MATHEMATICAL MODEL OF OPTIMIZATION FOR MIXED PROJECTS. José Gregorio Medina Cepeda. Bogotá, Colombia

Size: px
Start display at page:

Download "MATHEMATICAL MODEL OF OPTIMIZATION FOR MIXED PROJECTS. José Gregorio Medina Cepeda. Bogotá, Colombia jomedina@lasalle.edu.co"

Transcription

1 MATHEMATICAL MODEL OF OPTIMIZATION FOR MIXED PROJECTS José Gregorio Medina Cepeda Bogotá, Colombia 1. Abstract Inside the Investigation and the Administration of Operations, the General Theory of Networks and particularly the models of Networks of Activity, are a key tool in the planning of complex projects that involve many activities. At the moment, the planning concepts and administration of projects are very used in the managerial environment as a tool for the evaluation of costs and time of execution, as well as a mechanism of control of the same ones. If the duration of each activity is known with certainty, you can use the method C.P.M. (Critical Path Method) to determine the time required in the realization of the project. If the duration of the activities is not known with certainty, you can use the technical PERT (Program Evaluation and Review Technique), to estimate the probability of termination of the project in an estimated date. A mathematical model of optimization that analyzes mixed projects (with activities with execution time are know and activities with execution time are uncertain), it will be of great help for the planning and taking of decisions. This can observe it in the sector of the construction, which is developed by projects, where each residence development an individual element with a specific objective that can contain activities in advance of known execution (installation of doors and windows) and activities with uncertain times of execution (masonry, armada and fused of badge) that which embraces the basic characteristics of the mixed projects. The development of applications in the real sector is a way to evaluate and to validate the proposed mathematical model. With the collaboration of Builder's, located in the city of Bogotá, it is presented and evaluates the applicability of the proposed model in a real situation. In a same way, we validate the new theoretical proposal for the development and analysis of MIXED PROJECTS. 2. Key words Theory of networks, CPM, PERT, Mixed projects. 3. Introduction The palpable difficulty of making decisions has made the man to be met in the search of a tool or method that it allows him to make the best decisions according to the available resources and to the objectives that it pursues. Such a developed tool at the end of the years forty, receive the name of Operations Research [1]. The focus of this technique is the same of the scientific method. In particular, the process begins with the careful observation and the formulation of the problem, and it continues in general with the construction of a model mathematical that tries to abstract the essence of the real problem. The network models are applicable to an extensive variety of decision problems, which can be modeled as problems of optimization of network that can be efficient and exactly resolved. Some of these problems of decision are really physical problems, such as the transport or flow of raw material. The family of network flow includes among other models: Assignment problems, critical path, maximum flow, shorter road, transport and minimum cost of flows. The problems are established easily by means of the use of arches and nodes. For the elaboration of a network diagram one must keep in mind that two focuses exist. The first of them is Activities on Arrow (AOA) and the second is Activity on Nodes (AON). When using AOA the arches they represent the activities and the nodes represent the events. In the nets AON, the nodes identify to the activities, and the arches represent the relationships between the activities and the nodes. A 2 C 4 E A C 1 D 5 START END B 3 B Figure 1. Activity on arrow Figure 2. Activity on node The critical path method (CPM) it is used if the duration of each activity is known with certainty and it allows determining the required time to carry out the project. This method, is an administrative process of planning, programming, execution and control of all and each one of the component activities of a project that it should be developed in a critical time and at the good cost, designed in 1957, compound number initially as CPPSM (Critical Path Planning and Scheduling Method), it was used for the programming and control of projects demonstrating its big advantages regarding the classic methods. The method PERT (Program Evaluation and Review Technique), it was designed in the same time of the method CPM and it is fundamental if the duration of the activities is not known with certainty. You can use the technique to estimate the probability that the

2 project ends in a certain date, for that reason it is of great help in the research and development projects for the uncertainty in the runtime of the tasks. At the present time, to differ between CPM and PERT is a difficult task, since from the origins of these two techniques toward the years 50s, the main difference is in the focus in the run-times that some modern authors speak that is to say of a single method PERT/CPM that integrates the analysis element time cost of a project type CPM, with normal well-known times and of cutting. In this way, the mathematical model of optimization that evaluates projects with activities with run-times known with certainty and activities with run-times not known with certainty, will allow to enlarge the field of application of the techniques of optimization of control or project networks. 4. Mathematical model of optimization for mixed projects and application in a construction company. For the development of this document, it is necessary to revise some important theoretical topics as they are it the method CPM, the method PERT and the method PERT/COST, to be able to present the structure mathematical proposal for the mixed projects [2] Project management. A project can be defined as the group of economic, organizational measures and techniques directed to the elaboration of a new object, construction of systems, and elaboration of topics of scientific investigation or of execution of tasks you specify [3]. According to, Anderson, Sweeney and Williams [4] often these projects are so big and complex that the administrators require technical of support for their appropriate gliding, control and execution. Each project you can represent applying the techniques of gliding of nets that it is composed of guided arrows, which are in certain way related reciprocally. It should also be kept in mind that these activities are in function of the time (f t ), also that some dependence relationships should exist among the activities that allow that these they follow a sequence for the achievement of the proposed objective, as well as some resources assigned for each activity. Krajewski and Ritzman [5], they present the methods of planning of nets like a tool for the managers that it allows to watch over and to control the projects. This requires an identification of the required data, to organize and to identify the reciprocal relationships among the activities. They allow to estimate the time and execution cost and to determine the key events of control, it also allows to evaluate the consequences of the exchanges of some resources for other envelope the times and costs. According to Schroeder [6], the gliding of a project refers to those necessary decisions when beginning a project that they establish the general limits, the fundamental objectives, the required resources, the organization type and people key that they will administer it. The programming phase is given when the development team identifies in more detail the plan of the project. The control is in charge of the direction team, which supervises each activity, and it makes the pursuit of the time, the cost and the acting of the in agreement project with the proposed plan. The best form of to watch over and to control the development of the project is by means of the methods of planning in net. These methods [5] consider the project like a group of related activities to each other that can be represented visually by means of a net diagram, the one which this formed by nodes (circles) and arches (arrows) that describe the relationships among the activities. In the last years, they have been used with more frequency the methods that have allowed a better gliding and control of projects and an use of the resources, what has improved the administration and taking of decisions, the current organizations, require the support of technical of administration, gliding and control in the development of their projects every time but complex. To determine the structure of time of the project, it is the starting point that will allow later on developing a project plan [7]. The basic steps of a project are presented: Step 1. Fix the objectives. Step 2. Search and organize the necessary means to reach the previously fixed objectives. Step 3. Control the plan fixed with what being carried out, to make the necessary adjustments on the resources and to make in front of the real conditions. The two methods but used in the planning of project nets they are the method PERT (program evaluation and review technique) and the CPM (critical path method). For the development of the methods PERT and CPM can be considered the following steps: Define the project and all their activities or component tasks. Develop the relationships among the activities. Decide the logical sequence of execution. Trace the network that connects all the activities. Assign the times (or the estimates of time) and cost for each activity. Calculate the line of time but it releases through the net (route criticizes of the project). Use the network for the planning, programming, supervision and control of the project [8] Activity nerwork. They can be defined like a representation of two aspects peculiar of any project [9]: a. Precedence relationships among the different activities of the project, and b. The duration and the cost of each activity In a same way, the precedence is defined like a binary relationship that is: a. Transitive: if the activity "o" precedes to the activity "v" and this in turn precedes to the activity "z", then "o" it precedes "z". b. Not reflexive: the activity "o" it cannot be preceded itself, and c. Not symmetrical: if the activity "o" precedes to the activity "v", then "v", cannot precede to the activity "o". A network diagram, it should flow from the left to the right, and their size doesn't have direct relationship with the run-time of the project, contrary to the diagram of Gantt that is graph in relation to a scale of time [10]. For the construction of these concepts, we take like reference some authors [9], [11]: - Activity: It is the smallest unit in working effort that consumes time and resources; which have to be programmed and controlled. - Arch: The arches can have a flow of some type that goes by them.

