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scheduling problem can be classified as a variant of a so-called hybrid flow shop (HFS) scheduling problem, if we identify each mining operation from the production cycle as a stage,
see Schulze et al. (2016). Note that we assume the mining operations as non-preemptable,
because an assigned machine stays at the corresponding working place after an interruption
(due to workers’ breaks or end of a shift) and processing will be resumed at the next possible
occasion. In comparison to the classical HFS scheduling problem, due to the short planning
horizon of one single working shift, it is not possible to perform all mining operations at all
working places. Thus, on the one hand, it has to be decided whether a job at a working place
will be processed within the shift under consideration or not, and on the other hand, some
possible interruption of the processing of a job at the end of the working shift must be taken
into account.
The machines in the problem at hand are mobile and travel from job to job, therefore, no
buffers are needed between the stages. Instead, we have to consider driving times between
jobs that are processed by the same machine what results in sequence-dependent setup times.
In addition, there are so-called technical services that have to be performed for the machines.
Before processing the first operation assigned to a machine, a preventive maintenance (first
technical services) must be done. After processing the last job assigned to a machine as well
as before the end of the working shift if a job has to be interrupted, each machine must be
cleaned and fueled (last technical services). Furthermore, for the case in which a worker
changes his machine, he has to perform the first technical services for the new machine.
The second problem type, an employee timetabling problem, comprises the assignment of
suitable workers to machines within a working shift. We assume that a worker can handle at
most one machine at the same time and a machine can be operated by at most one worker
at the same time. Since the workers have particular skills on different levels, not all workers
can handle all machines. The different skill levels result in different handling times for each
machine. Furthermore, the machines on each stage can have different speeds, which means
that the processing time of a job depends on both the assigned worker and machine.
In order to generate a schedule that is accepted from the shift supervisor and that meets
legal obligations, we furthermore have to satisfy the following mining-specific requirements.
R1: Due to legal regulations, a Δ-minute break for the workers has to be incorporated in the
schedule within a predetermined time window. It has to be noted that the break can lead
to a delay in the processing of a job.
R2: We have to consider disjunctive constraints for subsets of jobs that are physically close
to each other (these jobs “belong” to so-called underground locations). Due to security
reasons, it is not allowed that more than one machine is processing there at the same
time, i.e., only one job in an underground location can be processed at any point in time.
R3: Although a consistent progress at all working places of the underground locations would
be desirable, different excavation states appear, i.e., not the same operation can be performed there. In order to achieve a harmonized state, we prioritize the jobs in an underground location in a way that the progress strives for consistency.
R4: Jobs that are interrupted at the end of the pre-shift have a higher priority than the other
jobs within the same underground location.
R5: The operations that symbolize the step drilling large diameter bore holes are non-interruptible. If those operations cannot be finished until the end of the corresponding working shift, they must not be started.
R6: The number of assigned worker to a machine is limited by two. That means no more than
two workers can be assigned to a machine and a worker is not allowed to work on more
than two machines during a working shift.
In the literature, most works concerning machine scheduling neglect the assignment of
workers, while in the field of employee timetabling (i.e., staff scheduling and personnel
assignment) the machine scheduling problem is rarely considered. Therefore, we confined our
literature review to the integrated employee timetabling and machine scheduling problems.
An overview of the studied literature is given in Table 1, where the abbreviations in column
production environment characterize, whether the authors analyzed a flow shop (FSP), job
scheduling problem can be classified as a variant of a so-called hybrid flow shop (HFS) scheduling problem, if we identify each mining operation from the production cycle as a stage,
see Schulze et al. (2016). Note that we assume the mining operations as non-preemptable,
because an assigned machine stays at the corresponding working place after an interruption
(due to workers’ breaks or end of a shift) and processing will be resumed at the next possible
occasion. In comparison to the classical HFS scheduling problem, due to the short planning
horizon of one single working shift, it is not possible to perform all mining operations at all
working places. Thus, on the one hand, it has to be decided whether a job at a working place
will be processed within the shift under consideration or not, and on the other hand, some
possible interruption of the processing of a job at the end of the working shift must be taken
into account.
The machines in the problem at hand are mobile and travel from job to job, therefore, no
buffers are needed between the stages. Instead, we have to consider driving times between
jobs that are processed by the same machine what results in sequence-dependent setup times.
In addition, there are so-called technical services that have to be performed for the machines.
Before processing the first operation assigned to a machine, a preventive maintenance (first
technical services) must be done. After processing the last job assigned to a machine as well
as before the end of the working shift if a job has to be interrupted, each machine must be
cleaned and fueled (last technical services). Furthermore, for the case in which a worker
changes his machine, he has to perform the first technical services for the new machine.
The second problem type, an employee timetabling problem, comprises the assignment of
suitable workers to machines within a working shift. We assume that a worker can handle at
most one machine at the same time and a machine can be operated by at most one worker
at the same time. Since the workers have particular skills on different levels, not all workers
can handle all machines. The different skill levels result in different handling times for each
machine. Furthermore, the machines on each stage can have different speeds, which means
that the processing time of a job depends on both the assigned worker and machine.
In order to generate a schedule that is accepted from the shift supervisor and that meets
legal obligations, we furthermore have to satisfy the following mining-specific requirements.
R1: Due to legal regulations, a Δ-minute break for the workers has to be incorporated in the
schedule within a predetermined time window. It has to be noted that the break can lead
to a delay in the processing of a job.
R2: We have to consider disjunctive constraints for subsets of jobs that are physically close
to each other (these jobs “belong” to so-called underground locations). Due to security
reasons, it is not allowed that more than one machine is processing there at the same
time, i.e., only one job in an underground location can be processed at any point in time.
R3: Although a consistent progress at all working places of the underground locations would
be desirable, different excavation states appear, i.e., not the same operation can be performed there. In order to achieve a harmonized state, we prioritize the jobs in an underground location in a way that the progress strives for consistency.
R4: Jobs that are interrupted at the end of the pre-shift have a higher priority than the other
jobs within the same underground location.
R5: The operations that symbolize the step drilling large diameter bore holes are non-interruptible. If those operations cannot be finished until the end of the corresponding working shift, they must not be started.
R6: The number of assigned worker to a machine is limited by two. That means no more than
two workers can be assigned to a machine and a worker is not allowed to work on more
than two machines during a working shift.
In the literature, most works concerning machine scheduling neglect the assignment of
workers, while in the field of employee timetabling (i.e., staff scheduling and personnel
assignment) the machine scheduling problem is rarely considered. Therefore, we confined our
literature review to the integrated employee timetabling and machine scheduling problems.
An overview of the studied literature is given in Table 1, where the abbreviations in column
production environment characterize, whether the authors analyzed a flow shop (FSP), job