Multiobjective Linear Programming Model for Scheduling Linear Repetitive Projects

Linear repetitive construction projects require large amounts of resources which are used in a sequential manner and therefore effective resource management is very important both in terms of project cost and duration. Existing methodologies such as the critical path method and the repetitive scheduling method optimize the schedule with respect to a single factor, to achieve minimum duration or minimize resource work breaks, respectively. However real life scheduling decisions are more complicated and project managers must make decisions that address the various cost elements in a holistic way. To respond to this need, new methodologies that can be applied through the use of decision support systems should be developed. This paper introduces a multiobjective linear programming model for scheduling linear repetitive projects, which takes into consideration cost elements regarding the project’s duration, the idle time of resources, and the delivery time of the project’s units. The proposed model can be used to generate alternative schedules based on the relative magnitude and importance of the different cost elements. In this sense, it provides managers with the capability to consider alternative schedules besides those defined by minimum duration or maximizing work continuity of resources. The application of the model to a well known example in the literature demonstrates its use in providing explicatory analysis of the results.     

Productivity Scheduling Method: Linear Schedule Analysis with Singularity Functions

This paper describes a new integrated method of linear schedule analysis using singularity functions. These functions have previously been used for structural analysis and are newly applied to scheduling. Linear schedules combine information on time and amount of work for each activity. A general model is presented with which activities and their buffers can be mathematically described in detail. The algorithm of the new method forms the body of the paper, including the steps of setting up initial equations, calculating pairwise differences between them, differentiating these to obtain the location of any minima, and deriving the final equations. The algorithm consolidates the linear schedule under consideration of all constraints and, thus, automatically generates the minimum overall project duration. The model distinguishes time and amount buffers, which bears implications for the definition and derivation of the critical path. Future research work will address float and resource analysis using the new model.     

Optimized Scheduling of Linear Projects

This paper presents a model, designed to optimize scheduling of linear projects. The model employs a two-state-variable, N-stage, dynamic programming formulation, coupled with a set of heuristic rules. The model is resource-driven, and incorporates both repetitive and nonrepetitive activities in the optimization process to generate practical and near-optimal schedules. The model optimizes either project construction duration, total cost, or their combined impact for what is known as cost-plus-time bidding, also referred to as A+B bidding. The model has a number of interesting and practical features. It supports multiple crews to work simultaneously on any activity, while accounting for: (1) multiple successors and predecessors with specified lead and lag times; (2) the impact of transverse obstructions, such as rivers and creeks, on crew assignments and associated time and cost; (3) the effect of inclement weather and learning curve on crew productivity; and (4) variations in quantities of work in repetitive activities from one unit to another. The model is implemented in a prototype software that operates in Windows? environment. It is developed utilizing object-oriented programming, and provides for automated data entry. Several graphical and tabular output reports can be generated. An example project, drawn from the literature, is analyzed to demonstrate the features of the developed model.     

Planning and Scheduling Highway Construction

This paper presents a model designed to integrate the planning and scheduling phases of highway construction projects, focusing primarily on the planning aspects. The model automatically generates the work breakdown structure (WBS) and precedence network respecting job logic and stores a list of construction operations typically encountered in highway projects. The generated network can subsequently be modified to suit the unique requirements of the project being considered. An object-oriented model is developed for planning highway construction operations. The model employs resource-driven scheduling in order to suit the repetitive nature of this class of projects. It accounts for (1) resource availability; (2) multiple preceding and succeeding activities; (3) transverse obstructions; (4) activities with varying quantities of work along the highway length; (5) the impact of inclement weather on crew productivity; and (6) the beneficial effect of the learning curve. At the core of the model is a relational database designed to store available resources and their respective unavailability periods. The model enables both: (1) activities executed by own force; and (2) activities subcontracted out. The model is incorporated in a prototype software that operates in the Microsoft Windows environment and generates schedules in both graphical and tabular formats. An example project is analyzed to demonstrate the features of the developed model.     

Optimal Planning and Scheduling for Repetitive Construction Projects

This paper presents a multiobjective optimization model for the planning and scheduling of repetitive construction projects. The model enables construction planners to generate and evaluate optimal construction plans that minimize project duration and maximize crew work continuity, simultaneously. The computations in the present model are organized in three major modules: scheduling, optimization, and ranking modules. First, the scheduling module uses a resource-driven scheduling algorithm to develop practical schedules for repetitive construction projects. Second, the optimization module utilizes multiobjective genetic algorithms to search for and identify feasible construction plans that establish optimal tradeoffs between project duration and crew work continuity. Third, the ranking module uses multiattribute utility theory to rank the generated plans in order to facilitate the selection and execution of the best overall plan for the project being considered. An application example is analyzed to illustrate the use of the model demonstrate its new capabilities in optimizing the planning and scheduling of repetitive construction projects.     

