## Time-Cost-Quality Tradeoff Modeling based on Resource Allocation

### Introduction

The time, quality, and cost are usually three contradictive objectives which are often traded off in project practices by managers randomly if they lack efficient tools. The time, quality, and cost are interdependent parameters in a building project.

When the construction time is shortened, the project cost should be added. It is a tough challenge to balance those objectives in practice. The cost is usually the most important determinant of selecting a contractor in current construction industry. A contractor is undergoing fewer profit margins now than ever when current construction industry is more competitive. He might lose all profit or even go bankrupt if he fails to implement one or two projects properly in right quality, time, and cost. In order to reduce cost, some contractors risk using inferior construction materials and incapable labor which frequently results in poor quality and thus compromise safety standards. Local government offices have to monitor and regulate construction quality to secure the minimum standards. Otherwise any contractor might be punished or ousted by governments if he fails to obey regulations of construction quality and safety. Besides, the time is such a top visible parameter that contractors would deliver the construction project within their promised schedule based on agreements and contracts. Obviously the time is sensitive in contracting projects and controlling cost. A construction manager should deliberately balance the cost, time, and quality, as well as construction resources, in the early planning phase.

Since the cost and time are two of the most important objectives which are easily quantified in a construction project, time-cost tradeoff problem has been researched for a long time. Basic common assumptions for cost-time tradeoff are deterministic durations and linear time-cost functions where discrete construction resources such as labor and machine are crashed up to a continuous extent. In order to reach global optimum in a large-scale time-cost tradeoff model, numerous trials are usually needed. There are more than 23 optimal techniques thought to be the most effective in achieving time-cost tradeoff problems. The evolutionary algorithms are more efficient to avoid local optimization. A practical method to solve construction time-cost tradeoff problems is the genetic algorithm (GA). Recently the ant colony optimization (ACO) algorithm and the particle swarm optimization algorithm are applied to obtain a global optimization solution. Geem employed the harmony search algorithm to perform time-cost biobjective tradeoff where a network of up to 18 nodes was tested well. These new paradigm algorithms were able to obtain optimal solutions for cost-time tradeoff models within only moderate computational effort.

Quality is an important parameter correlating highly with time and cost parameters. But it is not a quantitative parameter in nature, practical time-cost-quality tradeoff models are seldom developed from previous research works of the literature. Babu and Suresh proposed a framework to study the tradeoff among time, cost, and quality using three interrelated linear programming models. Then Khang and Myint applied the linear programming models in an actual cement factory construction project, which was depicted by a 52-activity CPM incorporated with their time, cost, and quality individually, and quality parameter in every activity varied from 0.85 to 1. Tareghian and Taheri assumed the duration and quality of project activities to be discrete and developed a three interrelated integer programming model but simplified the optimization algorithm with solving one of the given entities by assigning desired bounds on the other two. El-Rayes and Kandil presented a multiobjective model to search for an optimal resource utilization plan that minimizes construction cost and time while maximizing its quality, applied genetic algorithm to provide the capability of quantifying and considering quality, and visualized optimal tradeoffs among construction time, cost, and quality by an application example.

Although the objectives of cost and time might be mentioned frequently by natural numbers, the objective of quality is seldom described in quantities, which worsens numerical tradeoff among project time, cost, and quality. This paper will present a new solution for solving time-cost-quality tradeoff problem based on project breakdown structure method and task resource allocation.