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53 Cards in this Set
- Front
- Back
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project
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collection of tasks that must be done in a min. time or at min. cost
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objectives of project scheduling
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completing project as early as possible
calculating likelihood that it will be done withing a certain amt. of time finding min. cost schedule to get project done by a certain date investigating results of certain delays progress control resource allocation |
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task issues
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est. time associated with each activity
completion time is related to amt. of resources committed to tasks |
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how to determine optimal project schedules
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identify all activities of project
determine the precedence relations among activities base on this we can develop managerial tools for project control |
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PERT/CPM approach
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uses network presentation of project to:
- reflect activity precedence relations - activity completion time used for scheduling activities to minimize completion time |
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earliest start time
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ES = 0
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earliest finish time
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EF = duration of activity
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fining earliest start for each activity
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ES = max. EF of all of it immediate predecessors
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finding earliest finish for each activity
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EF= ES + activity duration
** EF of finish node = earliest completing time for the project |
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how to determine latest start time/ latest finish time
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make a backward pass through the network chart
evaluate all activities that immediately precede each finish node - LF = minimal project completion time - LS = LF - activity duration evaluate LF of all nodes for which LS of all immediate successors have been determined - LF = min. LS of all its immediate successors - LS = LF - activity duation repeat this backward process until all nodes have been evaluated |
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slack times
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delays may affect overall completion date
to learn about these effects we calculate slck time and form the critical path defined as the amt. of time that an activity can be delayed without delaying the project completion date, assuming not other delays are taking place slack time = LS - ES slack time = LF - EF |
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critical path
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set of activities that have no slack, connecting the start and finish node
longest path in the network ** sum of completion times for the activities in the critical path is the min. completion time of the project |
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single delay
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delay in a certain amt. of critical activity, causes the entire project to be delayed by the same time amount
a delay in a certain amt. of noncritical activity will delay the project by the amount that the delay exceeds the slack time; if they delay is less than the slack time, the project will not be delayed |
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linear programming approach to PERT/CPM
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vars: xj = start time of activities
x(fin) = finish time of project obj function: complete project in min. time constraints: for each arc a constraint of M must occur before the finish time of the immediate predecessor minimize x(fin) |
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gantt charts
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used as a tool to monitor and control the project progress
graphical presentations: - time is measured on the horizontal axis; horizontal bars are drawn proportionately to an activity's exp. completion time - each activity is listed on the vertical axis |
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earliest time gantt chart
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each bar begins and ends at the earliest start/finish time that an activity can take place
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advantages of gantt charts
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easy to contruct
gives earliest completion date provides schedule of earliest possible start and finish times of activities |
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disadvantages of gantt charts
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gives only one possible schedule (earliest)
does not show whether the project is behind schedule does not demonstrate the effects of delays in any one activity on the start of another activity, thus on the project completion time |
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resource leveling and allocation
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desired that resources be evenly spreadout through duration of project
leveling methods/hueristics: designed to: - control resource reqs. - generate relatively similar usage over time |
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heuristic approach the resource leveling
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assumptions:
when an activity has started, it is worked on continuously until it is done costs can be allocated equally throughout activity duration steps: 1. consider the schedule that begins each activity at its earliest start time 2. determine which activity has slack at peak periods of spending 3. attempt to reschedule non-critical activities performed during these peak periods of less spending, but within the time period betwee their ES and LF |
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probability approach to project scheduling
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- activity completion times are rarely known with 100% accuracy
- completion time estimates are obtained by the three time estimate approach |
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three time estimate approach
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provides completion time estimate for each activity
notation: a = optimistic time to perform activity m = the most likely time to perform the activity b = pessimistic time to perform activity based on the beta distribution mean completion time = (a + 4m + b)/6 standard deviation = (b - a)/6 |
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assumption of project completion time distribution
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1. the critical path can be determined using th mean completion times for activities; mean completion time is determined solely by the completion time of the activities on the critical path
2. time to complete one activity is the independent time to complete any other activity 3. there are enough activities on the critical path so that the distribution of overall project completion can be approximated by the normal distribution |
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normal time distribution of project completion
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mean = sum of mean completion times on critical path
variance = some of completion time variances on the critical path standard deviation = Square root of variance |
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why expected value approach should be used for cost analysis
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spending extra money should generally decrease product duration
is this operation effective? the expected value criterion is used to answer this question use only critical values in this evaluation! |