Scheduling∕Cost Optimization and Neural Dynamics Model for Construction

A general mathematical formulation is presented for the scheduling of construction projects and is applied to the problem of highway construction scheduling. Repetitive and nonrepetitive tasks, work continuity constraints, multiple-crew strategies, and the effects of varying job conditions on the performance of a crew can be modeled. An optimization formulation is presented for the construction project scheduling problem, with the goal of minimizing the direct construction cost. The nonlinear optimization is then solved by the neural dynamics model developed recently by Adeli and Park. For any given construction duration, the model yields the optimum construction schedule for minimum construction cost automatically. By varying the construction duration, one can solve the cost-duration trade-off problem and obtain the global optimum schedule and the corresponding minimum construction cost. The new construction scheduling model provides the capabilities of both the critical path method (CPM) and linear scheduling method (LSM) approaches. In addition, it provides features desirable for repetitive projects, such as highway construction, and allows schedulers greater flexibility. It is particularly suitable for studying the effects of change order on the construction cost. This research provides the mathematical foundation for development of a new generation of more general, flexible, and accurate construction scheduling systems.     

Object-Oriented Model for Repetitive Construction Scheduling

This paper presents the development of an object-oriented model for scheduling of repetitive construction projects such as high-rise buildings, housing projects, highways, pipeline networks, bridges, tunnels, railways, airport runways, and water and sewer mains. The paper provides an overview of the analysis, design, and implementation stages of the developed object-oriented model. These stages are designed to provide an effective model for scheduling repetitive construction projects and to satisfy practical scheduling requirements. The model incorporates newly developed procedures for resource-driven scheduling of repetitive activities, optimization of repetitive construction scheduling, and integration of repetitive and nonrepetitive scheduling techniques. The model is named LSCHEDULER and is implemented as a windows application that supports user-friendly interface including menus, dialogue boxes, and windows. LSCHEDULER can be applied to perform regular scheduling as well as optimized scheduling. In optimized scheduling, the model can assist in identifying an optimum crew utilization option for each repetitive activity in the project that provides a minimum duration or cost for the scheduled repetitive construction project.     

Comparison of Linear Scheduling Model and Repetitive Scheduling Method

Various linear scheduling techniques have been proposed over the years. The limitations on these techniques have been the inability to determine critical activities. Contractors and departments of transportation have identified this need. Recently two different methods have been proposed—the linear scheduling model and the repetitive scheduling method. This paper discusses basic linear scheduling techniques and then the calculation of critical activities of basic linear scheduling elements using the two methods. The results of the two techniques are compared.     

Linear versus Network Scheduling: A Critical Path Comparison

Linear scheduling methods provide an alternative way of scheduling repetitive projects, to the commonly used network methods. Critical path identification is a major attribute for both methods; therefore, it is very important for practitioners to understand the function of the two methods in this area. The present paper compares the critical path of the recently developed Kallantzis-Lambropoulos repetitive project model against the network scheduling critical path method (CPM), aiming at delving into and pointing out the differences and similarities between them. Initially, the rules for transforming the linear project into an equivalent CPM network are proposed. Then, the rules are applied on a sample linear project. Due to the additional constraint for maintaining resource continuity that the linear method takes into account, the critical paths vary. The constraint is subsequently removed from selected activities and comparison is repeated; the critical paths then coincide. In order to validate the findings and ensure impartiality of results, a random linear project generator is developed. A group of twenty-five random linear projects and their equivalent networks is produced. Their critical paths are analyzed, compared and classified. Conclusions support that the proposed comparison could be beneficial to users of linear scheduling methods, while the random project generator can serve other related research.     

Fuzzy Repetitive Scheduling Method for Projects with Repeating Activities

In projects with repeating activities (such as multistory buildings, highways, or pipelines consisting of reiterating identical or similar units) and in which the activity unit production rates are characterized by uncertainty or imprecision, fuzzy set theory and the well-established repetitive scheduling method (RSM) can be combined to ensure uninterrupted usage of resources between similar activities in different units. The reason for this approach is that in practice the application of RSM may be hindered by several considerations, for example, repetitive units may be slightly different from each other, the performance of construction crews may vary, and there may be complex resource matching and sharing between activities and work sites. The proposed methodology is termed fuzzy repetitive scheduling method (F-RSM), and it requires a generalization of RSM in which schedules are represented by two- or three-dimensional graphs and whereby the concepts of a control segment and the controlling sequence area are introduced. The resulting methodology addressing the original RSM scheduling problem is presented in this paper.     

