Chapter 8—Nonlinear Programming and Evolutionary Optimization

Chapter 8—Nonlinear Programming and Evolutionary Optimization

Chapter 8—Nonlinear Programming and Evolutionary Optimization

PROJECT

69. Project 8.1- Truck Company Expansion

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Kornfield Trucking handles private and commercial moves. They
currently own 500 moving vans and employ 2000 full-time workers. Their trucks
are used to pick-up and deliver office and household goods throughout the
Eastern and Southeastern states. Kornfield mans each truck with three workers.
This allows driver swaps providing increased miles-covered-per-hour ratio while
staying within safety requirements for individual driving time. A 3-person crew
also reduces company reliance on local help. Local distributors and warehouses
provide a pool of laborers for loading and unloading the moving trucks. While
in the past this arrangement has worked well, the arrangement has soured
recently as the temporary workers have demanded higher wages while produced
less work. Despite their pay and benefits package, Kornfield still finds that
the nature of the work (lifting and time on the road) makes for a high rate of
turnover. Thus, Kornfield maintains an excess of workers/drivers, but no more
than 3.75 workers per truck at any time.

The following information is available on the trucks in the
Kornfield inventory and their options for new purchases.

Purchase
Price

Salvage
Value

Yearly
Maintenance

Miles Per
Year

Miles per
Gallon*

New Truck

$55,000

$ 750

100,000

12.5 mpg

Old Truck

$25,000

$1500

100,000

10 mpg

*assume $1.50/gal

The following information applies to Kornfield personnel actions.

Hiring Cost

Firing Cost

Salary

New Worker

$1000

$28,000

Old Worker

$1500

$35,000

Kornfield has an operating budget of $ 75M next year and wants to
expand their operations. As a part of this expansion, they are considering
options for their truck fleet and may purchase new trucks, sell old trucks to
salvage or some combination of the two. Any salvage money received is rolled
into the operating budget. Kornfield is also considering possible changes to
their work force. Their current force has a fairly high average salary and
their operating budget is not greatly affected by releasing current employees.
On the other hand, newer employees carry a much lower average salary and do not
tax the operating budget heavily in hiring and training costs.

The Cobb-Douglas production function is used to model the number
of vehicle miles driven per year. This function represents the quantity
Kornfield management would like to maximize as they expand their operations.
The general form of the Cobb-Douglas production function is the following:

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where y is the output, each Xi represents an input and
the letters represent constants. This function generalizes to fewer or a
greater number of parameters than the three depicted above. The constants for
the Kornfield Trucking production function are (a, b, c, d) = (9.1, 0.05, 0.40,
0.50).

Formulate the Kornfield Trucking problem as a non-linear
programming problem. Implement the problem in Excel and use Risk Solver
Platform (RSP) generalized reduced gradient (GRG) routing to obtain a solution
to the problem. What is a recommended solution for Kornfield Trucking?

 

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