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MD 021 - Management and Operations Managing Project Processes Outline Definition of a project Network methods using deterministic estimates Probabilistic estimates Cost considerations 1 Definition of a project A project is an interrelated set of activities that has a definite starting and ending point and results in unique product or service. Examples of projects include building construction, introducing a new product, and redesigning the layout of a plant or office. 2 PERT and CPM Network Methods Definitions Activity - The smallest unit of work effort consuming both time and resources that the project manager can schedule and control Precedence relationship - A sequencing constraint between interrelated activities by which one activity cannot start until a preceding activity has been completed Schedule - A plan that sets priorities, determines start and finish times, and allocates resources to accomplish the activities 3 Project Management Using Network Models First two steps: Describe the project a) Define project activities. b) Determine precedence relationships. Diagram the network a) Nodes (circles) and arcs (arrows) b) Activity-on-node (AON) network Nodes are activities and arcs show precedence relationships Activity-oriented 4 Project Management Example St. Adolph’s Hospital Immediate Activit Description Predecessor(s y ) A Select administrative and medical staff. --B Select site and do site survey. --C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, A support staff, maintenance, and security. G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop an information system. A J Install the equipment. E, G, H K Train nurses and support staff. F, I, J 5 Network Time Calculations Earliest finish time (EF) for an activity EF = ES + t Earliest start time (ES) for an activity ES = Max [EF times of all immediately preceding activities] Latest start time (LS) for an activity LS =LF – t Latest finish time (LF) for an activity LF = Min[LS times for all immediately following activities] 6 Calculating Time Estimates a) Optimistic time (a): Shortest time during which an activity can be completed. b) Most likely time (m): Best estimate of average time. c) Pessimistic time (b): Longest time an activity can take. d) Activity’s time ( te ) and variance ( 2 ) with beta distribution te a 4m b 6 2 ( ba 2 ) 6 7 Calculating Probabilistic Estimates St. Adolph’s Hospital Example Activity Optimistic ( to ) A B C D E F G H I J K 11 7 5 8 14 6 25 36 10 1 5 Time estimates (weeks) Most likely Pessimistic (tm ) (t p ) 12 8 10 9 25 9 36 40 13 2 6 13 15 15 16 30 18 41 45 28 15 7 8 Expected time ( t e ) Variance ( 2 ) 10 10 24 10 35 40 15 4 6 2.78 1.78 7.11 4.00 7.11 2.78 9.00 5.44 0.11 Analyzing Probabilities Probabilities can be assessed using the z-transformation formula: Z T TE T = specific time, TE = expected time (path mean), = standard deviation of path mean. Assuming the activity times are independent, the path standard deviation activity time variances. is the square root of the sum of the To determine the probability of completing a project in a specified amount of time: Calculate the probability of each of the paths being completed in that amount of time based on the value of z. For any value of z that is greater than 3, the probability that the corresponding path will be completed in that amount of time can be considered to be 100%. If all paths are independent, then the probability of completing a project in the specified amount of time is the product of the individual path probabilities. 9 Hospital Project Completion Probabilities How likely is it that the hospital project will be completed in 72 weeks? Path A-F-K A-I-K A-C-G-J-K B-D-H-J-K B-E-J-K z 72 Expected path duration Path standard deviation (72 – 28)/2.05 = 21.5 (72 – 33)/3.04 = 12.8 (72 – 67)/3.94 = 1.27 (72 – 69)/3.45 = 0.87 (72 – 43)/3.80 = 7.6 10 Probability of completion in 72 weeks 100% 100% 90% 81% 100% Analyzing Costs in a Project 1. Direct costs and times normal time normal cost crash time crash cost 2. Cost assumptions: linear costs per unit of time 3. Indirect costs and penalty costs 11 Determining the Minimum-Cost Schedule Step 1: Determine the project’s critical path(s). Step 2: Find the cheapest activity or activities on the critical path(s) to crash. Step 3: Reduce the time for this activity until the first of (a) it cannot be further reduced, (b) another path becomes critical, or (c) the increase in direct costs exceeds the savings that result from shortening the project. If more than one path is critical, the time for an activity on each path may have to be reduced simultaneously. Step 4: Repeat this procedure until the increase in direct costs is less than the savings generated by shortening the project. 12 Activit y A B C D E F G H I J K Direct Cost and Time Data for the Hospital Project Normal Normal Crash Crash Max. time Cost of time cost time cost reduction crashing per (wks) ($K) (wks) ($K) (wks) week 12 9 10 10 24 10 35 40 15 4 6 Totals $12 50 4 16 120 10 500 1,200 40 10 30 $1,992 11 7 5 8 14 6 25 35 10 1 5 13 64 7 20 200 16 530 1,260 52.5 13 34 $2,209.5 13 1 2 5 2 10 4 10 5 5 3 1 $1,000 7,000 600 2,000 8,000 1,500 3,000 12,000 2,500 1,000 4,000 Hospital Project Minimum-Cost Schedule Assume: Indirect cost = $8,000/week Penalty cost = $20,000/week after Week 65 Critical path B-D-H-J-K Crash activity Project duration Crash cost 69 weeks 14 Indirect cost change Penalty cost change Total cost change