07/09/2011. A.AMRANI-ZOUGGAR IMS-Lab, University Bordeaux1. These products specific management

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1 A.AMRANI-ZOUGGAR IMS-Lab, University Bordeaux These products specific management

2 What leads the industrialist to start projects? BENEFITS Ageing of the range Benchmarking, comparing the market and industrial evolution Appearance of a new technology Ex: AMOLED screen Leads the company to develop new project Arrival of a new low cost competitor Risk of threat for the company necessity to design new projects 3 3 Project Activity Non repetitive Irreversibles Decisions Strong uncertainty Production Activity Repetitive Periodic Decisions Weak uncertainty Strong influence of external variables Strong Influence of internal variables

3 Staff Turnover Management g change Hardware unavailability Requirements change Size underestimated 5 Projects don t often reach their objectives : No respect of lead time Important over costs Product technical quality insufficient Projects are running in a complex environment : Various actors in enterprises: engineering, production, marketing, having different objectives and different measures External environment difficult to master: market, policy, Competition NEED TO SPECIFC METHODS AND TOOLS 6 3

4 PERT method. How to draw PERT network? Kind of constraints Concepts Steps to follow margins calculation Total margin Free margin. Advanced PERT Probabilistic PERT PERT costs Kind of constraints Execution of a project, often, requires succession of tasks linking by some constraints. - Constraints of time: Leadtime to respect in performing the task (taking account the time of using resources) - Constraints of anteriority: Some tasks must be executed befor others - Constraints of simultaneity: Some tasks are performed in the same time PERT (Program Evaluation and Review Technique) charts represents the project schedule as an activity network.

5 Concepts - Task of project is represented by node - Duration of task is represented by an arc (branch) -Start nodeand Finish node are also represented For each activity, these values are estimated ES Earliest start time EF Earliest finish time LS Latest start time LF Latest finish time The length of each path has to be calculated The LONGEST path in the project is the CRITICAL PATH Steps to follow To draw PERT, 6 Big steps are required. Establish a list of tasks. Determine anteriority conditions 3. Draw PERT network. Calculate the earliest and latest dates 5. Calculation of margins 6.Found the critical path of the project 5

6 Steps to follow. Establish a list of tasks Enounce a list of tasks to perform Assess the durations of tasks (processing times) to determine the required resources Assign a codification to tasks to make easier the construction of the network. Establish a list of tasks Exemple : The building of storage warehouse Tasks Duration (t.u) A Study, realization and acceptance of plans B Preparation of the ground C Order materials (wood, bricks, cement, sheet for the roof) D Digging of the foundations E Doors, Windows orders F Delivery of materials G Casting of the foundations H Delivery of doors, windows 0 I Construction of the walls, the roof J Installation doors and windows 6

7 Steps to follow To draw PERT, 5 big steps are required. Determine anteriority conditions By answering these questions : Which task must be ended before another could start? Which task have to follow some tasks?. Determine anteriority conditions Previous tasks Task Following tasks - A C,D,E - B D A C F A,B D G A E H C F G D,F G I E H J G I J H,I J - 7

8 Steps to follow 3. Draw PERT network Network is made of enounced tasks. Tasks are the node and arcs are constraints of precedence E H 0 0 Start 0 A C F G I J End 0 B D. Calculate the earliest and latest dates Earliest start date of task i: The earliest date on which task i could start taking account the required time to process previous tasks Task i ESi ES = max( ES + p i j P(i) j ji ) Latest start date of task j: Task LSi The latest date on which task i must i absolutely start in order to not disturb and delay the overall project. LSi = min( LS j pij ) j F(i) 8

9 . Calculation of ES and LS 0/0 Start 0 0 0/0 A B D 0/7 /9 / 6/6 E H /7 C 5/8 7/0 F G I J 9/ 6/6 0 7/7 End ESi: Forward computation LSi: Backward computation 5. Calculation of margins Total margin Allowed flexibility for task without changing project duration M T i = LSi ESi 0 ESi Task i LSi MT EEi MT EEi Free margin Allowed flexibility of task i without delaying following tasks M F i = min( ES pij ESi) 0 j Task i EEi MF ESj Task j 9