Construction Project Scheduling with Time, Cost, and Material Restrictions Using Fuzzy Mathematical Models and Critical Path Method

This article evaluates the viability of using fuzzy mathematical models for determining construction schedules and for evaluating the contingencies created by schedule compression and delays due to unforeseen material shortages. Networks were analyzed using three methods: manual critical path method scheduling calculations, Primavera Project Management software (P5), and mathematical models using the Optimization Programming Language software. Fuzzy mathematical models that allow the multiobjective optimization of project schedules considering constraints such as time, cost, and unexpected materials shortages were used to verify commonly used methodologies for finding the minimum completion time for projects. The research also used a heuristic procedure for material allocation and sensitivity analysis to test five cases of material shortage, which increase the cost of construction and delay the completion time of projects. From the results obtained during the research investigation, it was determined that it is not just whether there is a shortage of a material but rather the way materials are allocated to different activities that affect project durations. It is important to give higher priority to activities that have minimum float values, instead of merely allocating materials to activities that are immediately ready to start.     

Challenges in Line-of-Balance Scheduling

The line-of-balance (LOB) method of scheduling is well suited to projects that are composed of activities of a linear and repetitive nature. The objective of this study is to set down the basic principles that can be used in the development of a computerized LOB scheduling system that overcomes the problems associated with existing systems and creates solutions to problems encountered in the implementation of repetitive-unit construction. The challenges associated with LOB scheduling include developing an algorithm that handles project acceleration efficiently and accurately, recognizing time and space dependencies, calculating LOB quantities, dealing with resource and milestone constraints, incorporating the occasional nonlinear and discrete activities, defining a radically new concept of criticalness, including the effect of the learning curve, developing an optimal strategy to reduce project duration by increasing the rate of production of selected activities, performing cost optimization, and improving the visual presentation of LOB diagrams.     

Finance-Based Scheduling of Construction Projects Using Integer Programming

Construction scheduling is the process of devising schemes for sequencing activities. A realistic schedule fulfills the real concerns of users, thus minimizing the chances of schedule failure. The minimization of total project duration has been the concept underlying critical-path method/program evaluation and review technique (CPM/PERT) schedules. Subsequently, techniques including resource management and time-cost trade-off analysis were developed to customize CPM/PERT schedules in order to fulfill users’ concerns regarding project resources, cost, and time. However, financing construction activities throughout the course of the project is another crucial concern that must be properly treated otherwise, nonrealistic schedules are to be anticipated. Unless contractors manage to procure adequate cash to keep construction work running according to schedule, the pace of work will definitely be relaxed. Therefore, always keeping scheduled activities in balance with available cash is a potential contribution to producing realistic schedules. This paper introduces an integer-programming finance-based scheduling method to produce financially feasible schedules that balance the financing requirements of activities at any period with the cash available during that same period. The proposed method offers twofold benefits of minimizing total project duration and fulfilling finance availability constraints.     

Application of Linear Scheduling

Many projects, such as the construction of roadways, pipelines, and high‐rise buildings, involve repetitive activities. A method for scheduling such work, the Linear Scheduling Method (LSM) is presented. In an LSM schedule, the repetitive activities are plotted as lines of constant or varying slopes on two axes, distance versus time. Discrete activities may be shown at their appropriate times and locations and then referenced to a network schedule for additional detail. The Linear Scheduling Method is illustrated by applying it to an actual roadway construction project. The simplicity of the system and advantages for certain types of projects are revealed. A sample schedule is used to derive information that is comparable to what may be obtained from an equivalent CPM network.     

Linear Scheduling Model with Varying Production Rates

Activity production rates drive the development and accuracy of linear schedules. The nature of linear projects dictates an assortment of variables that affect each activity’s production rate. The purpose of this research was to expand the capabilities of linear scheduling to account for variance in production rates when and where the variance occurs and to enhance the visual capabilities of linear scheduling. This new linear scheduling model, a linear scheduling model with varying production rates (LSMVPR), has two objectives. The first is to outline a framework to apply changes in production rates when and where they occur along the horizontal alignment of the project. The second objective is to illustrate the difficulty or ease of construction through the time-location chart. This research showed that the changes in production rates because of time and location can be modeled for use in predicting future construction projects. Using the concept of working windows, LSMVPR allows the scheduler to develop schedule durations on the basis of minimal project information. The model also allows the scheduler to analyze the impact of various routes or start dates for construction and the corresponding impact on the schedule. The graphical format allows the construction team to visualize the obstacles in the project when and where they occur by using a new feature called the activity performance index (API). This index is used to shade the linear scheduling chart by time and location with the variation in color indicating the variance in predicted production rate from the desired production rate.     