3 - Addressed arch: when the flow through the arch, is allowed exclusively in certain sense, the address is indicated the addition a head from the arrow to the end of the line that represents the arch. - Arch without address: when the flow to the inclination of the arch is allowed in both addresses. The flow is in a selected address and not in both senses at the same time. However in the process of taking of decisions on the flow in a non managed arch, it is allowed to make a sequence of assignments of flows in opposed addresses but in the understanding that the real flow will be the net flow (the difference of the flows assigned in the two addresses.) - Capacity of the arch: the maximum quantity of flow that can circulate in a managed arch. - Cycle: it is a trajectory that begins and it finishes in the same node. - Event: It is the point in the one which an or several activities will be completed and another activity or activities will begin. - Node source: it is also known as node origin. This node, has the property that the flow that leaves the node, exceeds the flow that this entering. The inverse case is a node it demands or also called node destination, where the flow that arrives exceeds to the flow that leaves him. It also exists that is to say the transfer node or intermission which satisfies the conservation of the flow, the flow that l enters in the node is similar to the one that comes out. - Project: Group of related activities among if that has defined points of beginning and final; and whose final result is a product or specific service. The projects are also temporary activities in those which the personnel, the materials and the resources combine among if to reach a goal, inside the mark of the specification time. - Network: It is a group of points and a group of lines that certain couples of points unite. The points call themselves NODES, and the lines call themselves ARCHES, bonds or branches. The arches are labeled to give name to the nodes in their extreme points. - Network address: A network that has single managed arches. - Network without address: A network that contains single not directed arches. - Residual network: It shows the remaining capacities to assign additional flows. - Trajectory: it is a succession of different arches that you/they connect two nodes. When some or all the arches of a net are managed arches, the distinction is made among managed and not directed trajectories. A managed trajectory of the node i to the node j, is a succession of arches whose address is toward the node j. A not directed trajectory of the node i to the node j, is a succession of arches whose address (if they have it) it can be from toward or from the node j Algorithm to determine the time of the project for the method CPM and PERT. The critical path methods are an administrative process of scheduling, programming, execution and control of all and each one of the component activities of a project that it should be develop in a critical time and at the good cost. The algorithm presents a series of necessary steps to determine the time of the project, beginning with the evaluation of the early times, which are conceived as the times of beginning minima for an activity, where execution of the proposed plan is given. Then an evaluation of the times late should be made, what it is supposed it is the maximum times of beginning or termination an activity without affecting the plan of the project. Lastly, the difference among these two, allows us to evaluate the ease of the activities, the critical activities (those whose ease is similar to put to zero) and the critical path. PERT. The PERT method (Program Evaluation and Review Technique) it is an instrument designed especially for the manage projects, allowing him to plan, to program and to control the resources that it prepares, with the purpose of obtaining the wanted results. Their main application is in stochastic projects Difficulties of the method PERT Supposition that the durations of the activities are independent is difficult to justify The durations of the activities cannot follow a distribution beta The supposition that the critical path found by CPM will always be the critical road for the project cannot be justified. Supposition that the critical road found by CPM will always be the critical road for the project cannot be justified. Differences between PERT and CPM CPM is a deterministic method PERT is a stochastic method CPM infer that the cost can varied changed the level of resources CPM requires for each activity two execution times: NT: Normal Time CT: Crash Time Where the normal time is the maximum time in which you can execute the activity and the time of court is the smallest time in which you can execute, chord with the established parameters for the project. For each activity PERT requires the project manager to suggest the following times of execution: t.o. = optimistic time t.m. = more probable time t.p. = pessimistic time where 0 a m b (1) PERT assumes that the time of execution of each activity (t ) it is the random variable of duration of the activity that goes from the node i to the node j

4 Each activity follows a distribution Beta. If t correspond to a Beta distribution then: Hope: a + 4m + b E( t ) = 6 (2) Standard Deviation: b a δ ( t ) = 6 (3) Variance: 2 b a 2 δ ( t ) = ( ) 6 (4) PERT supposes that the durations of all the activities are independent. PERT supposes that the durations of all the activities are independent. Then for any trajectory in the net the stocking and the variance of the times required to finish the activities about the trajectory will be given by the sum of the hopes about the trajectory, the same as the sum of the variances. PERT use the Theorem of the central limit PERT supposes that the critical road found by CPM contains enough activities that allow us to use the Theorem of the central limit and it concludes then that: CP (Critical Path) = Σ (t ); about the critical trajectory, where. CP behaves inside a normal distribution 4.4. Mixed project 1. It is a project that contains some activities with determined run-times and other activities with uncertain run-times [jg]. For example, suppose that you want to determine the time that would spend in carrying out a bank transaction. If the group of activities only outside: first, to obtain the bank form and second, to wait to be assisted by the cashier. The serious answer is: K + f (Probability) (5) Where k DETERMINES the time required to obtain the form and f (Probability) it ESTIMATES time of wait to be assisted. According to this, it is necessary to define a mathematical algorithm that allows evaluating from the general theory of networks, this new type of projects that from now on will call as MIXED PROJECTS. Proposed solution algorithm The next steps presented that should follow the project director and their work group in the moment to outline a type of mixed project: Step 1. Define the problem situation In this point, the manager of the project should determine the Specific Objective to solve Step 2. Determine the Project Activity Plan After outlining a problem to solve, the director of the project should determine the group of activities that you/they will allow the development of the same one, determining the dependence relationships among the activities, as well as the necessary resources. Step 3. Estimate the times of execution for each activity Chord with the characteristic of the activity (well known or not well known), to determine the time of execution: Table 1. Structure of run-time of the activities. Activity with known execution duration Activity with duration of uncertain execution NT : Normal time (it is considered as the time of standard execution more the supplements) CT : Crash time (it is considered as the time of standard execution) NT > CT > 0 t.o. = Optimistic time (it is considered as the minimum time possible of execution of an activity) t.m. = More probable time (it is considered the time of balance of probabilities of execution of an activity) t.p. = Pessimistic time (it is considered as the maximum time possible of execution of an activity) 0 < to < tm < tp 1 This definition is one of the main contributions of this investigation