10 6. Find a critical path / 6/6 E H 0/0 Start 0 0 0/0 /7 5/8 7/0 A C F G I J 9/ 6/6 B D 0/7 /9 Find the critical path each task whose MT=O Project duration (critical path) = 7 t.u Critical tasks are: A, E, H, J 0 TASK MT MF A 0 0 B 7 C 3 0 D 5 E 0 0 F 3 0 G 3 0 H 0 0 I 3 3 J 0 0 7/7 End P.E.R.T method. How to draw PERT network? Kind of constraints Concepts Steps to follow margins calculation Total margin Free margin. Advanced P.E.R.T Probabilistic PERT PERT costs 0

11 Probabilistic PERT Inside project appears some difficulties to get the exact durations of tasks Probabilistic PERT considers the uncertainity about the dates and durations of tasks Uncertainity of durations? Necessity to taking account delay variation in margins computations For each task, it is important to define to: Optimistic time, tr: realistic time (the most probabilistic) tp: pessemistic time Probabilistic PERT An assessment of random duration of tasks often follows probability distribution of type β β distribution is characterized by these parameters: Frequency of time existence The mean m Variance V Standard deviation σ to + tr + tp moyenne Mean = tm = 6 ( tp to) V = 6 to tr tm tp Time

12 Probabilistic PERT Objectives Probabilistic PERT allows to determine the probability of fulfilling project in certain duration with variable task s durations What is the probability that project would be performed in x units of time? Total duration of project is distributed according «normale distribution» gaussian curve, with a mean m equal to the sum of average durations of critical tasks The variance of sum of random variables is equal to the sum of variables. It becomes possible to determine standard deviation of critical path. n σ = σ i= i Probabilistic PERT Notions: Gauss/normal distribution * Sets of data to collect: Weights, Heights * Number of results (pulling) according to a sample Study of the distribution Normal distribution if the found values are distributed around a mean μ with standard deviation sigma σ Noted N(μ, σ ) Z has a standard normal distribution Z N(0, ), mean 0 and variance Its probability density function is usually denoted by F and is given by If X has a general normal distribution X~N(μ, σ ) Z P(X<Z) = F(Z) P(X<Z) = F(Z) It is necessary to transform in order to use probabilistic table: Standradizing transformation is of upmost importance. Then Z, defined by the standardizing transformation has a standard normal distribution.

p T = F(Z) α ) σ F(Z) π(α) is a value to find in the table of normal distribution (it is a probability)

13 Probabilistic PERT Once the mean and standard deviation calculated, the probability of realization is deduced The probability of realizing project of duration T in x unit of times P(T X) z X tm p ( T X ) = p T = F(Z) α ) σ F(Z) π(α) is a value to find in the table of normal distribution (it is a probability) Probabilistic PERT Normale distribution z Distribution function F(Z) Z Represent a probability F(-Z) =? 3

14 Probabilistic PERT: exercise The project manager of a Warehouse building has just made the assessment of durations. Task Durations (u.t) Previous Optim Real Pess tasks A 3 5 C, G, L B 3,5 8 - C 3 B, H D,5 3,5 7,5 B E B, G, L F A, D G D H,5 6 B I,5,5 6,5 J J 3 G, L K 9 A, F, I L,5 5 B, C, H Probabilistic PERT: exercise Classical PERT: Build the network of the project Calculate the average durations for each task Determine margins (free and total) for each task Deduce the critical path of this project Probabilistic PERT What is the probability to realize the construction in 35 days? What is the probability to realize the project in 9 days? What would be the limit path duration that ensures probability of 95% to realize the building

15 Probabilistic PERT : exercise Tâche to tr tp tm A 3 5 B 3,5 8 C 3 5 D,5 3,5 7,5 E F G to + tr + tp H,5 6 3 mean = tm = I,5,5 6,5 3 6 J 3 3 K 9 3 L,5 5 The mean of the values (tm) follows β distribution moyenne Continue to solve the problem 30 5

11/8/2018. Overview. PERT / CPM Part 2

11/8/2018. Overview. PERT / CPM Part 2 /8/08 PERT / CPM Part BSAD 0 Dave Novak Fall 08 Source: Anderson et al., 0 Quantitative Methods for Business th edition some slides are directly from J. Loucks 0 Cengage Learning Overview Last class introduce