757 5 PRUEBA DE INSPECCIÓN ADMINISTRATIVA 758 5.1 OPERADORA Y LARROC

Based on the approach of solving FJSP, we add PM in the program. We use two different approaches to solve FJSP with PM. One is Simultaneous Scheduling Algorithm (SSA), the approach ofGao et al.(2006), where jobs and PM tasks are scheduled simultaneously. The second is our new proposed Inserting Algorithm (IA), to insert PM after all jobs have been scheduled. Both are based on the same initialization of starting time of PM which is set at the latest moment of time window. Flowchart of the two algorithms is shown in Figure 3.9.

Figure 3.9: Two algorithms of solving FJSPPM

Simultaneous Scheduling Algorithm (SSA)

Although SSA is already used byGao et al. (2006), we would like to examine the effectiveness of their algorithm. We propose another two methods to compare with their algorithm.

Firstly, all PM tasks are initialized to start at the latest moment in time windows. Then begin to schedule jobs. When one operation of a job meets a PM, i.e., a collision occurs, compact the PM task to the left side as possible, and then range the operation after PM. The procedure of compacting PM for treating collision of PM and job is illustrated in Figure 3.10.

Figure 3.10: Compact PM to left when PM is initialized to latest moment (2) Initializing starting time of PM at the latest moment in time windows and compact PM to right side.

Based on the algorithm in literature, firstly we initialize PM tasks, but at the earliest moment of their time window. When an operation meets a task of PM, delay PM to right side and just after the operation. The activity of delay is surely constrained in time window of PM. Illustration of this method of treating collision of PM and job is shown in Figure 3.11.

Figure 3.11: Compact PM to right when PM is initialized to earliest moment (3) Change machines for jobs when there are collisions with PM tasks. Firstly initialize PM tasks, either at the latest or earliest moment in time win- dow. In our example, we take the latest moment of time window. The difference to the two algorithms above is the policy of treating collision of PM tasks and

3.1 Reducing unavailability of machines in FJSP

jobs. Unlike the two methods above, in which operations still use the machine, another policy of treating the collision of PM and job is to change machine of processing the job. That is to say, PM remains where it is initialized, but job choose another machine. Take the example in Figure 3.12. Operation Oij ar- ranged on machine g meets a task of PM. We need not to move PM, but to find another machine available, e.g. machine g′ _{for O}

ij.

Figure 3.12: Change machine to treat collision of PM and job

For choosing a new machine for a job having collision with PM task, we can use different rules:

(a) Randomly choose a machine available;

(b) Choose the machine with the least processing time for the operation; (c) Choose the machine with the earliest available moment. Machines’ avail- able moments are the ending time of last operation at current moment;

(d) Take the machine with a least sum of processing time and idle time for the operation. Idle time occurs when the job’s available moment is later than available moment of machine.

The methods corresponding to the four rules are summarized as to choose random machine, choose machine with minimum processing time, choose machine with earliest available time, choose machine with least idle time, respectively. In these 4 methods, we initialize the starting time of PM at the latest moment of time window. The test of comparison of these 6 methods of SSA is executed on

example J8M8, the same as testing example J8M8 in preceding section. IGA is used, with the same parameters in preceding testing examples. Data of PM refer to literature. We execute the programme of each method 10 times. Mean value and best value of makespan are compared as well. Parameters are the same as in preceding test of GA. The results are shown in Table 3.12, from which we can see that initializing staring time of PM at the end of time windows is a good choice. Moreover, we have tried to use IACO to find an optimal initialized starting time of PM, the results are not good as the one used, neither. The performance of methods of (b) and (d) with changing machines is better than methods of moving PM used in literature. Therefore, in following tests, starting time of PM initialized at the latest moment of time window, meanwhile we adopt the three good performing methods as three different kinds of SSA: traditional method in literature without changing machines; choose new machine with minimum processing time; choose new machine with minimum sum of processing time and idle time.

Table 3.12: Comparison of different methods of SSA

best value mean value machines do not change

PM initialized starting at tE _{19 19.3}

PM initialized starting at tL _{17 17.2}

choose a new machine

(a) random machine 20 20.6

(b) machine with minimum processing time 17 17

(c) machine with earliest available time 18 18.5

(d) machine with minimum idle time 17 17

Inserting Algorithm (IA)

In IA, PM tasks are inserted into idle intervals of jobs after all of them have been scheduled. We aim to make full use of the idle intervals, which always exist and are unavoidable in scheduling. IA is described as follows:

(1) Find effective idle time intervals from left to right on the scheduling se- quence of each machine, in the range of time windows of PM task.

3.1 Reducing unavailability of machines in FJSP

(2) If the maximal effective idle time interval cannot satisfy the duration time of the PM task, perform PM task at the beginning of the maximal idle time interval, and then delay all its posterior sequence of operations.

(3) For the preschedule where there is no useful idle time for inserting PM tasks, insert it at the moment close to the latest moment of time window and then push the following tasks.

Complete approach for FJSPPM

The two algorithms above must be combined with the approach for FJSP to solve FJSP with PM. We propose to use the following combination: Integrated GA with SSA; Integrated GA with IA; Integrated ACO with SSA. As we men- tioned in section above, three different kinds of SSA can be used in it. Strictly, there are seven different approaches in total. We compare and differentiate the 7 approaches in the section of experiments.

(1) IGA with SSA:

(1a) IGA with SSA1, without changing machine;

(1b) IGA with SSA2, choosing new machine with minimum processing time; (1c) IGA with SSA3, choosing new machine with minimum sum of processing and idle time.

(2) IGA with IA; (3) IACO with SSA:

(3a) IACO with SSA1, without changing machine;

(3b) IACO with SSA2, choosing new machine with minimum processing time; (3c) IACO with SSA3, choosing new machine with minimum sum of processing and idle time.