web – How does the design of algorithms work?

A consulting company can execute tasks requested to its clients either with
Personnel hired or with self-employed workers. The set of tasks is presented in a subset S of time
instants {1 ,. . . , T}. Yes homework jt
is assigned to a hired employee of the consulting firm, the
The cost is given by your daily salary s. Yes homework jt
subcontracted to an independent worker, the cost paid
it is ct and it depends on the specific task and the instantaneous moment. A worker can be hired at any time.
paying you a contracting cost C and firing it at any later time paying a cost of separation S.
Objective: Design an optimal strategy that is executed in polynomial time that minimizes the total
Cost of execution of tasks. The total cost must include the costs paid to independent workers.
and the costs paid for the hiring, dismissal and salaries of the personnel hired. Prove that the
The algorithm is correct and provides an analysis of its execution time. Implement the algorithm with
A programming language of your choice.
Suppose now that the task jt requires a set Wt ⊆ W, | W | = k, of a constant number k of
Different types of workers. Therefore, the company must decide what types of workers to hire
and what types of workers to subcontract. The wage cost for any moment of time is the same for
All types of workers, as well as hiring and the cost of dismissal. The cost of the worker j ∈ W varies
over time: the cost of the worker j ∈ W equals c
j
t
.
Objective: Design an optimal strategy that is executed in polynomial time that minimizes the total
Cost of execution of tasks.