5 Step 4. Determinate the activity cost It is necessary to determine for each activities an execution cost. This cost should allow evaluating the investment level in which will incurred when executing the activity in certain time. That is to say, the execution cost has a relationship inversely proportional with the execution cost. At more time of execution smaller cost, and at smaller time bigger cost. For the activities whose time of execution known with certainty, the basic approach of CPM used, that is to say, normal cost and crash cost. For the activities with probabilistic time of execution, it is important in the moment of the assignment of resources and their corresponding evaluation of costs, to keep in mind the deviation that can exist in the information. It assumed that the hope cost (Ce ) has a similar behavior at the hope time: where. Ca + 4Cm + Cb Ce = (6) 6 Co: Cm: Cp: Optimist cost to activity A More probable cost to activity A Pessimist cost to activity A Step 5. Determine the Execution Approach In this point, chord with the proposed methodology, should be a model of decision tree structured (or some other model that allows a scenario of analysis of possible solution alternatives associated to the time of execution of the same one) that allows establishing three clear politicians for her development Execution approach Table 2. Execution approach for the Mixed Project Risk level Satisfaction level Time structure (according to cpm) NT CT (Normal Time) (Crash Time) Optimist High Low Neutral Medium Medium Pessimist Low High te te tp to te te Step 6. Determine the Project Variability After determining the execution approach, the network diagram corresponding of Network should it built. With base in the CPM Algorithm, the group of critical activities identified CA (Critical Activity) = All activities that have total looseness is zero and the corresponding critical paths i=1,.., n CPi (Critical Path) = Critical Activities group that form one path to beginning endingin i=1,.., n VP = Max VP ) ( k where (7) 2 VP = Σ( δ ) (8) k k where k = Activities that form one critical path on the way to beginning end, k = 1,.,n Step 7. CPM basic solution In this point the director of the project and their work team, have two (2) tools for their analysis: a model of decision tree (or other tool of used decision) and a CPM network model

6 Application. With the purpose of being able to validate the proposed algorithm, it is developed the application of the mathematical model to optimize time and cost of execution of mixed projects in a company of construction of the city de Bogotá D.C., to be able to evaluate in a real situation the functionality of the model. Next some separate of this application are presented. Step 1. Problem situation. The MC Co. builder wants to establish the politics (optimist, pessimist or neutral) for the development of its new project located in Chía City that represents the biggest level of utility and that it will develop in two stages. Key topics: A project of urban development Three options: optimist, pessimist and neutral 2 ID Step 2. Determine the Project Activity Plan Step 3. Estimate the times of execution for each activity ACTIVIDADES Table 3. Civil engineering department information [12] MODULO A (22 CASAS) D P Tiempo Normal Tiempo Limite Optimista (to) Más probable (tm) Pesimista (tp) Tiempo esperado (te) A Excavación manual x B Vigas de cimentación x C Armada y fundida pantallas 1er piso x D Mampostería 1er Piso x E Columneta 1er Piso x F Armada y fundida placa 2do piso x G Armada y fundida pantallas 2do piso x H Mampostería 2do piso x I Alistada y fundida de placa de contrapiso x J Columneta 2do Piso x K Armada y fundida placa 3er piso x L Mampostería - cuchillas 3er piso x M Columneta 3er piso x N Vigas cubierta x O Encorozada y remates x P Escaleras 1er piso - 2do piso x Q Escaleras 2do piso - 3er piso x R Entramado de cubierta x S Instalación de cubierta asbesto cemento x T Instalación ventanearía x U Instalación puertas x V Instalación mesón cocina x W Limpieza fachada x X Aparatos eléctricos y sanitarios x Y Aseo x Z Liberación del Producto x D = Deterministica, P = Probabilistica ID Step 4. Determinate the activity cost ACTIVIDADES TIPO DE ACTIVIDAD Tiempos CPM Tiempos PERT Table 4. Cost information TIPO DE ACTIVIDAD COSTOS CPM [Millones de pesos] MODULO A (22 CASAS) Determinística Probabilística Costo Normal Costo Limite A Excavación manual x Costo Optimista (o) Costo más probable (m) Costo Pesimista (p) B Vigas de cimentación x Costo esperado (Ce) C Armada y fundida pantallas 1er piso x D Mampostería 1er Piso x E Columneta 1er Piso x F Armada y fundida placa 2do piso x G Armada y fundida pantallas 2do piso x H Mampostería 2do piso x I Alistada y fundida de placa de contrapiso x J Columneta 2do Piso x K Armada y fundida placa 3er piso x L Mampostería - cuchillas 3er piso x M Columneta 3er piso x N Vigas cubierta x O Encorozada y remates x P Escaleras 1er piso - 2do piso x Q Escaleras 2do piso - 3er piso x R Entramado de cubierta x S Instalación de cubierta asbesto cemento x T Instalación ventanería x U Instalación puertas x V Instalación mesón cocina x 8 10 W Limpieza fachada x X Aparatos eléctricos y sanitarios x Y Aseo x 5 6 Z Liberación del Producto x 5 7 COSTOS PERT [Millones de pesos] Varianza 2 This concept is taken of decision theory

7 Step 5. Determine the Execution Approach. For the complete presentation of the proposed methodology, the three types of execution approaches will be developed like they are it: Optimist, Neutral and Pessimistic, to be able to obtain a summary square that allows the analysis of time cost of the project. Execution approach Normal time of the project Table 5. Summary of execution approach. Crash time of the project Normal cost of the Project Crash cost of the project OPTIMIST NEUTRAL PESIMIST Time in days. Cost in millions. Step 6. Determine the Variability of the Project. With base in the results obtained in the previous point, the basic analysis of probability will be applied proposed in the pattern PERT, to determine which can be more beneficent of the three approaches for the development of the proposed project. Been worth that the optimistic approach is the most expensive (when being developed in time limit it increases the cost with relationship at the minimum cost of execution in 21.97%), but that in a same way with relationship to the maximum run-time (pessimistic approach - normal time) one could obtain a reduction of the run-time in 25.22%. This analysis type, they become a new tool of evaluation of the projects in their initial stage of programming to be able to make a better control of the costs and run-times. It is determined that the critical path for the optimistic approach is: CP = {A, B, C, D, E, F, G, H, J, K, L, M, N, O, R, S, T, V, W} It should be kept in mind that this can vary in each project, for each one of the valued approaches. With base in the critical route of the project, and chord with it formulates it Eq.(8) the variability of the project is For example with base in the variance of the project, they can think about some questions as: that probability is of developing the project in but of 152 days? In this case, it is observed that the probability that the project is developed in more than 152 days it is approximately of 5.65 that in relation to the previous analysis, it generates a better dependability of execution of the project. This way, they can be evaluated another type of alternative of execution and to determine their respective associate probability. Step 7. Solution of the selected approach with base in the method CPM With base in the information of the previous step, the decision is assumed of evaluating the project from the optimistic approach, since chord with the impact of the project, this would have a positive effect in the market reducing the times of delivery. The analysis CPM time/cost, can give a bigger analysis level for the team of decision. This is one of the important elements of contribution of this investigation, since the analysis CPM time/cost, single possible in situations with well-known run-times, leaving the problems with uncertain run-times, relegated to a basic analysis PERT. Table 6. Analysis of optimization time/cost for the Mixed Project - Optimistic Approach. FASE ACTIVIDAD(ES) A DECREMENTO INCREMENTO COSTO TIEMPO DEL COSTO DEL ACELERAR DE TIEMPO EN EL COSTO ACUMULADO PROYECTO PROYECTO V O, V E, O, W T, W S, T B, L, S B, M, R G, N, R A, G H, J, K C, F, K D, F Tiempo en días. Costo en millones de pesos This mathematical analysis is captured in a graphic time/cost to evaluate the different alternatives of execution of the project in the feasible range of execution proposed by the optimistic approach (149.5 to 126 days). This is an important tool in the analysis of feasibility of any project.

