**Abstract**

Resources planning and operations are essential concerns and specialty areas within industrial engineering and project management. Crew configuration plays a significant role in resource planning and operations. Crew configuration inefficiency is one of the most common reasons for the low productivity of manpower. Resources planning contains some inherent uncertainties and risks because it is an estimate of unknown values. Many factors affect resource planning. Some of these factors are fuzzy variables such as expert's judgment, and some of them are random variables such as direct cost of equipment. The objective of this chapter is to present a method that combines fuzzy logic and Monte Carlo simulation (MCS) for the selection of the best crew configuration to perform a certain task. The model presented in this chapter is a joint propagation method based on both the probability theory of MCS and the possibility theory of fuzzy arithmetic. The research outcomes indicate that the presented model can reduce the duration and cost of a certain task, which will help reduce the cost and duration of the project.

**Keywords:** fuzzy logic, Monte Carlo simulation, manpower productivity, resources planning, optimization

### **1. Introduction**

Project schedule can often be shortened by assigning excess crews (labor and equipment) to critical activities. However, the ultimate cost consequences to the project are often difficult to estimate. This schedule compression strategy may adversely impact project cost performance because the overstaffing of critical activities may result in wasted or idle time in these activities. Trade-offs between elapsed time and the associated cost of crew is required to determine the best crew configurations [1]. This is not a trivial issue because of the complex relationships between elapsed time, crew configurations, and their associated costs.

Monte Carlo simulation (MCS) has been used widely to solve probabilistic uncertainty in range estimating for projects [2]. It has been extensively used for generating many scenarios by considering the random sampling of each probability distribution. In practice, the probability of an event can be estimated according to the frequency of that event occurring in a number of experiments [3]. However, if the number of experiments is not large enough to be significant, and more experiments cannot be performed, it is not possible to accurately estimate the event's probability. In these circumstances, we can engage human experts who are usually

good at supplying the required information. Some researchers try to convert experts' knowledge into probabilistic distributions. However, this can lead to pointless and unreliable results since the results are obtained based on experts' subjective judgments and assumptions [4]. Fuzzy Logic has been used successfully for representing such uncertainties in experts' judgments [5].

In a Monte Carlo simulation, an arbitrary value is selected for each of the activities, based on the range of estimates. The model is calculated based on this arbitrary value. The result of the model is recorded, and the process is repeated [6]. A traditional Monte Carlo simulation calculates the model hundreds/thousands of times, each time using different randomly selected values. When the simulation is complete, we have a large number of outcomes, each based on random input values. These outcomes are used to describe the likelihood, or probability, of reaching

*Fuzzy Monte Carlo Simulation to Optimize Resource Planning and Operations*

Fuzzy logic is a technique that offers a clear conclusion from unclear and inaccurate data. The Fuzzy Set concept was first introduced by Zadeh in 1965 [7]. He was inspired by witnessing that human thinking could utilize ideas that do not have precise borders [8]. Fuzzy logic and fuzzy hybrid methods have been used to capture and model risk, thereby improving workforce and project management [8]. Fuzzy logic can effectively capture expert knowledge and engineering judgment and combine these subjective elements with project data to improve construction decision making, performance, and productivity [9]. The triangular fuzzy number (TFN) is a common shape of fuzzy logic (**Figure 3**). The α-cut method is a common technique to do arithmetic operations on a Triangular Membership Function [10]. The α-cut signifies the degree of risk that the project managers are ready to take (i.e., no risk to full risk). Because the value of α could significantly affect the

solution, it should be wisely chosen by project managers [11].

**4. Fuzzy Monte Carlo simulation (FMCS)**

*Triangular fuzzy set developed based on experts' judgment.*

The proposed FMCS is a joint propagation method based on both the probability theory of MCS and the possibility theory of fuzzy arithmetic. A generalized problem in which we have both types of uncertainty, fuzzy and probabilistic. Here, we need to determine the output Y of a function (M) that has R1, R2, … , Rn being random

various results in the model [6] (**Figure 2**).

*DOI: http://dx.doi.org/10.5772/intechopen.93632*

**3. Fuzzy logic**

**Figure 3.**

**173**

This research proposes a fuzzy Monte Carlo simulation (FMCS) model that provides the capability of considering fuzzy and probabilistic uncertainty simultaneously to help improve decisions regarding crew configurations.
