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数学代写|运筹学代写Operations Research代考|MATH3202 PROJECT SCHEDULING

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数学代写|运筹学代写Operations Research代考|PROJECT SCHEDULING

The critical path method provides the critical path and its length $(L)$. The length of the critical path is the sum of the activity times of the critical activities. In order to complete the project within $L$, the critical activities have to be scheduled sequentially so that they are completed within $L$ units. The non-critical activities can be scheduled in parallel and the floats associated with these activities provide us the time slabs within which the non-critical activities can be completed. The project schedule is a time-table for carrying out the activities.

We require resources to carry out the various activities and in practice we use multiple resources. When we analyzed the project using CPM, we assumed that required amount of the resources are available at any point in time. In practice, we could encounter limited resources or have to estimate the amount of resource actually required to execute the project. We consider one resource and explain the ideas using Illustration 14.10.

ILLUSTRATION $14.10$
Consider the project involving six activities shown in Table 14.11. The precedence and estimates of the activity times (in days) are shown in the table. Draw a schedule and find out the amount of resource required at different points in time.

数学代写|运筹学代写Operations Research代考|MANAGING WITH LIMITED RESOURCES

Illustration $14.11$ explained a way to compute the minimum amount of the resource required (say, $R$ ) to schedule and complete the project within $L$ units. The approach explained through this illustration is heuristic and is not expected to guarantee the optimum always. Better methods are available to find the minimum amount of resource available.

It is also possible that we have fewer than $R$ amount of the resource. This means that some activities have to delayed to get the resources which would delay the project completion beyond $L$. The next issue is to find out the completion time of the project considering limited resources. We present a heuristic solution using the following rule:

From the list of activities that are available, schedule the activity that takes minimum time for the required amount of resource is available. This is an adaptation of the familiar shortest processing time (SPT) rule.

We explain the resource constrained project scheduling (RCPS) using Illustration 14.11.

数学代写|运筹学代写Operations Research代考|ONSIDERING BACKORDERING

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$$T C=\frac{D C_o}{Q}+\frac{(Q-s)^2 C_c}{2 Q}+\frac{s^2 C_s}{2 Q}$$

$$s=\frac{Q C_c}{\left(C_c+C_s\right)}$$

$$Q^*=\sqrt{\frac{2 D C_o\left(C_c+C_s\right)}{C_c C_s}}$$

MATLAB代写

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