8 Costo de ejecucion en millones Costo limite Costo optimo limite Serie Figure 3. Curved time/cost for the Mixed Project - Optimistic Approach. Tiempo de ejecucion en dias Figure 3. Curved time/cost for Mixed Project - Optimistic Approach. The previous graph, allows to validate the correct application of the algorithm CPM time/cost, since when diminishing the run-time of the project the cost it increases gradually. In a same way the algorithm allows to obtain a cost good inferior limit at the cost it limits proposed [7]. Summations. The existence of projects is evidenced in advance with component activities of known execution and with activities in advance of uncertain execution, what allows proposing a definition for this type of projects, at the same time of a gliding methodology, evaluation and analysis. The sector of the construction, presents an excellent scenario for the application of the mathematical pattern for proposed mixed projects, since the existence of activities is evidenced in advance in advance of known execution and activities of uncertain execution. With base in the theory of the method PERT, the analysis with uncertainly of the execution of the project is developed, what allows another analysis option for the taking of decision on the run-time. When applying the three approaches proposed for the execution of the mixed projects: optimist, neutral and pessimistic, a chart of results is obtained that becomes in the base of the analysis time/cost of the proposed pattern. The applicability of the mathematical pattern is shown proposed in real managerial situations, as well as the new theoretical proposal for the development and Mixed Project analysis from the theory of the classic models of project nets CPM and PERT. 5. References 1. MOSKOWITZ, Herbert y WRIGHT, Gordon P. Investigación de Operaciones. Prentice Hall. USA, MEDINA CEPEDA, José Gregorio. DISEÑO DE UN MODELO MATEMÁTICO DE OPTIMIZACIÓN DEL TIEMPO Y COSTO DE EJECUCIÓN PARA PROYECTOS MIXTOS. Investigación. Facultad de Administración de Empresas. Universidad de La Salle. Colombia, KALENATIC, Dusko. y BLANCO, Luis Ernesto. Aplicaciones Computacionales en Producción. Fondo de publicaciones Universidad Distrital. Colombia, ANDERSON, David., SWEENEY, Dennos y WILLIAMS, Thomas. Métodos Cuantitativos para los Negocios. Novena Edición. Thomson. USA, KRAJEWSKI, Lee J. y RITZMAN, Larry P. Administración de Operaciones, Estrategia y análisis. 5ª edición. Pearson Educación. USA, SCHROEDER, Roger G. Administración de Operaciones: Casos y conceptos contemporáneos. Segunda Edición. McGraw-Hill. USA, KALENATIC, Dusko. Técnicas de Planeación de Redes. Fondo de publicaciones Universidad Distrital. Colombia, 1993

9 8. RENDER, Barry., STAIR, Ralph. and HANNA, Michael. Quantitative Analysis for Management. 9th edition. Pearson Education. USA, PRAWDA, Juan. Métodos y Modelos de Investigación de Operaciones. Volumen 1. Editorial Limusa. México, GIDO, Jack Y CLEMENTS, James. Administración exitosa de proyectos. 2ª edición. Thomson. USA, HILLIER, Frederick S. Y LIEBERMAN, Gerald J. Introducción a la Investigación de Operaciones. Octava edición. McGraw- Hill. USA, HERNÁNDEZ CARVAJAL, Arturo Y ROJAS ROMERO, José David. APLICACIÓN DEL ALGORITMO MATEMÁTICO MIXTO PARA OPTIMIZAR TIEMPO Y COSTO DE PROYECTOS EN LA CONSTRUCTORA TRIADA LIMITADA. Trabajo de Grado en curso. Facultad de Administración de Empresas. Universidad de La Salle. Colombia, 2007

Project Planning and Scheduling

Project Planning and Scheduling Project Planning and Scheduling MFS606 Project Planning Preliminary Coordination Detailed Task Description Objectives Budgeting Scheduling Project Status Monitoring When, What, Who Project Termination

More information

Operational Research. Project Menagement Method by CPM/ PERT

Operational Research. Project Menagement Method by CPM/ PERT Operational Research Project Menagement Method by CPM/ PERT Project definition A project is a series of activities directed to accomplishment of a desired objective. Plan your work first..then work your

More information

Project Management Chapter 3

Project Management Chapter 3 Project Management Chapter 3 How Project Management fits the Operations Management Philosophy Operations As a Competitive Weapon Operations Strategy Project Management Process Strategy Process Analysis

More information

Project Planning. Lecture Objectives. Basic Reasons for Planning. Planning. Project Planning and Control System. Planning Steps

Project Planning. Lecture Objectives. Basic Reasons for Planning. Planning. Project Planning and Control System. Planning Steps Project Planning What are you going to do in the project? Lecture Objectives To discuss the tasks in planning a project To describe the tools that can be used for developing a project plan To illustrate

More information

Application Survey Paper

Application Survey Paper Application Survey Paper Project Planning with PERT/CPM LINDO Systems 2003 Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM) are two closely related techniques for monitoring

More information

Project and Production Management Prof. Arun Kanda Department of Mechanical Engineering Indian Institute of Technology, Delhi

Project and Production Management Prof. Arun Kanda Department of Mechanical Engineering Indian Institute of Technology, Delhi Project and Production Management Prof. Arun Kanda Department of Mechanical Engineering Indian Institute of Technology, Delhi Lecture - 9 Basic Scheduling with A-O-A Networks Today we are going to be talking

More information

Project Scheduling: PERT/CPM

Project Scheduling: PERT/CPM Project Scheduling: PERT/CPM CHAPTER 8 LEARNING OBJECTIVES After completing this chapter, you should be able to: 1. Describe the role and application of PERT/CPM for project scheduling. 2. Define a project

More information

Goals of the Unit. spm - 2014 adolfo villafiorita - introduction to software project management

Goals of the Unit. spm - 2014 adolfo villafiorita - introduction to software project management Project Scheduling Goals of the Unit Making the WBS into a schedule Understanding dependencies between activities Learning the Critical Path technique Learning how to level resources!2 Initiate Plan Execute

More information

240ST1131 - Operations Management in the Supply Chain

240ST1131 - Operations Management in the Supply Chain Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2015 240 - ETSEIB - Barcelona School of Industrial Engineering 732 - OE - Department of Management MASTER'S DEGREE IN SUPPLY CHAINS,

More information

Project Time Management

Project Time Management Project Time Management Study Notes PMI, PMP, CAPM, PMBOK, PM Network and the PMI Registered Education Provider logo are registered marks of the Project Management Institute, Inc. Points to Note Please

More information

10 Project Management with PERT/CPM

10 Project Management with PERT/CPM 10 Project Management with PERT/CPM 468 One of the most challenging jobs that any manager can take on is the management of a large-scale project that requires coordinating numerous activities throughout

More information

Chapter 11 Monte Carlo Simulation

Chapter 11 Monte Carlo Simulation Chapter 11 Monte Carlo Simulation 11.1 Introduction The basic idea of simulation is to build an experimental device, or simulator, that will act like (simulate) the system of interest in certain important

More information

PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT)

PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) ABSTRACT Category: Planning/ Monitoring - Control KEYWORDS Program (Project) Evaluation and Review Technique (PERT) (G) is a project management tool used

More information

Scheduling Fundamentals, Techniques, Optimization Emanuele Della Valle, Lecturer: Dario Cerizza http://emanueledellavalle.org

