“Optimizing Quarry Truck Loading Processes: A Cost-Effective Analysis”

QUESTION

You are in charge of a quarry that supplies sand and stone aggregates to your company’s construction sites. Empty trucks from construction sites arrive at the quarry’s huge piles of sand and stone aggregates and wait in line to enter the station, which can load either sand or aggregate. At the station, they are filled with material, weighed, checked out, and proceeded to a construction site. Currently, 9 empty trucks arrive per hour, on average. Once a truck has entered a loading station, it takes 6 minutes for it to be filled, weighed, and checked out. Concerned that trucks are spending too much time waiting and being filled, you are evaluating two alternatives to reduce the average time the trucks spend in the system. The first alternative is to add side boards to the trucks (so that more material could be loaded) and a helper at the loading station (so that filling time could be reduced) at a total cost of $50,000. The arrival rate of trucks would change to six per hour, and the filling time would be reduced to 4 minutes. The second alternative is to add another loading station identical to the current one (second server model) at a cost of $80,000. The trucks would wait in a common line and the truck at the front of the line would move to the next available station. You realized adding another loading station is a 2 server model! Thus, you calculated the average waiting time in the system using Solver and the result is W= 0.1254 hour or 7.52 minutes! a. What is the average time a truck waits in the system with current setup? b. What is the average time a truck waits in the system if you apply the first alternative? c. Which alternative would you recommend if you want to reduce the current average time the trucks spend in the system, including service?

ANSWER

In the realm of quarry management, the optimization of truck loading processes is of paramount importance to ensure the smooth and cost-effective operation of supplying sand and stone aggregates to construction sites. In this essay, we will delve into the intricacies of evaluating two alternative solutions aimed at reducing the average time trucks spend in the system. This optimization is critical for maintaining efficiency in construction operations while keeping costs in check.

Average Time a Truck Waits in the System with the Current Setup

Currently, under the existing setup, the arrival rate of empty trucks at the quarry is approximately 9 trucks per hour. On average, it takes 6 minutes, which translates to 0.1 hours, for a truck to be filled, weighed, and checked out. To understand the average time a truck spends in the system, we turn to the M/M/1 queue formula.

�=1�−�W=μ−λ1​

Where:

$W$ is the average time a truck waits in the system.

$\mu$ is the service rate, equivalent to 1 truck per 0.1 hours.

$\lambda$ is the arrival rate, which is 9 trucks per hour.

Plugging in these values, we derive the following:

�=1(1/0.1)−9=110−9=1 hourW=(1/0.1)−91​=10−91​=1 hour

Thus, the current setup results in an average waiting time for a truck of 1 hour.

Average Time a Truck Waits in the System with the First Alternative:

The first alternative under consideration introduces several changes to the system. It includes adding sideboards to the trucks and employing a helper at the loading station. These modifications lead to a reduced arrival rate of 6 trucks per hour, and a shorter filling time of 4 minutes, equivalent to 0.067 hours. Using the same M/M/1 queue formula, we can now calculate the average time a truck waits in the system with this alternative:

�=1(1/0.067)−6≈0.1202 hoursW=(1/0.067)−61​≈0.1202 hours

With this alternative, the average waiting time for a truck is approximately 0.1202 hours or 7.21 minutes.

Recommendation

The choice of the optimal alternative hinges on not only improving efficiency but also ensuring cost-effectiveness. In this evaluation, the first alternative clearly stands out. It significantly reduces the average waiting time for trucks from 60 minutes in the current setup to just 7.21 minutes with the proposed changes. This represents a substantial enhancement in the efficiency of truck loading processes.

Furthermore, when considering costs, the first alternative is more financially viable, incurring an expense of $50,000. In contrast, the second alternative, which involves adding an additional loading station, comes at a higher cost of $80,000. The first alternative optimizes the loading process by augmenting the loading capacity through sideboards and reducing filling time with the inclusion of a helper, aligning perfectly with the primary objective of reducing the time trucks spend in the system.

In conclusion, for the quarry’s operations, the first alternative – incorporating sideboards on trucks and hiring a helper at the loading station – is the recommended course of action. This alternative not only enhances efficiency but also proves to be more cost-effective. By implementing this alternative, the quarry can significantly improve its service to construction sites, ensuring smoother operations and substantial cost savings. It’s a win-win solution that advances both operational efficiency and the bottom line.