scholarly journals Case Article—Coastal Shipping for Automobile Distribution

2021 ◽  
Vol 22 (1) ◽  
pp. 28-34
Author(s):  
Saurabh Chandra ◽  
Amit Kumar Vatsa
Keyword(s):  
Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Sustainable Transportation ◽  
Mixed Integer ◽  
Theoretical Discussion ◽  
Solution Quality ◽  
Mode Shift ◽  
Coastal Shipping ◽  
Solution Methods

With growing concerns related to the environment, sustainable transportation has gained importance. For geographies with an ample coastline, coastal shipping offers a sustainable transportation option to move massive freight quantities. This paper presents a case that allows students to appreciate the role of coastal shipping in multimodal logistics planning. Furthermore, it gives students an opportunity to mathematically model transportation planning at a strategic and tactical level for automotive distribution. The students learn how to assess the financial viability of a mode shift from roadways to coastal shipping. The instructors can use this case for theoretical discussion on multimodal logistics and the application of mixed-integer linear programming (MILP) and heuristics as solution methods. Furthermore, the case presents an opportunity to demonstrate the improvement in solution quality with an MILP solver compared with heuristics.

scholarly journals Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints

2020 ◽  
Vol 61 (5) ◽  
pp. 1977-1999
Author(s):  
H. Fairclough ◽  
M. Gilbert
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Geometry Optimization ◽  
Layout Optimization ◽  
Mixed Integer ◽  
Optimal Solutions ◽  
Problem Size ◽  
Solution Quality ◽  
Starting Point

AbstractTraditional truss layout optimization employing the ground structure method will often generate layouts that are too complex to fabricate in practice. To address this, mixed integer linear programming can be used to enforce buildability constraints, leading to simplified truss forms. Limits on the number of joints in the structure and/or the minimum angle between connected members can be imposed, with the joints arising from crossover of pairs of members accounted for. However, in layout optimization, the number of constraints arising from ‘crossover joints’ increases rapidly with problem size, along with computational expense. To address this, crossover constraints are here dynamically generated and added at runtime only as required (so-called lazy constraints); speedups of more than 20 times are observed whilst ensuring that there is no loss of solution quality. Also, results from the layout optimization step are shown to provide a suitable starting point for a non-linear geometry optimization step, enabling results to be obtained that are in agreement with literature solutions. It is also shown that symmetric problems may not have symmetric optimal solutions, and that multiple distinct and equally optimal solutions may be found.

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