Scheduling Fundamentals, Techniques, Optimization Emanuele Della Valle, Lecturer: Dario Cerizza http://emanueledellavalle.org Planning and Managing Software Projects 2011-12 Class 9 Scheduling Fundamentals, Techniques, Optimization Emanuele Della Valle, Lecturer: Dario Cerizza http://emanueledellavalle.org Credits 2 This slides

More information

Economic- Management. None. None

Economic- Management. None. None ANTIOQUIA SCHOOL OF ENGINEERING General Management ACADEMIC DOMAIN CURRICULUM FIELD (POSTGRADUATE AND MASTERS) PREREQUISITE(S) COREQUISITE(S) SUBJECT CREDITS - COLOMBIANS - ECTS (COLOM x1.8) DIRECT TEACHING

More information

Basic Concepts. Project Scheduling and Tracking. Why are Projects Late? Relationship between People and Effort

Basic Concepts. Project Scheduling and Tracking. Why are Projects Late? Relationship between People and Effort Basic s Project Scheduling and Tracking The process of building a schedule for any case study helps really understand how it s done. The basic idea is to get across to break the software project into well-defined

More information

Network analysis: P.E.R.T,C.P.M & Resource Allocation Some important definition:

Network analysis: P.E.R.T,C.P.M & Resource Allocation Some important definition: Network analysis: P.E.R.T,C.P.M & Resource Allocation Some important definition: 1. Activity : It is a particular work of a project which consumes some resources (in ) & time. It is shown as & represented

More information

Teaching guide ECONOMETRICS

Teaching guide ECONOMETRICS Teaching guide ECONOMETRICS INDEX CARD Subject Data Código Titulación Nombre Carácter Ciclo 1313.- Grado en Administración y Dirección de Empresas, Mención Creación y Dirección de Empresas, Itinerario

More information

Analysis of the critical path within a project with WinQSB software

Analysis of the critical path within a project with WinQSB software Analysis of the critical path within a project with WinQSB software GURAU MARIAN ANDREI, MELNIC LUCIA VIOLETA Faculty of Engineering and Technological Systems Management, Faculty of Mechanical Engineering

More information

A Generalized PERT/CPM Implementation in a Spreadsheet

A Generalized PERT/CPM Implementation in a Spreadsheet A Generalized PERT/CPM Implementation in a Spreadsheet Abstract Kala C. Seal College of Business Administration Loyola Marymount University Los Angles, CA 90045, USA kseal@lmumail.lmu.edu This paper describes

More information

Network Diagram Critical Path Method Programme Evaluation and Review Technique and Reducing Project Duration

Network Diagram Critical Path Method Programme Evaluation and Review Technique and Reducing Project Duration Network Diagram Critical Path Method Programme Evaluation and Review Technique and Reducing Project Duration Prof. M. Rammohan Rao Former Dean Professor Emeritus Executive Director, Centre for Analytical

More information

Project management: a simulation-based optimization method for dynamic time-cost tradeoff decisions

Project management: a simulation-based optimization method for dynamic time-cost tradeoff decisions Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections 2009 Project management: a simulation-based optimization method for dynamic time-cost tradeoff decisions Radhamés

More information

Schedule Risk Analysis Simulator using Beta Distribution

Schedule Risk Analysis Simulator using Beta Distribution Schedule Risk Analysis Simulator using Beta Distribution Isha Sharma Department of Computer Science and Applications, Kurukshetra University, Kurukshetra, Haryana (INDIA) ishasharma211@yahoo.com Dr. P.K.

More information

22 Project Management with PERT/CPM

22 Project Management with PERT/CPM hil61217_ch22.qxd /29/0 05:58 PM Page 22-1 22 C H A P T E R Project Management with PERT/CPM One of the most challenging jobs that any manager can take on is the management of a large-scale project that

More information

B. 2-4-6 D. 3-4-5 E. 3-5-7 F. 5-7-9

B. 2-4-6 D. 3-4-5 E. 3-5-7 F. 5-7-9 Lesson 01 Project Management Solutions #1: The network diagram for a project is shown below, with three time estimates (optimistic, most likely, and pessimistic) for each activity. Activity times are in

More information

Priori ty ... ... ...

Priori ty ... ... ... .Maintenance Scheduling Maintenance scheduling is the process by which jobs are matched with resources (crafts) and sequenced to be executed at certain points in time. The maintenance schedule can be prepared

More information

CISC 322 Software Architecture. Project Scheduling (PERT/CPM) Ahmed E. Hassan

CISC 322 Software Architecture. Project Scheduling (PERT/CPM) Ahmed E. Hassan CISC 322 Software Architecture Project Scheduling (PERT/CPM) Ahmed E. Hassan Project A project is a temporary endeavour undertaken to create a "unique" product or service A project is composed of a number

More information

Scheduling. Anne Banks Pidduck Adapted from John Musser

Scheduling. Anne Banks Pidduck Adapted from John Musser Scheduling Anne Banks Pidduck Adapted from John Musser 1 Today Network Fundamentals Gantt Charts PERT/CPM Techniques 2 WBS Types: Process, product, hybrid Formats: Outline or graphical organization chart

More information

Project Time Management

Project Time Management Project Time Management Plan Schedule Management is the process of establishing the policies, procedures, and documentation for planning, developing, managing, executing, and controlling the project schedule.

More information

PROJECT EVALUATION REVIEW TECHNIQUE (PERT) AND CRITICAL PATH METHOD (CPM)

PROJECT EVALUATION REVIEW TECHNIQUE (PERT) AND CRITICAL PATH METHOD (CPM) PROJECT EVALUATION REVIEW TECHNIQUE (PERT) AND CRITICAL PATH METHOD (CPM) Project Evaluation Review Technique (PERT) and Critical Path Method (CPM) are scheduling techniques used to plan, schedule, budget

More information

Scheduling Resources and Costs

Scheduling Resources and Costs Student Version CHAPTER EIGHT Scheduling Resources and Costs McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. Gannt Chart Developed by Henry Gannt in 1916 is used

More information

Use project management tools

Use project management tools Use project management tools Overview Using project management tools play a large role in all phases of a project - in planning, implementation, and evaluation. This resource will give you a basic understanding

More information

Course contribution to the programme: The course contributes to the programme by helping the students to:

Course contribution to the programme: The course contributes to the programme by helping the students to: Course: Operations Management I Code: 10BBA40002 Type: Required Year: 2 Semester: 1 ECTS Credits: 4 Language: Spanish Coordination: Faculty: Pere Batallé Descals Cristina Giménez Thomsen Miguel Angel Heras

More information

Time Management. Part 5 Schedule Development. Richard Boser

Time Management. Part 5 Schedule Development. Richard Boser Time Management Part 5 Schedule Development Richard Boser 6.5 Schedule Development Inputs Organizational Process Assets Scope Statement Activity List Activity Attributes Network Diagrams Resource Req ms

More information

Network Calculations

Network Calculations Network Calculations The concepts and graphical techniques described in this week s readings form the basis of the tools widely used today to manage large projects. There is no way of simplifying the tasks

More information

Project Time Management

Project Time Management Project Time Management Study Notes PMI, PMP, CAPM, PMBOK, PM Network and the PMI Registered Education Provider logo are registered marks of the Project Management Institute, Inc. Points to Note Please

More information

Chapter 6: Project Time Management. King Fahd University of Petroleum & Minerals SWE 417: Software Project Management Semester: 072

