Sun et al. [19,39], Verma and Verter [40] and Wang and Han [41] formulate the due date constraint based on the hard time point formulation that requires that the instants of accomplishing transportation orders by intermodal transportation should not be later than the prescribed due dates. ...
In our proposed model, an effective service means all the given requests of a passenger with multiple trips are satisfied, with each request accessed at most once. 3.1. Notation Table 3 lists the notation used in this study. Table 3. Sets, indices, and parameters used for model formulation....
In the case of integer linear programming formulation [7], we have O(N2) variables and subtour elimination constraints. As a direct solution is unfeasible, the model is relaxed to find a solution. In the proposal [8] a novel representation form was introduced to reduce the number of subtour...
3. Model Formulation This section of the manuscript focuses on description of the nomenclature that will be used throughout this study and presents a mixed integer linear mathematical model for the discrete dynamic berth scheduling problem with spatial requirements (BSPSR). A detailed description of ...
3.3. Mathematical Formulation The objective function of the MINLP model is to minimize the total cost in the closed-loop system under study, and it is composed of five main components: 1. Location cost, i.e., the cost of opening and operating HDCCs; 2. Shipping cost from HDCCs to ...
Theoretical problem-solving processes are often depicted as a sequence of steps encom- passing formulation, evaluation, and the identification of alternatives, all aimed at shifting Mathematics 2023, 11, 4642. https://doi.org/10.3390/math11224642 https://www.mdpi.com/journal/mathematics Mathematics ...
For a detailed description and mathematical formulation of the proposed problem, interested readers are referred to similar papers [6,19]. 4. Solution Approach Considering the complexity of the proposed problem, we devise a heuristic approach based on the ALNS and IP to solve it. The ALNS was ...
In the following, we will give the specific formulation of the model M3 in Section 3.1, then describe the task assignment algorithm we use in Section 3.2, followed by Sections 3.3 and 3.4 to show the two heuristics we propose, respectively. 3.1. Shift Design Model M3 The model M3 is ...
Experimental research in materials processing depends crucially on the selection of a promising initial design region within the available process parameters. When processing a material, there are many potential design variables by which to optimize its properties and performance, including formulation, ...
Finite element models of the time-dependent problems with time-varying coefficient can be developed in coupled formulation, where the time t is treated as an additional coordinate along the spatial coordinate x, the scaling function Φ(ξ, t) is time-space interpolation functions, and the wavelet...