Objective function. The optimization algorithm determines the optimal dispatch of the virtual storage that maximizes the revenue of the buyer, J, over the considered time horizon, T, while fulfilling the storage constraints. The revenues stem from day-ahead arbitrage, i.e. the possibility of buying and selling elec- tricity when it is most convenient: X T J = t = 1 pt(Vt — Ut)Dt (Equation 1) where Ut is the power used to charge the storage and Vt is the power discharged from the storage during the time step t, of duration Dt. The energy for charging and discharging the virtual storage is bought and sold, respectively, at the known day-ahead market price pt. Ut and Vt are decision variables of the optimi- zation problem for all time steps t ˛ {1;.; T }.
Objective function. (1) The variable is a binary variable that indicates if a vessel travels from node to customer carrying order in time t. The parameter is the cost pr tons dead weight carried from site to customer , multiplied with the parameter which is the order size of order product . The parameter is a distance matrix from node . The objective of (1) is to minimize the total shipment cost of transport of aggregates to the customers. In addition the objective function minimizes deadheading on the way to the next production site .
Objective function. The objective is maximizing the profit of the whole cluster with respect to all operations and investments in all plants. In other words, plants are interconnected and there is only one unified objective for all plants in the cluster. Objective function = Revenue from output – cost of input – investment cost- operation cost Maximize ∑∑∑(sp)ct Xi,'Market 'c,t - ∑∑∑( pp)ct X ' Market ',i,c,t c∈C t∈T i∈P - ( ∑(if )iYi + ∑(ic)i Li c∈C t∈T i∈P + ∑∑∑(icl)ijc Zijc ) i∈P i∈P i∈P j∈P c∈C - ( ∑∑(Yi + (ofc)i ) + ∑∑∑ ∑ i∈P t∈T i∈P j∈P t∈T c∈C (c=(co)i ) (oc)i ( Xijct +X jict ) )
Objective function. The objective function minimizes the total cost of production, transportation and holding cost at the customers and at the plant.
Objective function. In this model the goal is here to minimize the total number of workers used both from NOV and external contractors. To maximize each worker‟s utilization more jobs will be allocated to fewer people. min Zw is for minimizing the number of workers which NOV already is employing. By w W adding a penalty option for external contractors we minimize these by setting min as a parameter. This results in the following: Zw P w W
