CEM 514Modeling of Construction Operations     

The LP/IP hybrid method for construction time-cost trade-off analysis

By

Samir Abdallah Sulaiman

STUDY CONTENTS

I. IntroductionII. Objective III. Current Practice of time cost trade-off analysisIV. The LP/IP Hybrid Method For Construction

Time-cost Analysis1. The LP Model (Convex Hull Method)2. The IP Model

V. Case ExampleVI. Computer Implementation VII. Conclusion

I. Introduction

Critical Path Method (CPM) is used in project scheduling and control since 1960. Many techniques were developed to enhance the effectiveness of CPM. Time-Cost trade-off analysis is one of the best techniques used to improve CPM usage.

There is a certain relation between Time and cost to complete activities within a project. Optimization decisions in any project between these two factors. In big projects containing hundreds of activities, It is almost impossible to specify all possible combination to identify the best decision that the project can be completed in shortest time and less cost.

This presentation will explain an approach named LP/IP hybrid method to assist construction planners in making time-cost trade-off decisions

II. Objective

The objective of this presentation is to explain an approach named LP/IP hybrid method to assist construction planners in making time-cost trade-off decisions.

The LP/IP method first establishes a high quality lower bound of the time/cost relationship of a project using the Linear programming approach (LP). Once the lower bound generated, Integer Programming (IP) approach is used to identify the exact solution for one specified duration.

The lengthy and error-prone process of formulation linear and integer programming objective function and constraints are replaced by Excel sheet so the users can intuitively define time-cost and precedence relationship for activities.

III. Current Practice of time cost trade-off analysis

Mathematical and heuristic methods are two major approaches used to solve the time-cost trade-off problems in project scheduling. LP, IP or dynamic programming methods are used to solve for trade-off cost problems. The advantage of mathematical approaches include efficiency and accuracy. However, formulating constraints and objectives is time consuming and error-prone. Beside many construction planners are not trained to do perform this type of modeling and especially for large networks.

heuristic methods are non-computer approaches which require less computational effort than mathematical do. It is a good approach to obtain a good solutions but does not guarantee optimal solutions. Moreover, different scenario and what if analysis is difficult to apply.

Many project planners wish to have an easy to use tool to interface directly with Project planning system such as Primavera. As of that, the author of this paper targeted to use more efficient algorithms that yield to more accurate solutions and easy to use tool for practicality.

III. The LP/IP Hybrid Method For Construction Time-cost Analysis

Obtaining a good and nearly optimum solution with a reasonable amount of computation effort are the major motivating factors for this method. The IP/LP hybrid method is a hybrid approach which uses

1) LP to generate lower bound of the minimum direct cost curve efficiently.

2) IP to find the exact solution for a single specified duration

III. The LP Model (Convex Hull Method)

The idea here is to define the time-cost curve as “linear and continuous” when the durations of this curve are successive integers and the relationship between the options is linear. Fig.1

The convex hull algorithm in this method generates the convex hull formed by various options specified for each activity. The convex hull is established by the following steps:, Elimination of zones

LP algorithms, such as simplex method can be used to find the optimal solutions. LP establishes lower bounds for time-cost relationship of a project. These lower bounds give the planner the option to select desired durations. Finding the exact solutions will be by using the IP method.

IV. The IP Model

To get an exact solution for the time-cost trade-off problem, IP must be used. In the IP model, variable Xij is assigned to the option j within activity i. for each activity I, the sum of the variables Xij should be 1 because only one option will be selected as the optimal option for activity i. This model can be described as per the following program objective and constraints.

V. Case Example

• Simple network is presented here as an example• Utility data of the network activities are given as per tableSolution steps

1. Data input (table1, table2)2. Find the LP solutions (convex hull algorithm)3. Set desired duration (based on the previous step). Project

requirements.4. Use IP to solve the exact solution5. Plot the total cost curve (assuming indirect cost 1000$)

V. Conclusion

Comparing solutions obtained by convex hull algorithm with the exact solutions, the convex hull bound the exact solutions from below as shown in fig. The time required to solve the entire time-cost trade-off curve based on LP/IP algorithm is 5 min using 486 PC.

By this approach the construction planner will own an efficient analytical tool for time-cost trade-off decisions. This method obviously has the advantage of saving time and computation.

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