 21280 21280 21280 Monthly cost of trucks on 3 month lease 6450 6450 6450 0 Monthly cost of trucks on 2 month lease 0 3700 3700 0 Monthly cost of trucks on 1 month lease 0 0 4000 0 Total Monthly cost under original formulation 27730 31430 35430 21280 Average cost per truck 2773.00 2619.17 2530.71 2660.00 Sunk cost is one which is already incurred and cannot be recovered. In this case the trucks on long term lease are already available and the company needs to incur the cost irrespective of whether they use the trucks or not Costs Associated with long term lease Monthly Lease Charges 600 Driver cost 20 per hour fuel costs 100 per day Total No of days truck is used per month 20 days Total No of Hours per days truck is used 8 Total Number of Hours per month 160 Driver cost 3200 fuel costs 2000 Total monthly cost per truck under long term lease 5800 Short term leases rates 1 month 4000 2 months 3700 3 months 3225 4 months 3040 Optimal solution would when we use the lowest cost leases first and next costlier ones and so on Time taken to complete work 4 months months 1 2 3 4 Number of Trucks required 10 12 14 8 Number of Trucks taken on 4 month lease in month1 8 0 0 0 Number 4 month lease trucks working all the months 8 8 8 8 Remaining requirement 2 4 6 0 No of Trucks taken on 3 month lease in month 1 2 Number 3 month lease trucks working all three months 2 2 2 0 Remaining Requirement 0 2 4 0 No of trucks taken on 2 month lease in month 2 2 No of 2 month trucks working in month 2 and 3 0 2 2 0 Remaining requirement 0 0 2 0 No of trucks taken on 1 month lease in month 3 0 0 2 0 No of trucks taken on 4 month lease in month 1 would be the least number required in all 4 months No of trucks taken on 3 month lease in month 1 would be the least number required of the remiaining and so on

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