Compared to the empty column, the optimal foam-filled column may have better crashworthiness under pure axial loading, but the optimal empty column has more room to enhance the crashworthiness under oblique impact.
Comparing with the empty steel structure, the optimal EA capacity is promoted by 35.32% in criterion 1 and 34.35% in criterion 2, being able to bear the condition with crashing speed of 36 km/h and impacting mass of 55.3 t.
An optimal label of a parent in case of the empty intersection of the optimal intervals of its children lies between these intervals.
Lemma A.4 (parent optimal interval—(II)) An optimal label of a parent in case of the empty intersection of the optimal intervals of its children lies between these intervals.
Note that if in problem (1 - 3), (U t)), (tin T), are bounded, closed, and non-empty sets, then the optimal control (u (t ) ) exists for any initial state (x^) [13, p.31].
As expected, we observe that the difference between the expected time to empty the queues under the optimal policy and under the TDMA scheme increases as the initial queue sizes increase.
This paper has presented the optimal design for empty and foam-filled tailor welded tubes (TWTs).
We identify that the optimal sampling location is after emptying the blender, guaranteeing complete characterisation of the residual heterogeneity.
We investigate how the optimal policy changes with the initial inventories of empty containers at the dry port and seaport.
By creating a tight LP-relaxation, the optimal solution to the model that includes both empty and loaded trips is quickly found using general purpose optimization software.
