Project Management: A Managerial Approach Chapter – Resource Allocation © 2006 John Wiley Overview • • • • • Critical Path Crashing Resource Leveling Resource Constrained Schedules Multiproject Resource Management Critical Chain © 2006 John Wiley Critical Path Method - Crashing a Project • CPM includes a way of relating the project schedule to the level of physical resources allocated to the project • This allows the project manager to trade time for cost, or vice versa • In CPM, two activity times and two costs are specified, if appropriate for each activity © 2006 John Wiley Chapter 9-1 Critical Path Method - Crashing a Project • The first time/cost combination is called normal, and the second set is referred to as crash • Normal times are “normal” in the same sense as the ‘m’ time estimate of the three times used in PERT • Crash times result from an attempt to expedite the activity by the application of additional resources © 2006 John Wiley Chapter 9-2 Critical Path Method - Crashing a Project • Careful planning is critical when attempting to expedite (crash) a project • Expediting tends to create problems; and the solution to one problem often creates several more problems that require solutions • Some organizations have more than one level of crashing © 2006 John Wiley Chapter 9-3 Crashing – Sample Network 6 10 11 Critical Path = + + + = 23 Time Units © 2006 John Wiley Crashing – An Example Activity 1-2 2-3 2-4 2-5 3-6 5-7 6-7 Normal Time Normal Cost Crash Time Crash Cost 10 11 $50 $80 $60 $50 $100 $40 $70 6 $70 $160 $90 $150 $160 $70 $70 © 2006 John Wiley Slope Max Crsh Tm Crashing – Sample Network $100 $80 $50 $70 “Normal” Project Total Cost = $50 + $80 + $100 + $70 + $60 + $50 + $40 = $450 © 2006 John Wiley Crashing – An Example Activity 1-2 2-3 2-4 2-5 3-6 5-7 6-7 Normal Time Normal Cost Crash Time Crash Cost Slope Max Crsh Tm 10 11 $50 $80 $60 $50 $100 $40 $70 6 $70 $160 $90 $150 $160 $70 $70 20 40 30 25 30 30 © 2006 John Wiley Crashing – Sample Network Critical Path = 23 Days $80 $50 $100 6 $60 10 $70 $50 11 $40 “Normal” Project Total Cost = $50 + $80 + $100 + $70 + $60 + $50 + $40 = $450 © 2006 John Wiley Heuristic Methods • Most heuristic solution methods start with the PERT/CPM schedule and analyze resource usage period by period, resource by resource • In a period when the available supply of a resource is exceeded, the heuristic examines the tasks in that period and allocates the scarce resource to them sequentially, according to some priority rule • Technological necessities always take precedence â 2006 John Wiley Chapter 9-16 Heuristic Methods Common priority rules: – As soon as possible – As late as possible – Shortest task first – Most resources first – Minimum slack first – Most critical followers – Most successors – Arbitrary © 2006 John Wiley Chapter 9-17 Heuristic Methods • Most priority rules are simple adaptations of the heuristics used for the traditional “job shop scheduling” problem of production/operations management • Most heuristics use a combination of rules: a primary rule, and a secondary rule to break ties • As the scheduling heuristic operates, one of two events will result: – The routine runs out of activities before it runs out of resources – The routine runs out of resources before all activities have been scheduled © 2006 John Wiley Chapter 9-18 Optimizing Methods • The methods to find an optimal solution to the constrained resource scheduling problem fall into two categories: – Mathematical programming – Enumeration • Mathematical programming can be thought of as liner programming (LP) for the most part © 2006 John Wiley Chapter 9-19 Optimizing Methods • Linear programming is usually not feasible for reasonably large projects where there may be a dozen resources and thousands of activities • In the late 1960s and early 1970s, limited enumeration techniques were applied to the constrained resource problem • Tree search, and branch and bound methods were devised to handle up to five resources and 200 activities © 2006 John Wiley Chapter 9-20 Multiproject Scheduling and Resource Allocation • The most common approach to scheduling and allocating resources to multiple projects is to treat the several projects as if they were each elements of a single large project • Another way of attacking the problem is to consider all projects as completely independent • To describe such a system properly, standards are needed by which to measure scheduling effectiveness © 2006 John Wiley Chapter 9-21 Multiproject Scheduling and Resource Allocation • Three important parameters affected by project scheduling are: – Schedule slippage – Resource utilization – In-process inventory • The organization (or the project manager) must select the criterion most appropriate for its situation © 2006 John Wiley Chapter 9-22 Multiproject Scheduling and Resource Allocation • Schedule slippage, often considered the most important of the criteria, is the time past a project’s due date or delivery date when the project is completed • Resource utilization is of particular concern to industrial firms because of the high cost of making resources available • The amount of in-process inventory concerns the amount of work waiting to be processed because there is a shortage of some resource © 2006 John Wiley Chapter 9-23 Multiproject Scheduling and Resource Allocation • All criteria cannot be optimized at the same time • As usual, the project manager will have to make tradeoffs among the criteria • A firm must decide which criterion to evaluate its various scheduling and resource allocation options © 2006 John Wiley Chapter 9-24 Mathematical Programming • Mathematical programming can be used to obtain solutions to certain types of multiproject scheduling problems • These procedures determine when an activity should be scheduled, given resource constraints • Mathematical programming, however, is rarely used in project management to handle the multiproject problem (mostly, heuristics are used) © 2006 John Wiley Chapter 9-25 Mathematical Programming • The three most common objectives of mathematical programming are: – Minimum total throughput time (time in the shop) for all projects – Minimum total completion time for all projects – Minimum total lateness or lateness penalty for all projects • These objectives are most appropriate for ‘job shop’ type solutions to resource constraints â 2006 John Wiley Chapter 9-26 Heuristic Techniques There are scores of different heuristic-based procedures in existence • They represent rather simple extensions of wellknown approaches to job-shop scheduling: – – – – – Resource Scheduling Method Minimum late finish time Greatest resource demand Greatest resource utilization Most possible jobs © 2006 John Wiley Chapter 9-27 Critical Chain • Eliyahu M Goldratt’s “Theory of Constraints” • Traditional Project Estimation Techniques Ineffective – Time and Resource Constraints Usually Violated – PMs Rely on “Padding” of Schedules and Budgets – Unknown Nature of Event Interaction • Fear, Uncertainty, Doubt • Psychological, Organizational, and Physical © 2006 John Wiley Critical Chain - Approach • Bottleneck Management – Activities with Several Predecessors and/or Successors – Add “Time Buffers” at Bottleneck Events • “Safety Stock” Equivalent in Manufacturing • Just-in-Time with “Just-in-Case” • Statistically-derived “Path Buffers” – Establish the Critical Chain for Scarce Resources – Prioritization of Resources in Chain Events • Communication of “Walt” Needs is Critical to Success © 2006 John Wiley Copyright 2006 John Wiley & Sons, Inc All rights reserved Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein © 2006 John Wiley ... timing and use of scarce resources • A fundamental measure of the project manager’s success in project management is the skill with which the trade-offs among performance, time, and cost are managed... common approach to scheduling and allocating resources to multiple projects is to treat the several projects as if they were each elements of a single large project • Another way of attacking... the associated costs also tend to be leveled • The project manager must be aware of the cash flows associated with the project and of the means of shifting them in ways that are useful to the parent