Why Queues? via Dynamic Stochastic PERT/CPM Networks

Transcription

1 Service Engineering September, 2002 Last Revised: May, 2004 Why Queues? via Dynamic Stochastic PERT/CPM Networks Product/Service development Project management Both "enjoy": Stochastic environment Multi-projects Scarce resources 1

2 History Product Development with Adler, P., Nguyen, V., Schwerer, E. (Management Science, HBR) Project Management Lamberg, Y. (M.Sc.) Israeli Electric Baron, Y. (M.Sc.) Conceptual Framework IE&M Projects Software Development Cohen, I. (Ph.D.) TOC vs. DS-PERT/CPM

3 3 Teaching Static Deterministic Models Static Probabilistic Dynamic Stochastic Models: DS-PERTs (Fork-Join, Split-Match,...). Important theoretically and practically. Intractable theoretically: simulation, approx. 3

4 4 Stochastic PERT / CPM Activities A B C Avg. Duration Distribution or 9 wp ½ and ½ A S B F Project time = max {3, 4, 1} = 4 wp ½ max {3, 4, 9} = 9 wp ½ C 4

5 5 Dynamic Stochastic PERT Activities, Resources, Random durations Multiple projects A Arrive S B F Depart Queues due to Scare Resources C Queues due to Synchronization Gaps 5

6 6 Arrest - to Arraignment (Larson,...) Lodged at Arrives at Arr. Precinct Arr. Courthouse (12 hrs.) (39 hrs.) Arrestee Arrest Arrive at Arrive at Arrives at Complaint Arraigned (0 hrs.) Arr. Off. Precinct (1 hr.) Arr. Off. Central Booking (5 hrs.) Off. Complaint Room (6 hrs.) Sworn (14 hrs.) Paperwork Completed (48 hrs.) Fingerprint. Transmit- -ted to Rap Sheet Received (18 hrs.) Off. = Arresting Officer. Arr. = Arrestee Cards Albany (10 hrs.) (15 hrs.) Source: Improving the N.Y.C A-to-A system Larson, R. Cahn, M. Shell, M. Interfaces 23,

7 7 Arrest to Arraignment Time Stochastic dynamic model: 18% 16% 14% 12% 10% 8% 6% Avg hours Std Should be less than 24 hours. 4% 2% 0% >100 Probability Total Elapsed Arrest to Arraignment Time (in Hours) 7

8 8 Traditional PERT/CPM Representation Project View Civil Eng. Programs w40 Specifications w50 Conceptual w10 Electro- Mechanics w20 Conceptual Schema Electrical w15 Start w0 General Layout w15 w40 Build Permit critical path Construction w110 End w0 w25 Locating Area w40 Repartition w75 Equipment 80 activities 25 departments 500 projects w50 T = 250 weeks? 8

9 9 Processing Network Representation Purchasing Equipment Mechanical Eng. Electro Mechanic Specifications Conceptual Conceptual Schema S Research Civil Eng. Construction E Conceptual Civil Area Programs Locate General Layout Conceptual Electric Resource Assets Electrical Eng. Synchronization Queue Service Queue Build Permit Repartition Workflow 9

10 10 Can We Do It? Capacity Analysis - [= Fluid-view (first moments)] Utilization as a function of the number of employees: Electrical Electro-Mechanic Electro-Mechanic Electro-Mechanic Combined Outdoor Indoor Employees Utilization Employees Utilization Employees Utilization Employees Utilization 6 129% % 4 79% 6 131% 7 117% 12 96% 5 67% 7 120% 8 108% 14 88% 6 59% 8 112% 9 101% 16 82% 7 54% 9 105% 10 95% 17 80% 7 54% % 11 91% 18 78% 7 54% 11 96% 12 87% 19 76% 7 54% 12 93% Utilization Electrical Mech-Combined Mech-Outdoor Mech-Indoor Employees 10

11 11 How long Will It Take? Stochastic static model (single project): Probability Cumulative Distribution Avg. 338 weeks Std % 475 Det. 250 Completion Time in Weeks 11

12 12 How Long Will It Take? Stochastic dynamic model: Probability Completion Time in Weeks Cumulative Distribution 4 Types: Type New sub-station 3.27 New switching stations 0.6 Improvements 3.4 Additional capacity 1.9 Avg. 485 weeks Std % 770 Det. 250 Per year 12

13 13 Can We Do Better? Relieving bottlenecks: Unlimited resources (static) weeks Electrical dept weeks Unlimited resources: ( = Stochastic static) Avg. 6 years. 10% over 9 years. Probability Civil Eng. dept Base case weeks 6 years avg. too long. => Resources NOT the problem! Completion Time in Weeks (Infinite-server models are important). 13

14 14 New location management and standardization: 0.5 Can We Do Better? Base New 0.4 New location mgt: 40 weeks, 8 weeks 0.5 prob. of repeat 0.8 prob. Probability Completion Time in Weeks Standardization: 8000 hrs. planning, 2000 repeats, none long execution times 25% Avg. 485 weeks 189 Std %

15 15 Summary E σ 90% Deterministic 251 weeks Stochastic Static Single-Project Stochastic Dynamic (14 years) Multi-Projects Infinite Resources Re-Engineering