Project Management: A Managerial Approach Chapter 9 – Resource Allocation

Overview Critical Path Crashing Resource Leveling Resource Constrained Schedules Multiproject Resource Management Critical Chain

Resource Allocation Some definitions Resource allocation, loading, leveling Expediting and crashing projects

Some Definitions Resource allocation permits efficient use of physical assets Within a project, or across multiple projects Drives both the identification of resources, and timing of their application There are generally two conditions: “Normal” “Crashed”

Normal and Crashing Normal: Most likely task duration, like “m” in Chapter 8 Crash: Expedite an activity, by applying additional resources Specialized or additional equipment More people (e.g., borrowed staff, temps) More hours (e.g., overtime, weekends)

No Free Lunch: Crashing Creates a Ripple Effect Crashing buys time, but nothing comes free Potential cost areas Additional equipment/material Extra labor Negative effects on other projects Reduced morale, from excessive hours/shifts Lower quality, from the pressure of time, inexperienced and tired staff “If you want it bad, you’ll get it bad . . .” Recent Example: Miami’s New Art Center.

When Trying to Crash a Project … Two basic principles 1. Generally, focus on the critical path Usually not helpful to shorten non-critical activities Exception: When a scarce resource is needed elsewhere, e.g., in another project 2. When shortening project duration, choose least expensive way to do it (use slope formula to calculate ratio)

Compute Cost per Day of Crashing a Project Compute cost/time slope for each expeditable activity Slope = crash cost – normal cost crash time – normal time

Another Approach to Expediting: Fast-tracking/Concurrency Different terms for similar concept “Fast-tracking” (construction), “Concurrent engineering” (manufacturing) Both refer to overlapping project phases E.g., design/build, or build/test

Fast-tracking/Concurrency Pros: Can shorten project duration Can reduce product development cycles Can help meet clients’ demands Cons: Can increase cost through redesigns, excessive changes, rework, out-of-sequence installation, and more

The Resource Allocation Problem Most scheduling procedures do not address the issues of resource utilization and availability Scheduling procedures tend to focus on time rather than physical resources Time itself is always a critical resource in project management It is unique because it can neither be inventoried nor renewed Chapter 9-5

The Resource Allocation Problem Schedules should be evaluated: in terms of meeting project milestones in terms of the timing and use of scarce resources Measure of the project manager’s success: skill with which the trade-offs among: Performance Time Cost Chapter 9-6

The Resource Allocation Problem The extreme points of the relationship between time use and resource use are these: Time Limited: The project must be finished by a certain time, using as few resources as possible. But it is time, not resource usage, that is critical Resource Limited:The project must be finished as soon as possible, but without exceeding some specific level of resource usage or some general resource constraint Chapter 9-7

The Resource Allocation Problem If all three variables - time, cost, specifications - are fixed, the system is “overdetermined” In this case, the project manager has lost all flexibility to perform the trade-offs necessary to successful completion of projects A system-constrained task requires a fixed amount of time and known quantities of resources Chapter 9-8

Resource Loading Describes the amounts of individual resources an existing schedule requires during specific time periods The loads (requirements) of each resource type are listed as a function of time period Gives a general understanding of the demands a project or set of projects will make on a firm’s resources Chapter 9-9

Resource Usage Calendar, Figure 9-3

AOA Network, Figure 9-4

Modified PERT/CPM AOA, Figure 9-5

Resource Leveling Resource leveling aims to minimize the period-by-period variations in resource loading by shifting tasks within their slack allowances The purpose is to create a smoother distribution of resource usage Several advantages include: Less day-to-day resource manipulation needed Better morale, fewer HR problems/costs Leveling resources also levels costs, simplifies budgeting and funding Chapter 9-12

Resource Leveling When resources are leveled, 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 firm Resource leveling is a procedure that can be used for almost all projects, whether or not resources are constrained Chapter 9-13

Resource Leveling – Fig 9-6

Network Before and After Resource Loading, Figure 9-7 Duration Qty Reqd.

Resource Loading Chart, Figure 9-9

Constrained Resource Scheduling There are two fundamental approaches to constrained allocation problems: Heuristic Methods Optimization Models Heuristic approaches employ rules of thumb that have been found to work reasonably well in similar situations Optimization approaches seek the best solutions but are far more limited in their ability to handle complex situations and large problems Chapter 9-14

Examples of Simple Heuristics ASAP As late as possible (do not engage in anything unless you have to) SPT (shortest processing time – good to reduce congestion) Most resources first (most requested resources first) Minimum slack first (critical jobs go first to avoid lead time delays) Most critical followers (most critical jobs that go after you, many jobs depend on that resource) Most successors Arbitrary Combination of the above (compound rules). Chapter 9-14

Examples of Complex Heuristics Simulated annealing Tabu search Genetic algorithms Greedy search with branch and bound In the graduate course Advanced Production Planning & Scheduling, focuses on scheduling heuristics. It is good to know that they exist. Chapter 9-14

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 Chapter 9-21

Multiproject Scheduling and Resource Allocation Much more difficult. May rely on an index called TRPT: (Total Remaining Processing Time) Based on the critical ratio. Among all the projects under your control, look at all the jobs of all the projects. Find out which are most critical. Chapter 9-21

Multiproject Scheduling and Resource Allocation Most critical... How do you know? Based on the amount of time before due date and the total amount of processing time remaining to be completed. This ratio is simple but helpful. Critical Ratio = TRPT (Total Remaining Processing Time) TRT (Total Remaining Time) The smaller the ratio, the more critical it is, more entitled to earlier allocation of resources. Chapter 9-21

