Abstract: We consider a typical problem in the assembly of
printed circuit boards (PCBs) in a two-machine flow shop system to
simultaneously minimize the weighted sum of weighted tardiness and
weighted flow time. The investigated problem is a group scheduling
problem in which PCBs are assembled in groups and the interest is to
find the best sequence of groups as well as the boards within each
group to minimize the objective function value. The type of setup
operation between any two board groups is characterized as carryover
sequence-dependent setup time, which exactly matches with the real
application of this problem. As a technical constraint, all of the
boards must be kitted before the assembly operation starts (kitting
operation) and by kitting staff. The main idea developed in this paper
is to completely eliminate the role of kitting staff by assigning the
task of kitting to the machine operator during the time he is idle
which is referred to as integration of internal (machine) and external
(kitting) setup times. Performing the kitting operation, which is a
preparation process of the next set of boards while the other boards
are currently being assembled, results in the boards to continuously
enter the system or have dynamic arrival times. Consequently, a
dynamic PCB assembly system is introduced for the first time in the
assembly of PCBs, which also has characteristics similar to that of
just-in-time manufacturing. The problem investigated is
computationally very complex, meaning that finding the optimal
solutions especially when the problem size gets larger is impossible.
Thus, a heuristic based on Genetic Algorithm (GA) is employed. An
example problem on the application of the GA developed is
demonstrated and also numerical results of applying the GA on
solving several instances are provided.
Abstract: Nature conducts its action in a very private manner. To
reveal these actions classical science has done a great effort. But
classical science can experiment only with the things that can be seen
with eyes. Beyond the scope of classical science quantum science
works very well. It is based on some postulates like qubit,
superposition of two states, entanglement, measurement and
evolution of states that are briefly described in the present paper.
One of the applications of quantum computing i.e.
implementation of a novel quantum evolutionary algorithm(QEA) to
automate the time tabling problem of Dayalbagh Educational Institute
(Deemed University) is also presented in this paper. Making a good
timetable is a scheduling problem. It is NP-hard, multi-constrained,
complex and a combinatorial optimization problem. The solution of
this problem cannot be obtained in polynomial time. The QEA uses
genetic operators on the Q-bit as well as updating operator of
quantum gate which is introduced as a variation operator to converge
toward better solutions.