l13sim_resplan04

l13sim_resplan04 - Simulation and ResourceBased Scheduling...

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Unformatted text preview: Simulation and ResourceBased Scheduling Nathaniel Osgood 3-30-2004 Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Static vs. Dynamic Scheduling Static Scheduling Dates known ahead of time Coordination with stakeholders Coordination with subcontractors Coordination pre-planned (e.g. reservation system) Can't take advantage of early finishes, arrivals, etc. Dynamic Scheduling ("Wait and See") Dynamic coordination takes time (queuing) Prevents needless waiting if finish early Both get done! Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Granularity of Scheduling Fine-grained (particular crews, indiv.) advantages Can reason about Crew productivity Balancing workload among crews Distance traveled for particular crews Coarser-grained advantages Combinatorially more challenging May inhibit creativity in dynamic scheduling Generally, leave dynamic (or "quasi-dynamic") factors that don't consider statically Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Major Types of Simulation Discussed here: Discrete Event Simulation Oldest: GERT/Q-GERT (Pritsker) Common representation: Activity Cycle Diagrams Transaction-based ("Process interaction") approaches SLAM GPSS Activity-scanning approaches CYCLONE STROBOSCOPE Not discussed today: System Dynamics NB: graphical rep. & implementation may differ GERT Basics Builds on Activity-on-Arrow diagrams Discrete semantics "Transactions" ("entities") flow through system Fire off additional transactions Transactions secure resources for processing Must wait until needed resources are available Probabilistic Durations Branching & Looping Time no longer linearly increasing to right! Most Common Q-GERT Node Arrows Represent activities Sometimes use dummies, sometimese not Representation 1: Exp() N(,) Exp() (Dummy) Representation 2: N(,) Branching GERT Looping/Branching Constructs Deterministic (like CPM/PERT) Probabilistic Rework Cycle Example of Probabilistic Branching and Looping-no Equivalent Arrow Diagram Possible. Drop project Evaluation of alternative engine development 1 1 10 1 1 20 Proceed to develop solid fuel engine Initial project activities Rework (Recycle loop) Proceed to develop liquid fuel engine Corresponding Aggregate CPM Representation Additional GERT Node Types Source/Sink nodes Statistics nodes First/all realizations Interarrival time Time interval from mark node Etc. Mark nodes Diversity in realization types, etc. Q-GERT: Introduces Queues Delivers entities to outgoing activities Outgoing activities are associated with # of servers # clients that can process in parallel Accumulates objects up to some capacity Backs up if cannot process immediately "Balks" if reaches capacity Combination elements to combine transactions Led to development of GASP, SLAM GERT Applications Offshore Oil Rigs (Granli) Alaska Pipeline Reservoir construction (Pena Mora) Construction Simulation Languages Equally powerful: All "Turing Equivalent" i.e. Any language can simulate any other Differ in terms of Ease of use Extensibility Expressiveness for construction domain How natural is it to describe construction scenarios? Two main framework: process interaction and activity scanning Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Activity Cycle Diagrams: Common Visual Representation Rectangles: Activities Circles: Queues (resources in particular state) ACD for Scraper and Pusher Operation RdyTo BkTrack RdyTo Haul Haul RdyTo Dump Dump and Spread Back Track Push Load Dumped Soil PshrsAt PshPnt Scrapers AtCut Return RdyTo Return Pusher Scraper Soil Scraper+Soil Simulation Example: Excavation and Transporting Given Front-end loader Output: ofront-end loader Instantaneous time between loads Trucks n vehicles nc ncsl se otrucks = = Capacity c d d d ( se + sl ) + Load time tl sl se Instantaneous dump time Fully loaded speed sl , empty speed se Distance to dumpsite d Nave productivity: min(ofront-end loader, otrucks) Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Process Interaction Frameworks Examples: SLAM, GPSS, ProModel, SimScript, ModSim, etc. Based on flow of transactions through system Capture and release resources ("machines") Good in "job shops" where have Clear items moving through system Resources temporarily claimed by items Process Interaction Shortcomings In construction, identifying what constitutes a "transaction" can be tricky Awkward to represent other entities Changing perspective to other entities difficult Risk of deadlock over resources during simulation Process Interaction Representation Process Interaction Flowchart for Scraper and Pusher Operation Split Generate All Scrapers at time 0 Loop Queue Scrapers Wait (B k T rack) Bk Track Advance BackTrack Leave Pushers Advance Haul