An algorithm for the hierarchical Chinese postman problem

Computers & Operations Research, 1988

Scope and Purpose-The Chinese Postman Problem (CPP) is to find a least cost way to traverse each arc of a network at least once and to return to the origin. Since its first appearance in Chinese Mathematics 1, 273-277 (1962), the CPP has been the focus of much research attention and found an abundance of applications, especially in municipal problems, such as the routing of street sweepers, household refuse collection vehicles, postmen, the spraying of roads, etc. This paper presents an algorithm for the "directed" Chinese Postman Problem, which, compared with the existing algorithms, is easier to be implemented and has a better computational complexity.

Grid computing is a continuous growing technology that alleviates the executions of largescale resource intensive applications on geographically distributed computing resources. For a computational grid environment, there are number of scheduling policies available to address the scheduling and load balancing problem. Scheduling techniques applied in grid systems are primarily based on the concept of queuing systems, and deals with the allocation of job to computing node. The scheduler, that schedules the incoming job can be based on global vs. local i.e. what information will be used to make a load balancing decision, centralized vs. de-centralized i.e. where load balancing decisions are made, and static vs. dynamic i.e. when the distribution of load is made. The primary objective of all load balancing algorithm is minimization of the makespan value, maximum load balanced and to gain more desirable performance. In this paper, we present the various load balancing strategies of job scheduling for grid computing environment. We also analyze the efficiency and limitations of the various approaches

Automation in Construction, 2002

1993

Abstract The mixed Chinese postman problem is a version of the well-known Chinese postman problem in which the underlying graph consists of both directed and undirected edges. We give an integer linear programming formulation for this problem and then show that the extreme points of its linear relaxation polyhedron are all half-integral.

2012

How to cite Complete issue More information about this article Journal's homepage in redalyc.org Scientific Information System Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Non-profit academic project, developed under the open access initiative

ArXiv, 2020

This paper studies large scale instances of a fairly general arc-routing problem as well as incorporate practical constraints in particular coming from the scheduling problem of the winter road maintenance (e.g. different priorities for and methods of road maintenance). We develop a new algorithm based on a bin-packing heuristic which is well-scalable and able to solve road networks on thousands of crossroads and road segments in few minutes. Since it is impossible to find an optimal solution for such a large instances to compare it with a result of our algorithm, we also develop techniques to compute lower bounds which are based on Integer Linear Programming and Lazy Constraints.

