Cross-docking is a strategy that distributes products directly from a supplier or manufacturing plant to a customer or retail chain, reducing handling or storage time. This study focuses on the truck scheduling problem, which consists of assigning each truck to a door at the dock and determining the sequences for the trucks at each door considering the time-window aspect. The study presents a mathematical model for door assignment and truck scheduling with time windows at multi-door cross-docking centers. The objective of the model is to minimize the overall earliness and tardiness for outbound trucks. Simulated annealing (SA) and tabu search (TS) algorithms are proposed to solve large-sized problems. The results of the mathematical model and of meta-heuristic algorithms are compared by generating test problems for different sizes. A decision support system (DSS) is also designed for the truck scheduling problem for multi-door cross-docking centers. Computational results show that TS and SA algorithms are efficient in solving large-sized problems in a reasonable time.

This paper presents a new method of calculation of the change of axial twisting angle of compressed helical spring’s end-coils in the case of rotary - free supports. The propriety of derived formulas was experimentally verified. The method is easy in application and gives results much closer to experiment than the presently used method that can be found in literature.