Multi-horizon time structures

TwoLevel

The main motivation for the TimeStruct package is to support multi-horizon optimization models. The time structure TwoLevel allows for a two level approach, combining an ordered sequence of strategic periods with given duration and an associated operational time structure.

julia> using TimeStruct
julia> periods = TwoLevel(
           [SimpleTimes(5,1), SimpleTimes(5,1), SimpleTimes(5,1)],
       );

The following example shows a typical usage of a TwoLevel strucure with investment decisions on a strategic level and operational decision variables. It is possible to iterate through each strategic period using the strat_periodsfunction.

julia> using JuMP
julia> m = Model();
julia> @variable(m, invest[strat_periods(periods)] >= 0);
julia> @variable(m, prod[periods] >= 0);
julia> for sp in strat_periods(periods)
           @constraint(m, sum(prod[t] for t in sp) <= invest[sp])
       end

It is also possible to combine a TwoLevel time structure with more complex operational structures like RepresentativePeriods and OperationalScenarios, alone or in combination, as shown in the following example and illustrated the figure below.

julia> oper = SimpleTimes(5,1);
julia> scen = OperationalScenarios([oper, oper, oper], [0.4, 0.5, 0.1]);
julia> repr = RepresentativePeriods(2, 5, [0.5, 0.5], [oper, oper]);
julia> repr_scen = RepresentativePeriods(2, 5, [0.5, 0.5], [scen, scen]);
julia> periods = TwoLevel([scen, repr, repr_scen]);

In the above examples, the duration of the operational time structures have been equal to the duration of the strategic periods, but this is not required. If the duration of the operational time structure is shorter than the strategic period, this will be accounted for with the multiple function.

It is also sometimes convenient to use a different time unit for the strategic periods than the operational time periods. This is controlled by the op_per_strat field of the TwoLevel structure that holds the number of operational periods per strategic period.

A typical use case is an investment problem where one uses years to measure duration at the strategic level and hours/days on the operational level. Below is an example with 3 strategic periods of duration 5, 5, and 10 years respectively, while the operational time structure is given by representative periods with duration in days. The op_per_strat is then set to 365.

julia> week = SimpleTimes(7,1);
julia> repr = RepresentativePeriods(2, 365, [0.6, 0.4], [week, week]);
julia> periods = TwoLevel(3, [5, 5, 10], [repr, repr, repr], 365.0);

TwoLevelTree