Traditionally, the time-cost problem is addressed by CPM-based analytical approach that involves lot of computation work. The method assumes unlimited resources and the existence of a continuous time-cost function. However, given the discrete nature of most resources, activities can often be crashed only stepwise. Also in many cases the time-cost function is non-linear. This makes the problem still more complicated to be solved by analytical methods. In this paper, a simple method has been presented for solving time cost trade-off problem through deterministic simulation. In heuristic methods several decision variables/ parameters are stipulated for selecting the activities for crashing. However it has been established that weights (relative importance) to be assigned to these decision parameters cannot be universally determined for optimality. So by using random numbers different combinations of weights are assigned to these decision parameters and different solutions are generated by deterministic simulation.
[...] For the project considered in our example, different paths of the network and their corresponding total normal durations are shown in table 2. This representation permits network activity paths to be represented by two dimensional arrays of elements. The element Aji pertains to element ‘i' of path ‘j'. Aji = 1 if activity ‘i' exists in path ‘j' else Aji = 0 Similarly normal duration of activities is represented by one dimensional array of elements. NDi = Normal duration of activity ‘i' Table Different Paths of Project Network Network Path Number Network Path Activities Network Path Duration A1-A2-A5-A6-A9-A10 A1-A3-A5-A6-A9-A10 A1-A2-A5-A7-A9-A10 A1-A3-A5-A7-A9-A10 A1-A4-A7-A9-A10 A1-A4-A8-A The other attributes of project activities can also be represented by arrays. [...]
[...] Since minimizing time and cost are both preferred by the project manager, the project expediting process can be transferred to the typical time-cost trade-off analysis Time-cost trade-off means that we can shorten (i.e. crash) the duration of an activity by using additional resources/ cost 9]. Traditionally, the time-cost problem is addressed by CPM-based analytical approaches 4]. In these traditional approaches we assume existence of unlimited resources and a continuous time-cost function. The analytical method involves lot of computation work and is difficult to apply even to a medium sized project consisting of hundreds of activities Further, in many practical situations time-cost function is not continuous. [...]
[...] Time Cost Trade-off Algorithm In this paper, we present a simple method based on some decision rules and computer simulation to solve activity crashing problem. The activities are selected for execution in expedited (crashed) mode based on mainly two parameters, i.e. criticality of activity and cost effectiveness of crashing. Based on intuitive reasoning the index for criticality of activity is determined as under. Decide target duration ‘T' up to which the project is to be crashed. ii) Determine amount of crashing required for different paths of the project so that total duration of each path does not the exceed target duration of project. [...]
[...] This way, number of solutions is generated by using different values of ‘W'. The best among these solutions is picked up, which is most likely the optimal or close to the optimal solution Implementation of Method For illustration purpose, the method was applied to project network given in table 1 for crashing its duration from 35 time units to say desired target duration of 30 time units. The project has 10 activities and each activity can be done in two ways (modes). So the project can be done in 1024 (210) ways. [...]
[...] This may be determined based on two aspects; reduction in activity duration should be at minimum cost, and reduction in activity duration should contribute towards reduction of project duration. Let the index for cost effectiveness of crashing be denoted by ‘C2'. The value of this index may be determined as under. For an activity determine the amount of crashing that can be done by executing it in crashed mode. Let it be denoted by ‘CDAi'. This is determined from the difference between normal duration and crashed duration of activity. [...]
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