Project Management - Labor, Material and Equipment Utilization

A common situation includes "users" whose needs are not deterministic and the arrival of materials that meet those needs occurring at random intervals. What is the impact on the smooth flow of work? How can bottlenecks and queues be minimized?

Let's look at a construction example in which a crane delivers a load at random intervals. Bunching will occur if loads are delivered faster than they can be used. Shortage will develop when the delivery rate is less than they rate at which loads can be used. While the average delivery rate may be optimal, temporary resource shortages and excesses will negatively effect project productivity.

Waiting Time With Random Arrivals

The best usage of labor, material and equipment can be calculated for various scenarios. The point of this article is note that mathematical tools are available to help us optimize the use of labor, material and equipment. Let's look at an example of determining the cost of waiting time when materials arrive at random intervals.

For this example an average of five trucks with project materials per hour arrive at random intervals. Each load must be inspected and inspection requires ten minutes. The cost of waiting time is $45 per hour.

Using the formula: w = a/2x²(I-a/x)

in which w is the average waiting time, a is the average inspection rate, and x is the deterministic service rate.

This gives us an average waiting time of 0.4 hour at a cost of (45)(0.4)(5) = $90 per hour.

If the inspection rate can be increased to ten loads per hour by using two inspectors, the expected waiting time for any one load become 0.05 hour. This has a cost of (45)(0.05)(5) = $11.25 per hour.

If the cost of an inspector is less than $78.75 per hour then two inspectors should be used.