Electronic Notes in Discrete Mathematics, 2004

THESIS ABSTRACT BRANZUELA, ROY IGBUHAY; ACOL, MYLENE B., Eastern Visayas State University, Tacloban City, March 2017, CHINESE POSTMAN ALGORITHM IN WASTE COLLECTION VEHICLE ROUTING PROBLEM IN POBLACION DOLORES, EASTERN SAMAR. Adviser: Stephen Paul G. Cajigas, BSMath Instructor I Mathematics and Statistics Department Eastern Visayas State University Tacloban City This study determined the following: the constraint/s considered in solving the waste collection vehicle routing problem; the Optimal Chinese Postman Route for the Waste Collection Vehicle of poblacion area of Dolores, Eastern Samar using the introduced method; the minimum total distance travelled by the waste collection vehicle given the optimal Chinese postman route; and to construct a schedule for the waste collection process in poblacion area of Dolores, Eastern Samar. The applied method of research was used in this study. It uses the road map and boundary map obtained from the office of the Municipal Planning and Development Coordinator of the Municipality of Dolores, Eastern Samar and the distances of the streets acquired from Google maps. The data gathered were used in finding solutions to the problems under the present study using the concept of Chinese Postman Problem and its algorithm. With the foregoing statements, the following conclusions were drawn: the constraint that were considered in solving the waste collection vehicle in poblacion area of Dolores, Eastern Samar is the Narrow Streets; the optimal Chinese Postman Route of the different barangays in Dolores, Eastern Samar are as follows: in barangay 1 and 3, the optimal Chinese Postman route of the garbage truck is L1 - K1 - J1 - B1 - A1 - R3 - A1 - B1 - G1 - I1 - H1 - I1 - C1 - B1 - P3 - J3 - C1 - D1 - I3 - G3 - E1 - G1 - H1 - K1 - H1- D1- E1 - F1 - W3 - F1 - L1. The optimal Chinese Postman route of the waste collection vehicle in barangay 2 and 4 is W3 -C2 - D2 - E2 - J2 - I2 - F2 - G2 - Q2 - H2 - Q2 - I2 - Q2 - M2 - N2 - P2 - N2 - L2 - I2- L2 - K2 - J2 - C2 - B2 - K2 - O2 - N2 - O2 - L1 - A2 - B2 - C2 - F1 - W3. Barangay 5 and 7 has an optimal Chinese Postman route of A3 - Q3 - O3 - M3 - K3 - H3 - F3 - G3 - W3 - E3 - W3 - G3 - H3 - I3 - J3 - K3 - C3 - D3 - H3 - K3 - M3- L3 -N3 - O3 - Q3 - P3 - R3 - S3 - V3 - S3 - U3 - T3 - S3 - Q3 - S3 - Q3 - O3 - M3 - B3 - A3. In Barangay 6, the optimal Chinese Postman route of the truck is W3 - E4 - A4 - B4 - E2 - F2 - C4 - D4 - G2 - D4 - C4 - B4 - A4 - D2 - W3. The optimal Chinese postman route of barangay 8 is E3 -F3 - H3 - D3 - A5 - F3 - A5 - B5 -E3. E3 - B5 - A6 - A4 - B4 - C6 - C4 - D4 - D6- D4 - C4 - B4 - A4 - E3 will be the route of Barangay 9. For the barangay 10, the optimal Chinese Postman route is B5 - A5 - K7 - M7 - L7 - I7 - J7 - D3 - C3 - H7 - G7 - N7 - E7 - F7 - B3 - A3 - T3 - D7 - T3 - U3 - A7 - D7 - C7 - B7 - A7 - D7 - E7 - F7 - H7 - J7 - K7 - M7 - B5. In barangay 11, the optimal Chinese Postman route is L7 - A8 - B8 - C8 - D8 - E8 - D8 - C6 - D8 - C8 - B6 - A6 - B8 - M7 - B5 - M7 - L7. The optimal Chinese Postman route of garbage truck in barangay 12 is G7 - F9 - G9 - H9 - G9 - F9 - E9 - D9 - E9 - B9 - C9 - B9 - A9 - B7 - C7 - B9 - E9 - N7 - G7. In barangay 13, the optimal Chinese postman route is L7 - I7 - G7 -F9 - A10 - I7 - A10 - B10 - L7. The optimal Chinese Postman route in barangay 14 is A11 - C11 - B11 - C11 - D11 - F11 - E11 - F11 - D11 - E11 - F11 - D11 - E8 - D11 - C11 - A11. Lastly, the route optimal Chinese Postman for barangay 15 is A11 - A12 - B12 - A12 - C12 -A12 -A11 - C11 - A11 -B10 - A11; the minimum distance travelled by the waste collection vehicle given the optimal Chinese Postman Route in poblacion area of Dolores, Eastern Samar is 18, 701.27 meters; the schedule of the waste collection process in poblacion area of Dolores, Eastern Samar is defined as follows: each barangay of the said place will be visited twice a week. Barangay 1 and 3 will be visited by truck 1 every morning of Monday and Thursday. Barangay 5 and 7 will be visited by truck 1 every morning of Tuesday and Friday. During the morning of Wednesday and Saturday, barangay 14 will be visited by truck 1. Barangay 9 is assigned to truck 2 every morning of Monday and Thursday. Truck 2 will also visit barangay 11 every morning of Tuesday and Friday. Barangay 10 will be visited by truck 2 every morning of Wednesday and Saturday. In the afternoon, truck 1 will visit barangay 2 and 4 every Monday and Thursday. Truck 1 will also visit barangay 12 every afternoon of Tuesday and Friday. Barangay 15 will be visited by truck 1 every afternoon of Wednesday and Saturday. During Monday and Thursday afternoon, barangay 13 will be visited by truck 2. Barangay 8 will be visited every Tuesday and Friday afternoon by truck 2 And, Barangay 6 will also visited every afternoon of Wednesday and Saturday. The following recommendations are hereby offered based on the conclusions configured hereafter: the researchers recommend the findings of the study to be utilize by the Municipality of Dolores, Eastern Samar for the waste collection process; the researchers recommend the Chinese postman algorithm as a mathematical approach in solving the waste collection vehicle routing problem be applied in bigger municipalities, cities or provinces; test the efficiency of the Chinese Postman Algorithm as a mathematical approach in solving the waste collection routing problem; and further studies can be conducted using other variables such as time, environmental concern, demand constraint and other constraints which were not considered in the study.

Networks

In this paper we address a real life optimization problem, the Rail Track Inspection Scheduling Problem (RTISP). This problem consists of scheduling railway network inspection tasks. The objective is to minimize the total deadhead distance while performing all inspection tasks. Different 0-1 integer formulations for the problem are presented. A heuristic based on both Benders and Dantzig-Wolfe decompositions is proposed to solve this rich arc routing problem. Its performance is analyzed on a real life dataset provided by the French national railway company (SNCF). The proposed algorithm is compared to a dynamic programming-based heuristic. Its ability to schedule the inspection tasks of one year on a sparse graph with thousand nodes and arcs is assessed.