https://web.stanford.edu/class/msande312/restricted/klos04facility.pdf

Facility location models for distribution system design

https://faculty.biu.ac.il/~shnaidh/zooloo/trnsprt2/Location-routing-%20Issues,%20models%20and%20methods.pdf

Location-routing: Issues, models and methods

WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

Location analysis: A synthesis and survey

Combined Location-Routing Problems: A Synthesis and Future Research Directions

The interdependence between distribution center location and vehicle routing has been recognized by both academics and practitioners. However, only few attempts have been made to incorporate routing in location analysis. This paper defines the Warehouse Location-Routing Problem (WLRP) as one of simultaneously solving the DC location and vehicle routing problems. We present a mixed integer programming formulation of the WLRP. Based on this formulation, it can be seen that the WLRP is a generalization of well-known and difficult location and routing problems, such as the Location-Allocation Problem and the Multi-depot Vehicle Dispatch Problem. It is therefore a large and complex problem which cannot be solved using existing mixed-integer programming techniques. We present a heuristic solution method for the WLRP, based on decomposing the problem into three subproblems. The proposed method solves the subproblems in a sequential manner while accounting for the dependence between them. We discuss a large-scale application of the proposed method to a national distribution company at a regional level.

A warehouse location-routing problem

Existing studies of transit network design deal separately with the problems of determining the optimal route spacing and operating headway, and that of determining the optimal stop spacing. This paper presents an analytic model for the design of an optimal feeder bus network for accessing an existing rail line, which avoids the sequential approach and combines these three basic variables. Our results with regard to bus‐route spacing and headway are similar to those obtained previously, indicating that route spacing and operating headway are not highly sensitive to changes in the relevant system parameters. With regard to bus‐stop spacing, three different cases are considered, reflecting three different stop‐spacing policies. In the first case, bus‐stop spacing is specified as uniform over the entire area. In the second case, stop spacing is constant along any given route. In the third case, stop spacing may vary both between and along routes. Closed‐form solutions are presented for the first two cases. T...

Optimization of feeder bus routes and bus-stop spacing

The potential for improving the cost-effectiveness of public transport operations by designing better integrated feeder-bus/rail rapid transit systems has been widely recognized. This paper defines the feeder-bus network-design problem (FBNDP) as that of designing a feeder-bus network to access an existing rail system. The FBNDP is considered under two different demand patterns, many-to-one (M-to-1) and many-to-many (M-to-M). We present a mathematical programming model for the M-to-1 FBNDP, and show that it can be generalized to the M-to-M FBNDP. The FBNDP is a large and difficult vehicle-routeing-type problem with an additional decision variable—operating frequency. A heuristic model is presented, which generalizes the ‘savings approach’ to incorporate operating frequency. The computational analysis shows that the proposed heuristic provides reasonable feeder-bus networks and consistent responses to ‘what if’ questions. A comparison indicates that the proposed heuristic provides solutions that are superior to manually designed networks. The advantages of this heuristic are particularly significant under variable demand.

The feeder-bus network-design problem

SYNOPTIC ABSTRACTCurrent mathematical models for analyzing distribution systems usually consider the long-term “strategic problem” of Distribution Center (DC) location, and the short-term “tactical problem” of vehicle routing, independently and sequentially. While in the short-term, both the capacities and variable costs at the DC's are given, existing vehicle routing models do not consider either the capacities of the variable costs at the DC's. The proposed Multi-Depot Routing Allocation Problem (MDRAP) is that of designing vehicle routes from multiple capacitated depots with different variable costs. It can be formulated as a zero-one integer programming problem. We present an efficient heuristic for the MDRAP based on a sequential savings approach. The computational analysis suggests that DC capacities and variable costs may have significant effects on vehicle routing.

The Multi-Depot Routing Allocation Problem

The U.S. transit industry faces financial difficulties. Among the strategies suggested for improving transit financial conditions, the development of better-integrated intermodal systems has the advantage of potentially achieving both cost reduction and improved service. A network optimization methodology for the design of an integrated feeder-bus--rail rapid transit system is presented. The Feeder-Bus Network Design Problem (FBNDP) is defined as that of designing a set of feeder-bus routes and determining the frequency on each route so as to minimize operator and user costs. The FBNDP is first considered under many-to-one demand and its formulation is discussed as a mathematical programming problem. Then the generalization of the formulation to the many-to-many demand pattern is reviewed. The FBNDP is a larger and complex routing-type problem that can be solved only heuristically. A heuristic method that generalizes the savings approach to consider operating frequency is presented. The analysis presented illustrates the capabilities of the proposed model as a strategic planning tool for feeder-bus network design. It indicates that changes that increase the relative weight of operator cost often result in feeder-bus networks with less circuitous routes operated at lower frequencies, whereas changes that increase the relative weight of user cost result in feeder routes operated at higher frequencies. The solutions provided by the proposed model have been tested and found superior to manually designed networks, particularly under variable demand.

Jossef Perl

Papers

A warehouse location-routing problem

Optimization of feeder bus routes and bus-stop spacing

The feeder-bus network-design problem

The Multi-Depot Routing Allocation Problem

A methodology for feeder-bus network design