Multiproject Scheduling and Resource Allocation Based on this, you can do multiple project scheduling. Most critical tasks should be the first to be assigned resources. This doesn’t mean that job will be assigned the resource first. Why? The resource in need may not be available. You can get first priority to claim it, but you may not get the first assignment. You may get preference due to the type of resource that you need. In case you have multiple projects, you have some way to do it. 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. Chapter 9-22

Multiproject Scheduling and Resource Allocation Schedule slippage (how much delay it has caused or it will cause) - 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 more utilization the better, the resource requirements become lower) WIP (to see how smooth your workflow is) concerns the amount of work waiting to be processed because there is a shortage of some resource 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 trade-offs among the criteria A firm must decide which criterion to evaluate its various scheduling and resource allocation options Chapter 9-24

“Cost, Schedule, or Performance: Pick Any Two . . .” Assuming fixed performance specifications, tradeoff areas must be in time or cost Time-limited or resource-limited If all three dimensions are fixed, the system is “overdetermined” Normally, no tradeoffs are possible But, something has to give . . .

Example: Project Crashing Compute cost/time slope for each expeditable activity Slope = crash cost – normal cost crash time – normal time Slope is the cost of crashing the project for the potential (or estimated) crashing time.

An Example (Table 9-1) Activity Predecessor Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 * Partial crashing allowed ** Partial crashing not allowed

Example (cont’d): Cost per Day to Crash (Table 9-2) Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days)

Example (cont’d): Crashing What to crash depends on how much we need to reduce the duration of the project. Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days) - Total Lead Time: 8 days 3 2 4 Normal Time $40 $60 $0 $30 - Ratios $70 - Total Cost: $120 $40 $20 $30 $10 Normal Cost - CP: a  b  e (ET=8) b e S a c F Activity Pred. Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 d

Example (cont’d): Crashing Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days) Normal Cost 2 $60 Ratios b 3 $70 2 $20* e 3 $40 $10* S a c 2 $0 F $40 $20* $80* d 4 $30 Activity Pred. Days (normal, crash) Cost (normal, crash) a - 3, 21 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 $30* - Crash a: (lowest) for 1 day (max1) - New Cost: $120 + $40 = $160 New Lead Time: 7 days (still on CP) v. a  c (4) vs a  d (6)

Example (cont’d): Crashing Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days) 1 Normal Cost 2 $60 Ratios b 3 $70 2 $20 $80* e 3 $40 $10* S a c 2 $0 F $40 $20* $80* d 4 $30 Activity Pred. Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 $30* - Crash b: (lowest) for 1 day (max) - New Cost*: $160 + $60 = $220 New Lead Time: 6 days (2 paths with same LT: a  b  e (6) vs a  d (6)

Example (cont’d): Crashing Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days) 1 Normal Cost 2 $60 Ratios b 3 $70 2 $20 $80* e 3 $40 $10* S a c 2 $0 F $40 $20* $80* d 4 $30 Activity Pred. Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 $30 3 $60* - Crash d for 1 day (partial crashing allowed) - New Cost*: $220 + $30 = $250 LT for path a  d = 5 (Not critical) CP is again a  b  e (6 days)

Example (cont’d): Crashing Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days) 1 Normal Cost 2 $60 1 Ratios b 3 $70 2 $20 $80* e 3 $40 $10 $80* S a c 2 $0 F $40 $20* $80* d 4 $30 Activity Pred. Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 $30 3 $60* - Crash e for 2 days (no partial crashing allowed) - New Cost*: $250 + $70 = $320 LT for path a  b  e = 4

Example (cont’d): Crashing Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days) 2 1 Normal Cost 2 $60 1 Ratios b 3 $70 2 $20 $80 $20* e 3 $40 $10 $80* S a c 2 $0 F $40 $20* $80* d 4 $30 Say that lead time of 5 days is acceptable. Can backtrack and undo the earlier crashing at b. Add 1 day and subtract $60. Now (a  b  e ) and (a  d ) have LT =5. New Cost*: $320 - $60 = $260 Activity Pred. Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 $30 3 $60*

Example (cont’d): Crashing Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days) 2 1 Normal Cost 2 $60 1 Ratios b 3 $70 2 $20 $80 $20* e 3 $40 $10 $80* S a c 2 $0 F $40 $20* $80* d 4 $30 Activity Pred. Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 LT (a  b  e ) = 4 Say that lead time of 5 days is acceptable. Can backtrack and undo the earlier crashing at b. Add 1 day and $60 back. Now (a  b  e ) and (a  d ) have LT =5. New Cost*: $320 - $60 = $260 If 5 days is acceptable, then stop. $30 3 $60*

Example (cont’d): Crashing Activity $ Saved/ Day (Slope) a 40 b 60 c - d 30 e 70 (2 days) 1 2 1 Normal Cost 2 $60 1 Ratios b 3 $70 2 $20 $80 $20 e 3 $40 $80* 2 $10 $80* S a c $0 F $40 $20* $80* $30 LT (a  b  e ) = 5 Assume that acceptable lead time is now 4 days. Crash d for 1 more day. Cost*: $260 + $30 = $290 Crash b again for 1 more day. New Cost*: $290 + $60 = $350 Now (a  b  e, a  c and a  d ) have LT =4. Addtn. Cost of reducing project from 8 to 4 days: $230 You could still crash d 1 more day, but it would be a waste of $. d 4 Activity Pred. Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, 80 b 2, 1 20, 80 c 2, 2 20, 20 d* 4, 1 30, 120 e** 3, 1 10, 80 $30 3 $60 2 $90*

Example (cont’d): Crashing

CPM Cost-Duration

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