Chapter 6: Project Time Management. King Fahd University of Petroleum & Minerals SWE 417: Software Project Management Semester: 072 Chapter 6: Project Time Management King Fahd University of Petroleum & Minerals SWE 417: Software Project Management Semester: 072 Learning Objectives Understand the importance of project schedules Define

More information

REVISTA INVESTIGACION OPERACIONAL VOL. 35, NO. 2, 104-109, 2014

REVISTA INVESTIGACION OPERACIONAL VOL. 35, NO. 2, 104-109, 2014 REVISTA INVESTIGACION OPERACIONAL VOL. 35, NO. 2, 104-109, 2014 SOME PRACTICAL ISSUES ON MODELING TRANSPORT. Gabriela Gaviño Ortiz, M. Liliana Antonia Mendoza Gutierrez, Rodolfo Espíndola Heredia and Enoc

More information

Project Scheduling: PERT/CPM

Project Scheduling: PERT/CPM Project Scheduling: PERT/CPM Project Scheduling with Known Activity Times (as in exercises 1, 2, 3 and 5 in the handout) and considering Time-Cost Trade-Offs (as in exercises 4 and 6 in the handout). This

More information

Module 3: The Project Planning Stage

Module 3: The Project Planning Stage Overview Once you've initiated the project and gathered all relevant information, you'll then begin planning your project. The planning stage depends on the size of your project, how much information you

More information

Project Management DISCUSSION QUESTIONS

Project Management DISCUSSION QUESTIONS 3 C H A P T E R Project Management DISCUSSION QUESTIONS. There are many possible answers. Project management is needed in large construction jobs, in implementing new information systems, in new product

More information

Chapter 11: PERT for Project Planning and Scheduling

Chapter 11: PERT for Project Planning and Scheduling Chapter 11: PERT for Project Planning and Scheduling PERT, the Project Evaluation and Review Technique, is a network-based aid for planning and scheduling the many interrelated tasks in a large and complex

More information

The management of the projects with MS Project

The management of the projects with MS Project The management of the projects with MS Project Author: AgimDerguti 1 What is Microsoft Project? Microsoft Project is a project management software program developed and sold by Microsoft Designed to assist

More information

PROJECT TIME MANAGEMENT. 1 www.pmtutor.org Powered by POeT Solvers Limited

PROJECT TIME MANAGEMENT. 1 www.pmtutor.org Powered by POeT Solvers Limited PROJECT TIME MANAGEMENT 1 www.pmtutor.org Powered by POeT Solvers Limited PROJECT TIME MANAGEMENT WHAT DOES THE TIME MANAGEMENT AREA ATTAIN? Manages the project schedule to ensure timely completion of

More information

SYLLABUS. Class B.B.A. V Sem. Subject Project Management

SYLLABUS. Class B.B.A. V Sem. Subject Project Management SYLLABUS Class B.B.A. V Sem. Subject Project Management UNIT I UNIT II UNIT III UNIT IV UNIT V UNIT VI Introduction to project and projects. Characteristics and types of projects. Gaining importance, project

More information

Project Management SCM 352. 2011 Pearson Education, Inc. publishing as Prentice Hall

Project Management SCM 352. 2011 Pearson Education, Inc. publishing as Prentice Hall 3 Project Management 3 SCM 35 11 Pearson Education, Inc. publishing as Prentice Hall Boeing 787 Dreamliner Delays are a natural part of the airplane supply business. They promise an unreasonable delivery

More information

Project Time Management Activity Definition Activity Sequencing Duration Estimating Schedule Development Schedule Control

Project Time Management Activity Definition Activity Sequencing Duration Estimating Schedule Development Schedule Control Project Time Management Activity Definition Activity Sequencing Duration Estimating Schedule Development Schedule Control Activity Definition Input Work Breakdown Structure Scope Statement Historical Information

More information

Cambridge International AS and A Level Computer Science

Cambridge International AS and A Level Computer Science Topic support guide Cambridge International AS and A Level Computer Science 9608 For examination from 2017 Topic 4.4.3 Project management PERT and GANTT charts Cambridge International Examinations retains

More information

A Robustness Simulation Method of Project Schedule based on the Monte Carlo Method

A Robustness Simulation Method of Project Schedule based on the Monte Carlo Method Send Orders for Reprints to reprints@benthamscience.ae 254 The Open Cybernetics & Systemics Journal, 2014, 8, 254-258 Open Access A Robustness Simulation Method of Project Schedule based on the Monte Carlo

More information

Evaluation of an exercise for measuring impact in e-learning: Case study of learning a second language

Evaluation of an exercise for measuring impact in e-learning: Case study of learning a second language Evaluation of an exercise for measuring impact in e-learning: Case study of learning a second language J.M. Sánchez-Torres Universidad Nacional de Colombia Bogotá D.C., Colombia jmsanchezt@unal.edu.co

More information

SE351a: Software Project & Process Management

SE351a: Software Project & Process Management SE351a: Software Project & Process Management W8: Software Project Planning 22 Nov., 2005 SE351a, ECE UWO, (c) Hamada Ghenniwa SE351 Roadmap Introduction to Software Project Management Project Management

More information

Table of Contents Author s Preface... 3 Table of Contents... 5 Introduction... 6 Step 1: Define Activities... 7 Identify deliverables and decompose

Table of Contents Author s Preface... 3 Table of Contents... 5 Introduction... 6 Step 1: Define Activities... 7 Identify deliverables and decompose 1 2 Author s Preface The Medialogist s Guide to Project Time Management is developed in compliance with the 9 th semester Medialogy report The Medialogist s Guide to Project Time Management Introducing

More information

12 Network Scheduling Techniques

12 Network Scheduling Techniques Page 671 12 Network Scheduling Techniques 12.0 Introduction Management is continually seeking new and better control techniques to cope with the complexities, masses of data, and tight deadlines that are

More information

Chapter 6. (PMBOK Guide)

Chapter 6. (PMBOK Guide) Chapter 6 Project Time Management (PMBOK Guide) Mohammad A. Rajabi Dept. of Geomatics Eng., University it of Th Tehran Tel: +98 21 8833 4341, Cell: +98 912 132 5823 Email: marajabi@ut.ac.irac ir Homepage:

More information

A. O. Odior Department of Production Engineering University of Benin, Edo State. E-mail: waddnis@yahoo.com

A. O. Odior Department of Production Engineering University of Benin, Edo State. E-mail: waddnis@yahoo.com 2012 Cenresin Publications www.cenresinpub.org APPLICATION OF PROJECT MANAGEMENT TECHNIQUES IN A CONSTRUCTION FIRM Department of Production Engineering University of Benin, Edo State. E-mail: waddnis@yahoo.com

More information

FIND ALL LONGER AND SHORTER BOUNDARY DURATION VECTORS UNDER PROJECT TIME AND BUDGET CONSTRAINTS

FIND ALL LONGER AND SHORTER BOUNDARY DURATION VECTORS UNDER PROJECT TIME AND BUDGET CONSTRAINTS Journal of the Operations Research Society of Japan Vol. 45, No. 3, September 2002 2002 The Operations Research Society of Japan FIND ALL LONGER AND SHORTER BOUNDARY DURATION VECTORS UNDER PROJECT TIME

