Abstract Multimodal processes planning and scheduling play a pivotal role in many different domains including city networks, multimodal transportation systems, computer and telecommunication networks and so on. Multimodal process can be seen as a process partially processed by locally executed cyclic processes. In that context the concept of a Mesh-like Multimodal Transportation Network (MMTN) in which several isomorphic subnetworks interact each other via distinguished subsets of common shared intermodal transport interchange facilities (such as a railway station, bus station or bus/tram stop) as to provide a variety of demand-responsive passenger transportation services is examined. Consider a mesh-like layout of a passengers transport network equipped with different lines including buses, trams, metro, trains etc. where passenger flows are treated as multimodal processes. The goal is to provide a declarative model enabling to state a constraint satisfaction problem aimed at multimodal transportation processes scheduling encompassing passenger flow itineraries. Then, the main objective is to provide conditions guaranteeing solvability of particular transport lines scheduling, i.e. guaranteeing the right match-up of local cyclic acting bus, tram, metro and train schedules to a given passengers flow itineraries.

Abstract The problems of designing supply networks and traffic flow routing and scheduling are the subject of intensive research. The problems encompass the management of the supply of a variety of goods using multi-modal transportation. This research also takes into account the various constraints related to route topology, the parameters of the available fleet of vehicles, order values, delivery due dates, etc. Assuming that the structure of a supply network, constrained by a transport network topology that determines its behavior, we develop a declarative model which would enable the analysis of the relationships between the structure of a supply network and its potential behavior resulting in a set of desired delivery-flows. The problem in question can be reduced to determining sufficient conditions that ensure smooth flow in a transport network with a fractal structure. The proposed approach, which assumes a recursive, fractal network structure, enables the assessment of alternative delivery routes and associated schedules in polynomial time. An illustrative example showing the quantitative and qualitative relationships between the morphological characteristics of the investigated supply networks and the functional parameters of the assumed delivery-flows is provided.

The objective of the milk-run design problem considered in this paper is to minimize transportation

and inventory costs by manipulating fleet size and the capacity of vehicles and

storage areas. Just as in the case of an inventory routing problem, the goal is to find a periodic

distribution policy with a plan on whom to serve, and how much to deliver by what

fleet of tugger trains travelling regularly on which routes. This problem boils down to determining

the trade-off between fleet size and storage capacity, i.e. the size of replenishment

batches that can minimize fleet size and storage capacity. A solution obtained in the declarative

model of the milk-run system under discussion allows to determine the routes for each

tugger train and the associated delivery times. In this context, the main contribution of

the present study is the identification of the relationship between takt time and the size

of replenishment batches, which allows to determine the delivery time windows for milkrun

delivery and, ultimately, the positioning of trade-off points. The results show that this

relationship is non-linear.