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cost analysis using the critical path method
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CPM = deterministic approach to project planning
completion time depends only on the amt. of money allocated to activities reducing the activity's completion time is called CRASHING |
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normal time vs. crash time
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normal completion time (Tn)
crash completion time (Tc) -- min. possible completion time cost spent on activities varies between normal cost and crash cost |
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crash time/crash cost -- linearity assumption
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max. crashing of activity time is Tc - Tn
- this can be achieved when spending Cn - Cc any percentage of max. extra cost (Cn - Cc) spent to crash an activity yields the same percentage reduction of the max. time savings (Tc - Tn) |
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marginal cost
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= additional cost to get max. time reduction/min. time reduction
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meeting a deadling at minimum cost
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if deadline cannot be met using normal times, additional resources must be spent on crashing activities
objective: meet deadline at minimal additional cost |
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small crashing problems can be solved huerisically
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observations:
- project completion time is reduced only when critical activity times are reduced - max. time reduction for each activity is limited - amt. of time a critical activity can be reduced before another path becomes critical |
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operating withing a fixed budget
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crash budget = (percentage above normal cost)(normal cost projection)
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PERT/cost
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helps mgmt. gauge progress against scheduled time and cost estimates
based on analyzing a segments project; each segment is collection of work packages |
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work packages assumption
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once started, a work package is performed continuously until it is done
the costs assosciated with a work package are spread evenly throughout its duration |
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work package forecasted weekly cost
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budgeted total cost of package/exp. completion time for work package (in weeks)
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value of work to date
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=p * budget for the work package
p = est. percentage of work package that is completed |
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expected remaining completion time
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(1-p)(original expected completion time)
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completion time analysis
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using the expected remaining completion time estimates to revise the project completion time
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cost overrun/uderrun analysis
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for each workpackage, comp. or not, calculate
cost overrun = actual expenditures to date - value of work to date |
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corrective actions of project progress
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a project may be found to be behind schedule or experiencing overruns
causes: - mistaken completion time and cost estimates - mistaken work package completion times and cost estimates - problematic departments or contractors that cause delays possible corrections: - focus on incomplete activities - determine whether crashing is desirable - in the case of underrun, channel more resources into problem activities - reduce resrouce allocation to non-critical activities |
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why simulation instead of analytic?
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simulation ca be used when:
- not all underlying assumptions for analytic model are valid - when math complexity makes it hard to provide useful results - when good solutions, not necessarily optimal, are satisfactory |
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simulation
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develops a model to numerically evaluate a system over some time period
by estimating characteristics of the system, the best alternative from a set of alternatives under consideration can be selected usually requires the use of a computer program |
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continuous simulation systems
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monitor the system each time a change instate takes place
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discrete simulation systems
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monitor changes in state of system at discrete points in time
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approaches for simulation
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- add-ins to excel such as @risk or crystal ball
-using general purpose programming languages such as FORTRAN, PL/1, Pascal, Basic - using simulation languages such as GPSS, SIMAN, SLAM - using simulation software |
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monte carlo simulation
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generates random events
random events are needed in simulation model when the input data includes random vars. to reflect frequencies of random vars., the random number mapping method is used |
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hypothesis test (not equal to)
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define aplha -- significance level
let n be number of replication runs build the t-statistic (for normal dist.) reject if t>t alpha/2 or t<-talpha/2 t alpha/2 has n-1 degrees of freedom |
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simulation modeling of inventory systems
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inventory simulation models are used when underlying assumptions needed for analytical solutions are not met
typical inputs to simulation model: order cost, holding cost, lead time, demand distribution |
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fixed-time simulation approach
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appropriate for modeling inventory problems
- systems are monitored periodically - activities assosciated with demand, orders, and shipments are determined and the system is updated accordingly typical output is the ave. total cost for a given inventory policy |
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AAC - the planned shortage model
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assume first a constant rate of deman, and use the planned shortage model
calculate the following: ave. weekly demand = (ave. # customers/wk.)/(ave. demand/customer) holding cost per unit per week= (ann. holding cost rate)(unit cost)/52 |
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simulation of queuing system
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in this system, time itself is random variable, therefore we use next event simulation approach
data are updated each time a new event takes place, not a fixed time period process interactive appraoch is used in this kind of simulation |
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simulation of M/M/1 queue
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new arrival time = previous random interarrival time
service finish time = service start time + random service time customer joins the line if there is a service in progress customer gets served when the server becomes idle waiting times and amt. of customers in line ad in the system are continuously recorded |
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hypothesis tests:
Ho: u1-u2 = 0 Ha: u1-u2 > 0 |
rejection region:
Z > Zalpha |