More information

March 30, 2007 CHAPTER 4

March 30, 2007 CHAPTER 4 March 30, 07 CHAPTER 4 SUPPORTING PLANNING AND CONTROL: A CASE EXAMPLE Chapter Outline 4.1 Background What was the cause of the desperation that lead to the development of the Program Evaluation and Review

More information

PROJECT TIME MANAGEMENT

PROJECT TIME MANAGEMENT 6 PROJECT TIME MANAGEMENT Project Time Management includes the processes required to ensure timely completion of the project. Figure 6 1 provides an overview of the following major processes: 6.1 Activity

More information

220514 - Supply Chain Management

220514 - Supply Chain Management Coordinating unit: 220 - ETSEIAT - Terrassa School of Industrial and Aeronautical Engineering Teaching unit: 732 - OE - Department of Management Academic year: Degree: 2015 MASTER'S DEGREE IN MANAGEMENT

More information

TIME MANAGEMENT TOOLS AND TECHNIQUES FOR PROJECT MANAGEMENT. Hazar Hamad Hussain *

TIME MANAGEMENT TOOLS AND TECHNIQUES FOR PROJECT MANAGEMENT. Hazar Hamad Hussain * TIME MANAGEMENT TOOLS AND TECHNIQUES FOR PROJECT MANAGEMENT Hazar Hamad Hussain * 1. Introduction The definition of Project as a temporary endeavor... refers that project has to be done within a limited

More information

Project Time Management

Project Time Management Project Time Management By Augsburg College 1 Learning Objectives Understand the importance of project schedules and good project time management Define activities as the basis for developing project schedules

More information

CHAPTER 1. Basic Concepts on Planning and Scheduling

CHAPTER 1. Basic Concepts on Planning and Scheduling CHAPTER 1 Basic Concepts on Planning and Scheduling Scheduling, FEUP/PRODEI /MIEIC 1 Planning and Scheduling: Processes of Decision Making regarding the selection and ordering of activities as well as

More information

Diagramming Techniques:

Diagramming Techniques: 1 Diagramming Techniques: FC,UML,PERT,CPM,EPC,STAFFWARE,... Eindhoven University of Technology Faculty of Technology Management Department of Information and Technology P.O. Box 513 5600 MB Eindhoven The

More information

Project Scheduling and Gantt Charts

Project Scheduling and Gantt Charts Project Scheduling and Gantt Charts Siddharth Gangadhar Dr. Prasad Kulkarni Department of Electrical Engineering & Computer Science Lab Presentation siddharth@ku.edu prasadk@ku.edu 4 November 2015 2015

More information

Quantitative Risk Analysis with Microsoft Project

Quantitative Risk Analysis with Microsoft Project Copyright Notice: Materials published by Intaver Institute Inc. may not be published elsewhere without prior written consent of Intaver Institute Inc. Requests for permission to reproduce published materials

More information

15. How would you show your understanding of the term system perspective? BTL 3

15. How would you show your understanding of the term system perspective? BTL 3 Year and Semester FIRST YEAR II SEMESTER (EVEN) Subject Code and Name BA7201 OPERATIONS MANAGEMENT Faculty Name 1) Mrs.L.SUJATHA ASST.PROF (S.G) 2) Mr. K.GURU ASST.PROF (OG) Q.No Unit I Part A BT Level

More information

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture - 36 Location Problems In this lecture, we continue the discussion

More information

CPM -100: Principles of Project Management

CPM -100: Principles of Project Management CPM -100: Principles of Project Management Lesson B: Time and Cost Management Presented by Bruce R. Shaw, P.E., PMP starshaw@starpower.net Ph: 703-922-2772 Presented at the PMI-CPM 2002 Fall Conference

More information

Chapter 6: Project Time Management

Chapter 6: Project Time Management CIS 486 Managing Information Systems Projects Fall 2003 (Chapter 6), PhD jwoo5@calstatela.edu California State University, LA Computer and Information System Department Chapter 6: Project Time Management

More information

Optimal Location and Management of a Biomass Inventory Facility

Optimal Location and Management of a Biomass Inventory Facility International Conference on Industrial Engineering & Industrial Management - CIO 2007 843 Optimal Location and Management of a Biomass Inventory Facility Pedro Sánchez Martín, Andrés Ramos Dpto. de Organización

More information

Chapter 4 DECISION ANALYSIS

Chapter 4 DECISION ANALYSIS ASW/QMB-Ch.04 3/8/01 10:35 AM Page 96 Chapter 4 DECISION ANALYSIS CONTENTS 4.1 PROBLEM FORMULATION Influence Diagrams Payoff Tables Decision Trees 4.2 DECISION MAKING WITHOUT PROBABILITIES Optimistic Approach

More information

Guidelines for Designing Web Maps - An Academic Experience

Guidelines for Designing Web Maps - An Academic Experience Guidelines for Designing Web Maps - An Academic Experience Luz Angela ROCHA SALAMANCA, Colombia Key words: web map, map production, GIS on line, visualization, web cartography SUMMARY Nowadays Internet

More information

A Comparison Study Between Event Chain Methodology And Critical Path Method In The Construction Industry

A Comparison Study Between Event Chain Methodology And Critical Path Method In The Construction Industry A Comparison Study Between Event Chain Methodology And Critical Path Method In The Construction Industry Pranam B 1, Madhusudan G Kalibhat 2, Sudharshan KR 3 1 Student, Master of Technology (Construction

More information

STRATEGIC CAPACITY PLANNING USING STOCK CONTROL MODEL

STRATEGIC CAPACITY PLANNING USING STOCK CONTROL MODEL Session 6. Applications of Mathematical Methods to Logistics and Business Proceedings of the 9th International Conference Reliability and Statistics in Transportation and Communication (RelStat 09), 21

More information

CRITICAL PATH METHOD (CEE 320 VDC SEMINAR)

CRITICAL PATH METHOD (CEE 320 VDC SEMINAR) CRITICAL PATH METHOD (CEE 320 VDC SEMINAR) 4 February 2009 Jesse Santiago & Desirae Magallon Overview Background & History CPM Defined The CPM approach Definitions Class Exercise Background & History Developed

More information

PERT/CPM. Network Representation:

PERT/CPM. Network Representation: - 1 - PERT/CPM PERT Program Evaluation & Review Technique It is generally used for those projects where time required to complete various activities are not known as a priori. It is probabilistic model

More information

The work breakdown structure can be illustrated in a block diagram:

The work breakdown structure can be illustrated in a block diagram: 1 Project Management Tools for Project Management Work Breakdown Structure A complex project is made manageable by first breaking it down into individual components in a hierarchical structure, known as

More information

Save Money and Increase Efficiency with Project Management

Save Money and Increase Efficiency with Project Management Save Money and Increase Efficiency with Project Management Session Description MEETING TITLE AND Are you utilizing project management at your sign shop? If not, this session MEETING will give an overview

More information

Information Technology Project Management, Sixth Edition. Note: See the text itself for full citations. More courses at cie-wc.edu

Information Technology Project Management, Sixth Edition. Note: See the text itself for full citations. More courses at cie-wc.edu Note: See the text itself for full citations. More courses at cie-wc.edu Understand the importance of project schedules and good project time management Define activities as the basis for developing project

More information

CRASHING-RISK-MODELING SOFTWARE (CRMS)

CRASHING-RISK-MODELING SOFTWARE (CRMS) International Journal of Science, Environment and Technology, Vol. 4, No 2, 2015, 501 508 ISSN 2278-3687 (O) 2277-663X (P) CRASHING-RISK-MODELING SOFTWARE (CRMS) Nabil Semaan 1, Najib Georges 2 and Joe

