Shipping problems with body clock constraints

Time window has been a common form of time constraint considered in the literature. Basically, a time window is a time period, defined by the earliest and latest times, when a node is available for traveling through. Although many variants of transportation problem in time-window networks have been proposed, no one consider the possibility that time windows may be associated with the moving travelers or vehicles so that they can travel only in these time periods. In this paper, this new variant of time-window constraint, called body clock constraint, is proposed. We assume that each vehicle has its own body clock and a capacity limitation for carrying goods, and we are requested to determine a minimal time schedule for sending a certain amount of goods from source to destination in a time-window network. Specifically, the problem is studied in two cases, where the first case considers single-vehicle scheduling and the second multiple vehicles. For both of them, algorithms are presented to find the optimum schedule. Time window has been a common form of time constraint considered in the literature. Basically, a time window is a time period, defined by the earliest and latest times, when a node is available for traveling through. There are many practical situations, where time windows can be used to describe the time constraints associated with the nodes and arcs on a network. For example, a time window in a transportation network may be the time period that a service or transition facility is available for the traveler to pass through. Similarly, a time window associated with an arc may be the time that a transportation channel is open. In vehicle routing problems and traveling salesman problem, a time window may represent the time period that a customer needs to be visited. Although there are many researches on the transportation problem in time-window networks, no previous researches consider the situation that time windows may be associated with the travelers or vehicles. In this paper we consider this new variant of time-window constraints, called body clock constraint. The body clock comes from the daily activities of people habits and the operation cycles of equipments. For example, a driver must temporarily stop his/her journey to have a meal or to rest at night. Likewise, a machine may need to be cooled to prevent from damage and to be maintained periodically. In this paper, we use the body clock constraint to model this kind of periodicity, and som