Table 3 Operating costs of each scheduling model Type of schedule Optimal Deterministic Stochastic Fuzzy stochastic Day-ahead schedule costs 46078 47831 45870 45939 Adjustment costs 0 − 158 559 290 Total costs 46078 46078 46078 46078.
On the other hand, demand response is studied in the stochastic day-ahead scheduling of electricity and natural gas systems in [7], while hydro system is considered in the mid-term stochastic coordination to cover outages of gas units with insufficient gas supplies [8, 9].
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This paper reviews the various optimization techniques applied to DSM as contrasting characteristics like individual users versus cooperative users, deterministic versus stochastic and day-ahead versus real time DSM.
For stochastic FDCs, 7-day FDCs for 10, 20-, 50- and 100-year return periods were derived for extraction of discharge values at every 5% probability of exceedance.
The energy price is calculated in a single scenario which describes the most-likely value of stochastic variables in day-ahead, while the imbalance price is calculated in real-time operation with full consideration of stochastic variables in the scenario tree.
In addition, historical and present-day stochastic mechanisms have been proposed as well to explain the observed large geographic frequency variation, at least in some parts of a species' distribution range [ 66, 67].
This analysis suggests the use of stochastic gross profit per day or gross profit per day when compared to gross profit.
The above-mentioned analysis recommends the use of stochastic gross profit per day objective and the use of gross profit per day objective plus quantity-and-freight sensitivity analysis of unconfirmed cargoes in case probability distribution cannot be identified for cargo transport demand.
The previous analysis suggests also that stochastic gross profit per day is expected to be more profitable than stochastic gross profit.
The contribution made in this model is in the formulation of the objective function so that it represents a stochastic gross profit per day objective, in addition to the formulation of all possible shipping elements and charter party clauses.