Advance Dump Enter Pushers Split Scrapers Wait Advance Return (So Depart Advance Push-Load il) Terminate 0 Soil (Loop) Transfer Terminate 1 Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Activity Scanning Simulation Packages General purpose Representation similar to activity cycle diagrams Identify conditions to allow activities to proceed Construction-specific CYCLONE STROBOSCOPE CYCLONE Elements NAME SYMBOL FUNCTION This element is always preceded by Queue Nodes. Before it can commence, units must be available at each of the preceding Queue Nodes. If units are available, they are combined and processed through the activity. If units are available at some but not all of the preceding Queue Nodes, these units are delayed until the condition for the combination is met This is an activity similar to the COMBI. However, units arriving at this element begin processing immediately and are not delayed This element precedes all COMBI activities and provides a location at which units are delayed pending combination. Delay statistics are measured at this element It is inserted into the model to perform special fucntion such as counting, consolidation, marking, and statistic collection Combination (COMBI) Activity Normal Activity Queue Node Function Node Accumulator It is used to define the number of times the system cycles Arc Indicates the logical structure of the model and direction of entity flow CYCLONE Brick Example Qualitative Description Labor: 3 masons, 1 laborer Scaffold can hold 3 pallets of 10 bricks each CYCLONE Brick Example Model 1 Laborer idle L 2 Resupply stack 3 Position occupied 4 Position available PP P 5 Mason removes packet 7 Mason waits resupply M M M 8 6 Mason lays brick CYCLONE Brick Example Underlying Code NAME 'MASONRY' LEN 500 CYC 9 NETWORK INPUT 1 QUE 'LAB IDLE' 2 COM SET 1 'RESUPPLY' FOL 1 3 PRE 1 4 3 QUE 'STACK OCCUP' 4 QUE 'STACK EMPTY' 5 COM SET 2 'PICKUP' FOL 4 6 PRE 3 7 6 NOR SET 3 'PLACE 10 BRK' FOL 8 7 QUE 'MASONS IDLE' 8 FUN COU QUA 10 FOL 7 RESOURCE INPUT 1 'LABORER' AT 1 3 'POSITIONS' AT 4 3 'MASONS' AT 7 DURATION INPUT SET 1 BETA 0.001 5.0 2.6 0.5 SET 2 1 SET 3 BETA 3 10 7 2.2 ENDDATA ACD for Scrapers and Pushers ACD for Scraper and Pusher Operation RdyTo BkTrack RdyTo Haul Haul RdyTo Dump Dump and Spread Back Track Push Load Dumped Soil PshrsAt PshPnt Scrapers AtCut Return RdyTo Return Pusher Scraper Soil Scraper+Soil Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Recall Basic Steps of Network Methods Define activities from WBS work packages Estimate $, time, resources for each activity Define precedence relationships between activities Iterate Perform CPM scheduling In a sense, we are assuming "infinite resources" here! Estimate time, cost, resource usage over project If acceptable, terminate If not acceptable, impose dependencies or added/reduced resources Resource Considerations Human resources most important Time to procure Difficult to release Difficult to reuse on demand Must consider different trades as different types of resources Equipment Highly specialized equipment Normal equipment relatively easy to procure on demand Note constraints -- Permitting issues, etc! Resource Algorithms Resource Leveling Moving activities within float to minimize fluctuations No change to schedule duration! Especially important for human resources No guarantee that falls within limits of available resources! Resource Scheduling ("Constrained-resource scheduling", "Limited Resource Allocation") Scheduling resources within constraints with minimal extension of schedule time Key assumption: Holding individual activity resource assignments, durations constant Optimal Resource Scheduling/Leveling Methods Combinatorial problem Computationally very expensive (NP-complete) In principle, would need to compare all possible orderings of conflicting activities Intuition: Lots of possible start/stop times within constraints Typically too large to realistically enumerate Locally best choice not necessarily globally best Approaches Linear Programminig Explicit Enumeration "Branch and Bound" (constrained search) Example of Combinatorial Factors Resource Scheduling 1 B 0 A 0 1 E 4 1 2 C 4 1 D 4 0 F 0 LEGEND: Required resources E Duration Best local choice! Possible Schedules Duration: 12 B CCCC EEEECCCCDDDD CCCC BEEEECCCCDDDD CCCC BCCCCEEEEDDDD CCCC BCCCCDDDDEEEE CCCC EEEEBCCCCDDDD CCCCEEEE BCCCCDDDD Duration: 13 Duration: 13 Duration: 13 Duration: 13 Duration: 9 Detailed (Crew-Level Scheduling) Section Work Duration A B C D E F G H I J K 9 9 8 8 7 7 6 6 6 5 5 Assignment of Crews to Activities Integer Programming Formulation Section i, crew j xij = 1 if section i assigned to crew j, 0 otherwise ti = time for section j Problem: Minimize z subject to constraints z nactivities i =1 ti xij Need to account for assignment of time to resources Only one crew assigned per resource