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PERT / CPM:RESOURCE SCHEDULING IN NETWORK

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VirtualUniversity of Pakistan
OperationsResearch (MTH601)
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RESOURCESCHEDULING IN NETWORK
In scheduling projects usingPERT or CPM, we have assumedthat the only constraintfor an activity is to
fixthe starting date andthe finishing date. An activity may be started as soon as all its predecessors havebeen
completed.Thus we have an early startschedule for all the activities. In such scheduling procedures it is assumed
thatthe resources required to perform activities are available to any unlimited extent or atleast sufficient resources
areavailable for the activity to be started sometime betweenearliest and latest startdates. But we comeacross
situationswhere the project managershave to face the problem of limited or fixed resourceslike manpower
availabilities, machine availabilities and capitalmobilization. Activities, whichoccur on parallel pathsthrough
network, may compete for thesame resource.
Recentlyconsiderable work is in progress in developing heuristic programmesfor solving large
combinatorial problems, A heuristic can be defined as a guide or method of reducing search in a problem-solving
situations. It gives a rule of thumb.Businessmen employ heuristics quiteoften for their problems. As an example we
considerthe classic management rule, "Handle only exceptional problemsand let the subordinatesdecide on routine
matters" as a heuristic. Sometime a simple rule of thumb may not be enough, butother rules are also to particular
problem is referred to as 'heuristic programme'requiring a computer for complex problems. A number of different
heuristicprogrammes for schedulingprojects with limitedresources have beendeveloped recently. These
programmesare classified in any one of the two following forms.
1.
Resource leveling programmes: These programmesseek an attempt to reducepeak resourcerequirements
andsmooth out period to periodassignments with a restriction on project duration. In otherwords, in these
programmesthe resource requirements(manpower or money power) arekept at a constant level by altering
thestart time of the different activities. But at the same time,the project duration andthe sequence arenot
violated.
2.
Resource allocation programmes: These programsmake an attempt to allocatethe availableresources
(manpower, machine hours, money) to project activites and to find the shortest projectschedule consistent
withfixed resource limits. Thefollowing articles deal withthese types of heuristicprogrammes.
Resourceleveling program: Resource leveling programmes aremost appropriate to situationswhere we maintain a
relatively stable employment levels andutilize the resources at a more constant rate. If thelevels change eitherway
theexpenses are involved in hiring, training, firing, unemployment insuranceand so on. The activityslack is a
measure of flexibility in the assignment of activity start times. We mayuse activity slack as a means to smoothing
peakresource requirements. Theprocedure involves preparing an early-start early-finish schedule forthe project on
timescale and then plotting a resource-loading chart forthe schedule. The activitesare shifted suitably to reducethe
peakresource requirements withoutviolating the sequence andpreserving the finishdate.
ResourceAllocation: In many cases the schedulingproblem does not involveonly smoothing of requirementsbut
also allocation of resources. Almost thereare some constraints, which may be in the form of limitedmen, machines
or finance. The various activities have to work at theiroptimum taking into considerations theserestrictions.
Theresource-leveling model could be modified to give us the desiredresults. The constraint of the fixed
duedate would have to be removed and concentrate on pushing down the triggerlevels until peakrequirements are
allunder resource limits. If the limits are confining, the jobs will be pushed to the right, thereby delayingthe project
duedate on the schedule graph.The constraints cannot be based both on project duedate and resourcelimits.
Resourcesare allocated on a period-by-periodbasis to accommodate someavailable job, aftertheir
predecessorshave been completed. Theessential elements aredetermining which jobs are to be scheduled and
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Table of Contents:
  1. Introduction:OR APPROACH TO PROBLEM SOLVING, Observation
  2. Introduction:Model Solution, Implementation of Results
  3. Introduction:USES OF OPERATIONS RESEARCH, Marketing, Personnel
  4. PERT / CPM:CONCEPT OF NETWORK, RULES FOR CONSTRUCTION OF NETWORK
  5. PERT / CPM:DUMMY ACTIVITIES, TO FIND THE CRITICAL PATH
  6. PERT / CPM:ALGORITHM FOR CRITICAL PATH, Free Slack
  7. PERT / CPM:Expected length of a critical path, Expected time and Critical path
  8. PERT / CPM:Expected time and Critical path
  9. PERT / CPM:RESOURCE SCHEDULING IN NETWORK
  10. PERT / CPM:Exercises
  11. Inventory Control:INVENTORY COSTS, INVENTORY MODELS (E.O.Q. MODELS)
  12. Inventory Control:Purchasing model with shortages
  13. Inventory Control:Manufacturing model with no shortages
  14. Inventory Control:Manufacturing model with shortages
  15. Inventory Control:ORDER QUANTITY WITH PRICE-BREAK
  16. Inventory Control:SOME DEFINITIONS, Computation of Safety Stock
  17. Linear Programming:Formulation of the Linear Programming Problem
  18. Linear Programming:Formulation of the Linear Programming Problem, Decision Variables
  19. Linear Programming:Model Constraints, Ingredients Mixing
  20. Linear Programming:VITAMIN CONTRIBUTION, Decision Variables
  21. Linear Programming:LINEAR PROGRAMMING PROBLEM
  22. Linear Programming:LIMITATIONS OF LINEAR PROGRAMMING
  23. Linear Programming:SOLUTION TO LINEAR PROGRAMMING PROBLEMS
  24. Linear Programming:SIMPLEX METHOD, Simplex Procedure
  25. Linear Programming:PRESENTATION IN TABULAR FORM - (SIMPLEX TABLE)
  26. Linear Programming:ARTIFICIAL VARIABLE TECHNIQUE
  27. Linear Programming:The Two Phase Method, First Iteration
  28. Linear Programming:VARIANTS OF THE SIMPLEX METHOD
  29. Linear Programming:Tie for the Leaving Basic Variable (Degeneracy)
  30. Linear Programming:Multiple or Alternative optimal Solutions
  31. Transportation Problems:TRANSPORTATION MODEL, Distribution centers
  32. Transportation Problems:FINDING AN INITIAL BASIC FEASIBLE SOLUTION
  33. Transportation Problems:MOVING TOWARDS OPTIMALITY
  34. Transportation Problems:DEGENERACY, Destination
  35. Transportation Problems:REVIEW QUESTIONS
  36. Assignment Problems:MATHEMATICAL FORMULATION OF THE PROBLEM
  37. Assignment Problems:SOLUTION OF AN ASSIGNMENT PROBLEM
  38. Queuing Theory:DEFINITION OF TERMS IN QUEUEING MODEL
  39. Queuing Theory:SINGLE-CHANNEL INFINITE-POPULATION MODEL
  40. Replacement Models:REPLACEMENT OF ITEMS WITH GRADUAL DETERIORATION
  41. Replacement Models:ITEMS DETERIORATING WITH TIME VALUE OF MONEY
  42. Dynamic Programming:FEATURES CHARECTERIZING DYNAMIC PROGRAMMING PROBLEMS
  43. Dynamic Programming:Analysis of the Result, One Stage Problem
  44. Miscellaneous:SEQUENCING, PROCESSING n JOBS THROUGH TWO MACHINES
  45. Miscellaneous:METHODS OF INTEGER PROGRAMMING SOLUTION