Fast strategies in biased Maker--Breaker games

We study the biased $(1:b)$ Maker--Breaker positional games, played on the edge set of the complete graph on $n$ vertices, $K_n$. Given Breaker's bias $b$, possibly depending on $n$, we determine the bounds for the minimal number of moves, depending on $b$, in which Maker can win in each of the two standard graph games, the Perfect Matching game and the Hamilton Cycle game

Fast winning strategies in Avoider-Enforcer games

In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for Maker-Breaker games; here we initiate their study for unbiased Avoider-Enforcer games played on the edge set of the complete graph $K_n$ on $n$ vertices. For several games that are known to be an Enforcer's win, we estimate quite precisely the minimum number of moves Enforcer has to play in order to win. We consider the non-planarity game, the connectivity game and the non-bipartite game

The Influence of Yard Trucks on Berth Operations in Smaller Container Terminals

Nowadays smaller container terminals are facing an increase in traffic and ship sizes and are consequently subject to extreme pressure form ship-owners that require rapid and efficient transhipment operations in the port, the achievement of which is only possible with the assignment of the proper type and number of quay cranes to each ship and with a good level of synergy between the cranes and the transfer mechanisation. The latter has a significant impact on the cranes working and waiting times and affects the entirety of berth operations. Existing terminals that cannot afford to invest in new modern horizontal transport technologies are most commonly using yard trucks that provide less efficient port transfer operations. That is why in the paper a simulation approach has been used in order to determine how a different number of yard trucks assigned to a single quay crane can affect the productivity of that crane and the productivity of the whole berth subsystem