ncrews i= j x ij =1 Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Heuristic Methods Use "rules of thumb" to get answer in acceptable time Typically reach local minimum "Greedy" algorithms do what is locally but not necessarily globally best Typically use empirical evaluation to judge Sometimes highly problem-specific (e.g. SPAR) sometimes very general (branch & bound, simulated annealing, genetic algorithms, etc.) Heuristic Scheduling Approaches "Serial" methods: Schedule activity-by-activity Consider prioritized activities in order Schedule as early as possible Less common "Parallel" methods: Schedule by timestep Start with some initial schedule For each timestep, decide which activities to delay Local optimization: Never reconsider activities in progress Based on characteristics of activities that would be active Most commonly used Heuristic Resource Scheduling Methods: Typical Approach Assign priorities. Example metrics: Shortest Task First Most Resources First Minimum Slack First Most Critical Followers Most Successors Wait until Predecessors complete Adequate resources available Empirical Studies Patterson and Davis (1975) compared multiple heuristics, in "serial" and "parallel" modes Examples: Minimum late finish time, function of EF&LS, greatest resource demand, minimize resource "idling", shortest durations first, greatest # of activities, random activity selection, min. slack Most effective: Min slack (i.e. min late start) Minimum late finish Non-optimal 60% of time Serial vs. parallel may be more important than rule Example Leveling Heuristic (Burgess) Sort activities in reverse order of precedence Assign activities to early start time Repeat until sum of squares of resource use = For each activity in sorted order Schedule at time that minimizes sum of squares of resource use (subject to precedence constraints) Repeat with different initial ordering if resource highly critical Adjust for any other factors omitted Example Heuristic Resource Scheduling Algorithm 1. 2. 3. 4. Rank all resources from the most important to the least important Set the scheduled start day for each activity to Early Start Starting at t = 0, compute demand for resource i If resource demand for i is greater than availability, select the activity with the greatest Late Start and shift its start to t + 1 Repeat [4] until resource constraint at t for resource i is satisfied. Repeat [4] for t = t + 1 Repeat [3] for resource i + 1 5. 6. 7. Note on Prioritization of Algorithm Assuming no changing of already scheduled activities, delaying activities in order of late start is same as prioritizing in terms of slack Same as minimizing extension to overall project duration Selecting minimum slack shown empirically to outperform others Late finish-based selection also effective SPAR Algorithm Probabilistic assignment of jobs Allows for finding multiple local minima Not simply "greedy": Reconsiders earlier decisions May change critical path (delay job or resources for crit) Linear time/resource tradeoff assumed i.e. Constant person-days required for activity Critical resources considered for higher resource allocation If necessary, borrow resources from previously scheduled jobs but only if don't extend entire project If absolutely necessary, delay other active jobs Topics Simulation Methods Static vs dynamic scheduling Scheduling granularity GERT Demos Process interaction languages Activity scanning languages Resource algorithms Optimal Heuristic Line of balance method Line-of-Balance Applicability Repetitive Activities Same Crew Rate of Progress Minimize Discontinuity by Crews Represented in the Network by Continuous Activities Repetitive Activities Use for planning Crew reuse Planning timing of work Planning speed of work Plotting Activity Progress Lines PLOTTING ACTIVITY PROGRESS LINES Location Es tim at ed Pr og re ss Time Linear Scheduling Method Diagram LOB Planning Steps Design Crews Determine Task for Crews Sequence of Trades Location or Work Type Routing around the Job Buffer between Trade Crews Use of Restraint on LSM Diagram Activity Interference Use of Activity Buffers in LSM Schedules Activity Intervals for LSM Schedules LOB Advantages Easier to Set-Up than Networks More Information Than Gantt Charts Graphically Shows Rate of Progress Activity Durations Resource assignments Resource assignments Calendar dates Graphical risk of conflicts Augment Network Scheduling on Projects with Repetitive and Discrete Activities Labor Histograms Can Be Prepared Resources May Be Balance Earnings Curves Can Be Developed LOB Disadvantages Less Effective When Work is Regularly Interrupted or When Activities Do Not Follow the Same Order in All Locations Difficult to Determine Minimum Interval and/or Buffers Hard to represent both horizontal and vertical progression ...
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