More information

ONLINE SUPPLEMENTAL BAPPENDIX PROJECT SCHEDULES WITH PERT/CPM CHARTS

ONLINE SUPPLEMENTAL BAPPENDIX PROJECT SCHEDULES WITH PERT/CPM CHARTS ONLINE SUPPLEMENTAL BAPPENDIX PROJECT SCHEDULES WITH PERT/CPM CHARTS Chapter 3 of Systems Analysis and Design in a Changing World explains the techniques and steps required to build a project schedule

More information

Project Management Seminars. Financial Management of Projects

Project Management Seminars. Financial Management of Projects Project Management Seminars Financial Management of Projects.inproject managementandsystems engineering, is a deliverable-oriented decomposition of a project into smaller components. (source: Wikipedia)

More information

8. COMPUTER TOOLS FOR PROJECT MANAGEMENT

8. COMPUTER TOOLS FOR PROJECT MANAGEMENT 8. COMPUTER TOOLS FOR PROJECT MANAGEMENT The project management is a complex activity that requires among others: Information intercourse referred to the project, information that is in big amounts more

More information

PROJECT COMPLETION PROBABILITY AFTER CRASHING PERT/CPM NETWORK

PROJECT COMPLETION PROBABILITY AFTER CRASHING PERT/CPM NETWORK PROJECT COMPLETION PROBABILITY AFTER CRASHING PERT/CPM NETWORK M Nazrul, ISLAM 1, Eugen, DRAGHICI 2 and M Sharif, UDDIN 3 1 Jahangirnagar University, Bangladesh, islam_ju@yahoo.com 2 Lucian Blaga University

More information

Systems Analysis and Design

Systems Analysis and Design Systems Analysis and Design Slides adapted from Jeffrey A. Hoffer, University of Dayton Joey F. George, Florida State University Joseph S. Valacich, Washington State University Modern Systems Analysis

More information

Curriculum Reform in Computing in Spain

Curriculum Reform in Computing in Spain Curriculum Reform in Computing in Spain Sergio Luján Mora Deparment of Software and Computing Systems Content Introduction Computing Disciplines i Computer Engineering Computer Science Information Systems

More information

Appendix A of Project Management. Appendix Table of Contents REFERENCES...761

Appendix A of Project Management. Appendix Table of Contents REFERENCES...761 Appendix A Glossary Terms of Project Management Appendix Table of Contents REFERENCES...761 750 Appendix A. Glossary of Project Management Terms Appendix A Glossary Terms of Project Management A Activity

More information

Application of Critical Path Method scheduling to research plan and management of graduate students research project in engineering education

Application of Critical Path Method scheduling to research plan and management of graduate students research project in engineering education OPEN ACCESS Engineering Leaders Conference 2014 Application of Critical Path Method scheduling to research plan and management of graduate students research project in engineering education M.O. Daramola

More information

Statistics 104: Section 6!

Statistics 104: Section 6! Page 1 Statistics 104: Section 6! TF: Deirdre (say: Dear-dra) Bloome Email: dbloome@fas.harvard.edu Section Times Thursday 2pm-3pm in SC 109, Thursday 5pm-6pm in SC 705 Office Hours: Thursday 6pm-7pm SC

More information

ANALYSIS OF PROJECT PLANNING USING CPM AND PERT

ANALYSIS OF PROJECT PLANNING USING CPM AND PERT ANALYSIS OF PROJECT PLANNING USING CPM AND PERT Rogelio Acuña Spring 2010 In Partial Fulfillment of Math 4395-Senior Project Department of Computer and Mathematical Sciences Faculty Advisor: Dr. Timothy

More information

BACHELOR S DEGREE IN BUSINESS ADMINISTRATION

BACHELOR S DEGREE IN BUSINESS ADMINISTRATION BACHELOR S DEGREE IN BUSINESS ADMINISTRATION Course Decision Analysis Code 802284 Module Character Credits 6 Cross sectional formation Compulsory Area Attendance 2.7 Non Attendance Year 3 Semester 5 Quantitative

More information

Chapter 4: Project Time Management

Chapter 4: Project Time Management Chapter 4: Project Time Management Importance of Project Schedules Managers often cite delivering projects on time as one of their biggest challenges Time has the least amount of flexibility; it passes

More information

Keywords: Forward Logistics, Reverse Logistics, Supply Chain Management, Mathematical Programming, Beverage Industry.

Keywords: Forward Logistics, Reverse Logistics, Supply Chain Management, Mathematical Programming, Beverage Industry. A Model for Coordination of Production Planning, Forward and Reverse Logistics Management in a Multi-product and Multiplant Environment, with Reusable Bottles Constraints Parra Peña J 1, Vicens-Salort

More information

The Basics of Graphical Models

The Basics of Graphical Models The Basics of Graphical Models David M. Blei Columbia University October 3, 2015 Introduction These notes follow Chapter 2 of An Introduction to Probabilistic Graphical Models by Michael Jordan. Many figures

More information

1.- NAME OF THE SUBJECT 2.- KEY OF MATTER. None 3.- PREREQUISITES. None 4.- SERIALIZATION. Particular compulsory 5.- TRAINING AREA.

1.- NAME OF THE SUBJECT 2.- KEY OF MATTER. None 3.- PREREQUISITES. None 4.- SERIALIZATION. Particular compulsory 5.- TRAINING AREA. UNIVERSIDAD DE GUADALAJARA CENTRO UNIVERSITARIO DE CIENCIAS ECONÓMICO ADMINISTRATIVAS MAESTRÍA EN ADMINISTRACIÓN DE NEGOCIOS 1.- NAME OF THE SUBJECT Selected Topics in Management 2.- KEY OF MATTER D0863

More information

NETWORK ANALYSIS OF A TOLLING PROJECT

NETWORK ANALYSIS OF A TOLLING PROJECT NETWORK ANALYSIS OF A TOLLING PROJECT Kamila JANOVSKÁ a, Šárka VILAMOVÁ a, Iveta VOZŇÁKOVÁ a, Petr BESTA a, Josef KUTÁČ a, Jakub GAJDA b, Eva Švecová a a VSB-Technical University of Ostrava, Czech Republic,

More information

Module 11. Software Project Planning. Version 2 CSE IIT, Kharagpur

Module 11. Software Project Planning. Version 2 CSE IIT, Kharagpur Module 11 Software Project Planning Lesson 29 Staffing Level Estimation and Scheduling Specific Instructional Objectives At the end of this lesson the student would be able to: Identify why careful planning

More information

Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary

Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:

More information

Pearson Education Limited 2003

Pearson Education Limited 2003 156 Activities Activity 9.1 (PP. 357 358) [Project planning exercise] You are required to construct a project plan for the following information system development project. Your objective is to schedule

More information

SCHEDULING AND TIME MANAGEMENT. Project Management and Leadership 2015D, PhD, PMP

SCHEDULING AND TIME MANAGEMENT. Project Management and Leadership 2015D, PhD, PMP SCHEDULING AND TIME MANAGEMENT Project Management and Leadership 2015D, PhD, PMP Our PROGRAMME: 1. INTRODUCTION TO PROJECT MANAGEMENT 2. STARTING A PROJECT 3. WORK MOTIVATION 4. COMMUNICATION 5: TEAMS

More information