Fuzzy Optimal Model for Resource-Constrained Construction Scheduling

Activity duration is uncertain due to the variation in the outside environment, such as weather, site congestion, productivity level, etc. Furthermore, resources for construction activities are limited in the real construction world so that scheduling must include resource allocation. A new optimal resource-constrained construction scheduling model is proposed in this paper, in which the effects of both uncertain activity duration and resource constraints are taken into account. Fuzzy set theory is used to model the uncertainties of activity duration. A genetic algorithm-based searching technique is adopted to search for the fuzzy optimal project duration under resource constraints. The model can effectively provide the optimal fuzzy profiles of project duration and resource amounts under the constraint of limited resources.     

Efficient Repetitive Scheduling for High-Rise Construction

A new scheduling and cost optimization model for high-rise construction is presented in this paper. The model has been formulated with a unique representation of the activities that form the building’s structural core, which need to be dealt with carefully to avoid scheduling errors. In addition, the model has been formulated incorporating: (1) the logical relationships within each floor and among floors of varying sizes; (2) work continuity and crew synchronization; (3) optional estimates and seasonal productivity factors; (4) prespecified deadline, work interruptions, and resource constraints; and (5) a genetic algorithms-based cost optimization that determines the combination of construction methods, number of crews, and work interruptions that meet schedule constraints. A computer prototype was then developed to demonstrate the model’s usefulness on a case study high-rise project. The model is useful to both researchers and practitioners as it better suits the environment of high-rise construction, avoids scheduling errors, optimizes cost, and provides a legible presentation of resource assignments and progress data.     

Integrated Simulation System for Construction Operation and Project Scheduling

Simulation modeling is important in predicting the productivity of construction operations and the performance of project schedules. It would be desirable if operation and project models are vertically integrated in practice. However, existing discrete event simulation systems do not allow integrating operation and project models. This paper introduces an integrated simulation system named “Construction Operation and Project Scheduling” (COPS). COPS analyzes the productivity of construction operations as well as the performance of a project schedule individually and jointly. It creates operation models, maintains these models in its operation model library, conducts sensitivity analysis with different resource combinations, finds the optimal resource combination that satisfies the user’s requirements relative to hourly production and hourly cost of the operation, feeds this information into a project schedule, and executes stochastic simulation-based scheduling. A case study is presented to demonstrate this integrated simulation system.     

Expanding Finance-Based Scheduling to Devise Overall-Optimized Project Schedules

Construction contractors often finance projects using bank credit lines that allow contractors to withdraw money up to certain credit limits. Finance-based scheduling provides schedules that ensure that the contractor’s indebtedness at any time during the construction stage does not exceed the credit limit. Generally, constricted credit limits tend to yield prolonged schedules. Provided that credit limits can be adequately relaxed, compressed schedules of compressed-duration activities can be attained. Devising a compressed schedule calls for the incorporation of time-cost trade-off (TCT) analysis to strike a balance between the decreased overhead costs and the increased direct costs of the activities. Since employing TCT analysis usually causes great fluctuations in the daily resource requirements by mixing compressed-duration activities of high resource demand with others of low resource demand, therefore, the need for resource management techniques becomes inevitable to ensure efficient utilization of resources. This note used genetic algorithms to expand finance-based scheduling to devise schedules for relaxed credit limits. A prototype system was developed and coded using VISUAL BASIC, then demonstrated using a five-activity example project. The prototype was validated by comparing the results with those obtained by using the integer programming. Expanding finance-based scheduling to handle the whole spectrum of credit limits helps devise overall-optimized schedules that consider cash, time, cost, and resources.     

Linear Scheduling Model: Float Characteristics

By definition, any activity not on the critical path must have float. The concept of float in the critical path method relates to how long an activity can be delayed before it becomes a critical activity. For linear construction activities, however, the concept of float is somewhat different from that of traditional scheduling techniques. Rather than start time and duration being the main attributes of float, production rate is a more fundamental attribute of a linear activity. As such, for float to be meaningful for a linear activity, it must be reflective of the activity's major characteristic. Rate float captures this characteristic and presents information to construction planners and managers in terms that are meaningful for linear projects. This paper describes rate float as it applies to the linear scheduling model developed by Harmelink and Rowings in 1998.