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attributable to the time value of money. Hence, the solver, wanting to maximize operational
value, will schedule as much production early in the year as possible, instead of distributing it more evenly throughout the year. We refer to this as “front-loading”. Operationally,
this “front-loading” is neither feasible, nor desirable. By modifying the MPKC to represent
monthly production targets, we see that frontloading is virtually eliminated and the production profile is significantly more consistent. Frontloading may still be occurring within the
month which may require using MPKC with shorter time horizons; however, considering the
long-term nature of the schedule, this is acceptable accuracy.
2.1.2 Enforcing start and completion dates
The desired outcome of an optimized underground production schedule is a collection of
activity start dates that maximize value while adhering to precedence and resource constraints.
Precedence among activities are used to control activity sequencing and often are associated
with operational or geotechnical limitations. For the most part, it is enough to formulate
the model with these precedence and resource constraint components to capture the essence
of the operation. There may be instances when activity start and completion requirements
are needed to satisfy a mine’s strategic goals. For example, a new shaft and other associated
capital development may need to be completed before the mine’s planned expansion can proceed. Disregarding such deadlines creates a less accurate model and may result in improper
resource allocation, i.e., equipment, and unrealistic production profiles.
To provide a fixed start date for an activity, we add a “dummy” activity, i.e., an artificial
activity that consumes no resources, to create a time delay between the start of the schedule
time horizon and the set start date activity. When using the OMP Solver, the activity start
date can be fixed by pre-defining the decision variable for a given time period as shown in the
model (1f) making this process simple and efficient.
To set a completion deadline for an activity, we use MPKC to provide some flexibility as
to when the activity can start, while ensuring that the activity is completed by the desired
deadline. In many cases, the activity is not necessarily required to be completed on a given
date, but that it be completed prior to the deadline. To accomplish this, the activity is evaluated as a unique resource. That resource is constrained by a MPKC where the associated
time horizon ends at the required completion date. The use of MPKC allows the schedule
flexibility to ensure that the activity is completed while also considering the global scheduling problem.
3 CONCLUSIONS
Improved computation power and solution algorithms have allowed practitioners to formulate and solve increasingly complex models for underground production scheduling. These
advances present another opportunity for each practitioner: enhancing model representation to more closely reflect reality. In this paper, we outlined useful tools and guidelines that
an underground mine scheduler can use to create more operationally representative schedules. MPKC can overcome the limitations of using averages for constraints and induce some
operational flexibility into the schedule, while still retaining integrality and take advantage of
the new solution algorithms. In addition, known activity start and completion information
should also be incorporated into the model to more closely adhere to the strategic mine plan.
Overall, MPKC help improve model and schedule quality, lessening the gap between theory
and implementation.
REFERENCES
Alford, C., M. Brazil, and D. H. Lee (2007). Optimisation in underground mining. In Handbook of
operations research in natural resources, pp. 561–577. Springer.
attributable to the time value of money. Hence, the solver, wanting to maximize operational
value, will schedule as much production early in the year as possible, instead of distributing it more evenly throughout the year. We refer to this as “front-loading”. Operationally,
this “front-loading” is neither feasible, nor desirable. By modifying the MPKC to represent
monthly production targets, we see that frontloading is virtually eliminated and the production profile is significantly more consistent. Frontloading may still be occurring within the
month which may require using MPKC with shorter time horizons; however, considering the
long-term nature of the schedule, this is acceptable accuracy.
2.1.2 Enforcing start and completion dates
The desired outcome of an optimized underground production schedule is a collection of
activity start dates that maximize value while adhering to precedence and resource constraints.
Precedence among activities are used to control activity sequencing and often are associated
with operational or geotechnical limitations. For the most part, it is enough to formulate
the model with these precedence and resource constraint components to capture the essence
of the operation. There may be instances when activity start and completion requirements
are needed to satisfy a mine’s strategic goals. For example, a new shaft and other associated
capital development may need to be completed before the mine’s planned expansion can proceed. Disregarding such deadlines creates a less accurate model and may result in improper
resource allocation, i.e., equipment, and unrealistic production profiles.
To provide a fixed start date for an activity, we add a “dummy” activity, i.e., an artificial
activity that consumes no resources, to create a time delay between the start of the schedule
time horizon and the set start date activity. When using the OMP Solver, the activity start
date can be fixed by pre-defining the decision variable for a given time period as shown in the
model (1f) making this process simple and efficient.
To set a completion deadline for an activity, we use MPKC to provide some flexibility as
to when the activity can start, while ensuring that the activity is completed by the desired
deadline. In many cases, the activity is not necessarily required to be completed on a given
date, but that it be completed prior to the deadline. To accomplish this, the activity is evaluated as a unique resource. That resource is constrained by a MPKC where the associated
time horizon ends at the required completion date. The use of MPKC allows the schedule
flexibility to ensure that the activity is completed while also considering the global scheduling problem.
3 CONCLUSIONS
Improved computation power and solution algorithms have allowed practitioners to formulate and solve increasingly complex models for underground production scheduling. These
advances present another opportunity for each practitioner: enhancing model representation to more closely reflect reality. In this paper, we outlined useful tools and guidelines that
an underground mine scheduler can use to create more operationally representative schedules. MPKC can overcome the limitations of using averages for constraints and induce some
operational flexibility into the schedule, while still retaining integrality and take advantage of
the new solution algorithms. In addition, known activity start and completion information
should also be incorporated into the model to more closely adhere to the strategic mine plan.
Overall, MPKC help improve model and schedule quality, lessening the gap between theory
and implementation.
REFERENCES
Alford, C., M. Brazil, and D. H. Lee (2007). Optimisation in underground mining. In Handbook of
operations research in natural resources, pp. 561–577. Springer.