13.3.5 Sequencing Models
Sequencing denotes the determination of an optimal sequence (order), for
performing a set of tasks in order to minimize the overall processing time
(or cost). Only simple problems of this kind have been solved analytically. For
others, simulation and heuristic methods have been used.
For sequencing problems involving given or imposed precedence relationships,
e.g. certain activities need to be completed before others can start, special techniques
have been developed. The two most powerful techniques are PERT (Programme
Evaluation and Review Technique) and CPM (Critical Path Method) which are used
for planning, scheduling and controlling complex projects concerning a high number
of activities. The fundamental principle in PERT, as well as CPM, is to construct
(draw) a network, where the activities and the events are represented in some logical
and sequential order. Completion time for each activity, start and finish times of each
event and the critical path (path taking longest time to complete the project) are
determined. (The critical path, in fact, indicates the minimum time required for
project completion). Construction of the network further helps in guiding the transfer
of resources from slack (non-critical) zones to critical areas so as to meet scheduling
requirements.
Although independently developed, the PERT and CPM techniques use similar
network principles. The basic departure of CPM from PERT is that it brings home
prominently the concept of cost. When times (activity durations) can be well
estimated and when costs can be calculated quite accurately in advance
(e.g. labour and materials cost), CPM is superior to PERT. However, if there is a
high degree of uncertainty and, control over time outweighs control over cost (as in
launching of a spacecraft), PERT may well be a better choice.
13.3.6 Routing Models
Problems which are related to sequencing occur as routing problems in networks.
There are two significant routing problems:
(a) The travelling salesman problem
(b) Minimal path problem
Starting from his home city, the travelling salesman needs to visit a number of
cities, which he would like to visit only once, before returning home. The distance
(or time or cost) between every pair of cities is known. The problem is to find the
shortest route in distance (or time or cost).
In the minimal path method, there are many routes available between one city
(origin) and the other (destination) and the problem is to find the shortest route.
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13 Modelling in Infrastructure Planning
Sequencing denotes the determination of an optimal sequence (order), for
performing a set of tasks in order to minimize the overall processing time
(or cost). Only simple problems of this kind have been solved analytically. For
others, simulation and heuristic methods have been used.
For sequencing problems involving given or imposed precedence relationships,
e.g. certain activities need to be completed before others can start, special techniques
have been developed. The two most powerful techniques are PERT (Programme
Evaluation and Review Technique) and CPM (Critical Path Method) which are used
for planning, scheduling and controlling complex projects concerning a high number
of activities. The fundamental principle in PERT, as well as CPM, is to construct
(draw) a network, where the activities and the events are represented in some logical
and sequential order. Completion time for each activity, start and finish times of each
event and the critical path (path taking longest time to complete the project) are
determined. (The critical path, in fact, indicates the minimum time required for
project completion). Construction of the network further helps in guiding the transfer
of resources from slack (non-critical) zones to critical areas so as to meet scheduling
requirements.
Although independently developed, the PERT and CPM techniques use similar
network principles. The basic departure of CPM from PERT is that it brings home
prominently the concept of cost. When times (activity durations) can be well
estimated and when costs can be calculated quite accurately in advance
(e.g. labour and materials cost), CPM is superior to PERT. However, if there is a
high degree of uncertainty and, control over time outweighs control over cost (as in
launching of a spacecraft), PERT may well be a better choice.
13.3.6 Routing Models
Problems which are related to sequencing occur as routing problems in networks.
There are two significant routing problems:
(a) The travelling salesman problem
(b) Minimal path problem
Starting from his home city, the travelling salesman needs to visit a number of
cities, which he would like to visit only once, before returning home. The distance
(or time or cost) between every pair of cities is known. The problem is to find the
shortest route in distance (or time or cost).
In the minimal path method, there are many routes available between one city
(origin) and the other (destination) and the problem is to find the shortest route.
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13 Modelling in Infrastructure Planning