Problem Solving Sample: Aurora Custom Cars Production Problem

Considering the costs of shipping cars via either of the two ports - Halifax or Vancouver, it is apparent that shipping through Vancouver is less costly than shipping through Halifax. To minimize costs where the cars to ship exceed the capacity of Vancouver, one will have ship the first cars through Vancouver and shift to Halifax after the exhaustion of Vancouvers capacity. There are three cars to ship to Saudi Arabia, four cars to ship to India and one car ship to Britain. To minimize the delivery costs, the company should ship all the Saudi Arabian cars through Vancouver, which will leave two more cars to be shipped through Vancouver. Shipping to India through Halifax costs $1000 more than shipping through Vancouver; thus, the company should use the two slots left at Vancouver to ship two of the Indian cars. The company should ship the remaining two Indian cars and One British car through Halifax. The lowest possible shipping cost is $25,400.

If the company must deliver all orders to customers by May 4, and shipping takes 7 days, it means it must complete work on all orders by April 27. The first job begins on the morning of Monday, April 10, which is 18 days (Monday, April 10 inclusive) before the last day by which the company should have completed work on all orders. Subtracting the weekends leaves the company with 14 days to complete work on all the job orders. There are nine work hours for each day, which puts the total work hours available to the company at 9*14 = 126 hours. However, the eight orders require a total 157 hours, meaning the company will not complete some orders. Consequently, the company will not work on the Mercedes Benz destined for Britain and the Jaguar destined for India these two orders require a total of 31 hours, which is the deficit the company faces.

The costs include the fixed and variable costs. The fixed costs include the overhead expenses, salary for the salesperson, and salaries for the permanent office employees. The variable costs include the purchase cost of the cars, wages of the shop employees, the cost of the parts, and the delivery cost of the cars. The average revenue per job is $306879.17, while the average cost per job stands at $260156.67; with total fixed costs standing at $135600, the break even number of jobs is 2.9, which means the company should complete three jobs to break even. The company can only complete six jobs this month at a profit of $144735. ACC should fly the cars instead of shipping them. The average contribution per job stands at $46722.50, which means flying the cars will increase contribution by $46722.5*2 = $93445. Incremental costs from flying the cars amount to $24000 in additional transportation costs, which reduces the additional contribution to $93445 - $24000 = $69445. Since flying the cars will increase the contribution without increasing the fixed costs, it is appropriate for the company to fly the cars because it will earn additional profit.