Mathematical Model. The supply vessel planning problem can be formulated mathematically as an arc flow model and has been already studied by Xxxxxxxxx-Xxxxx at al.(2009). min∑c jY j + ∑ ∑∑c jk X jkt subject to j∈V j∈V k∈Rj t∈T ∑∑ ∑aijk X jkt ≥ si , j∈V k∈R x x∈T ∀i ∈ N
Mathematical Model. The Contractor shall be responsible of providing a detailed transient model of the PV facility and to show that it is capable of complying with PREPA's transient Minimum Technical Requirements.
Mathematical Model. The objective of the model is to maximize the total profit of whole industrial cluster. Furthermore, it supports to perform further economic analysis. We should emphasize that the model below was only in Xpress code. Our first task was to convert the model into mathematical form, have better understanding of it and especially focusing on the integrated steel plant to see the shortcomings. In the beginning we will describe notations for used sets, common parameters and variables for the cluster. Then we will introduce the common objective function followed by the constraints grouped according to each plant.
Mathematical Model. While building the model, we have been inspired by the research done previously in this area as mentioned in literature review chapter. Furthermore our model contain some of the generalized forms of constraints from the code provided by SINTEF research team since it was required to be compatible with the initially provided model. Since it is definite that steel plant will be established and it is assumed that it will at least satisfy the demand for Norway, we have changed the model structure a bit. This means that sale of the steel plant is fixed to demand value so that there is no such objective for the plant as increasing the sales. We will absolutely sell as much as the demand. Therefore it was also important to perform reliable forecasted value for demand. The planning horizon is divided into several periods since there is also a life after our first decision. The number of periods can be changed as per planner’s wish our aim is to build multi-period model. Inventory balance is added to the model, because the planning horizon consists of several periods. At the beginning of the planning horizon the inventory is assumed as 0. There has to be a final inventory at the end of the planning horizon because it will be quite unrealistic to assume that the production and sales will stop right after the end of the planning horizon and the plant will not sell anything. We have determined the final inventory level as a fraction of the final demand. Moreover the model considers Carbon and Silicon reduction to the required level as well. All in all, the model aims to minimize the total cost of required raw materials, commodities, production and inventory holding cost while satisfying the demand. It gives the optimal amount of raw materials and commodities to be purchased as well as the optimal inventory levels at each period. Furthermore, flexible generation of compositions can be performed within the model in order to satisfy the concern of steel type variety. We will first give the notations of sets, parameters, variables and then will explain the objective function followed by all constraint explanations.
Mathematical Model. Formulation: AMPL names:
(1) min (Zw Zw P) NumberOfWorkers st (2) j J |S j t Fj 1, w W , t 1,...,Tmax MaxJobsAtATime
Mathematical Model. Aiming to offer an incentive structure for agricultural contracts between small scale soybean farmers and the biodiesel industry under the PNPB framework, a mathematical model was developed using a nonlinear programming technique. The objective function could be defined in several ways; maximizing the revenue of the firm, maximizing revenue of the xxxxxx with fixed productivity or maximizing the xxxxxx revenue with varied productivity. Following the proposal of Xxxxxxx (1998) concerning the relationship between incentives and performance, it was chosen to maximize the xxxxxx revenue with varied productivity. Thus, to run the model, the following input data were considered: Total revenue (TR) per hectare of the small scale soybean xxxxxx, considering the price of the soybean within a range of productivity (soybean per hectare). = � ( ) =1
