Number Of Salesmen Research Articles

Iterated two-phase local search for the colored traveling salesmen problem

The colored traveling salesmen problem (CTSP) is a generalization of the popular traveling salesman problem with multiple salesmen. In CTSP, the cities are divided into m exclusive city sets (m is the number of salesmen) and one shared city set. The goal of CTSP is to determine a shortest Hamiltonian circuit (also called route or tour) for each of the m salesmen satisfying that (1) each route includes all cities of an exclusive city set and some (or all) cities of the shared city set, and (2) each city of the shared city set is included in one unique route. CTSP is a relevant model for a number of practical applications and is known to be computationally challenging. We present the first iterated two-phase local search algorithm for this important problem which combines a local optima exploration phase and a local optima escaping phase. We show computational results on 65 common benchmark instances to demonstrate its effectiveness and especially report 22 improved upper bounds. We make the source code of the algorithm publicly available to facilitate its use in future research and real applications.

Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem

The multiple travelling salesman problem (MTSP), an extension of the well-known travelling salesman problem (TSP), is studied here. In MTSP, starting from a depot, multiple salesmen require to visit all cities so that each city is required to be visited only once by one salesman only. It is NP-hard and is more complex than the usual TSP. So, exact optimal solutions can be obtained for smaller sized problem instances only. For large-sized problem instances, it is essential to apply heuristic algorithms, and amongst them, genetic algorithm is identified to be successfully deal with such complex optimization problems. So, we propose a hybrid genetic algorithm (HGA) that uses sequential constructive crossover, a local search approach along with an immigration technique to find high-quality solution to the MTSP. Then our proposed HGA is compared against some state-of-the-art algorithms by solving some TSPLIB symmetric instances of several sizes with various number of salesmen. Our experimental investigation demonstrates that the HGA is one of the best algorithms.

Genetic Algorithms for the Multiple Travelling Salesman Problem

We consider the multiple travelling salesman Problem (MTSP) that is one of the generalization of the travelling salesman problem (TSP). For solving this problem genetic algorithms (GAs) based on numerous crossover operators have been described in the literature. Choosing effective crossover operator can give effective GA. Generally, the crossover operators that are developed for the TSP are applied to the MTSP. We propose to develop simple and effective GAs using sequential constructive crossover (SCX), adaptive SCX, greedy SCX, reverse greedy SCX and comprehensive SCX for solving the MTSP. The effectiveness of the crossover operators is demonstrated by comparing among them and with another crossover operator on some instances from TSPLIB of various sizes with different number of salesmen. The experimental study shows the promising results by the crossover operators, especially CSCX, for the MTSP.

A Study on Unfairness of Customers according to New Management Strategy at Polarization of Retail Business

The study examined effects of psychological change of distribution environment upon commercial areas to investigate consumers' experience and theory and to suggest power of new management strategy for growth of retailers A The study investigated actual conditions of business transaction of hyper market by blind interview. In April, 2016, the author visited 6 manufacturers to do depth interview. The questionnaire between food manufacturers and hyper market investigated the Association of Food Industries in Korea, NH Nonghyup and large manufacturers in July 2012. Questionnaires of 25 companies were used after excluding questionnaire having poor and inadequate answers. The sales commission with large scaled distribution business decreased (0.3 ~ 0.7) to increase additional expenses such as number of salesmen, interior expenses and economic costs (0.7 ~ 40%). (source: Fair Trade Commission). Fair Trade Commission released types and notice of unfair trade of large scaled retail business based on monopoly regulation and fair trade (hereinafter called 'notice of large scaled retail) to prevent large scaled distribution business from doing unfair trade. The notice controled unfair trade at different position between large scaled distribution business and small vendors.

Sales Force Incentives at Service Sales Corporation

The case is about restructuring of the sales force compensation system at Service Sales Corporation (SSC), a large shoe retailer in Pakistan. The organization went through many changes in its supply chain management starting in 2001, when a new COO, Omer Saeed, took over. There was a major increase in sales and the number of shops, and a decrease in the number of salesmen per shop with the net effect that some salesmen were drawing a compensation of ₹25,000–30,000 per month (standard salesmen salary in smaller shops was ₹8,000 per month). When the new COO Amer Mohsin joined in 2009, he was faced with the challenge of designing a salesmen compensation system that was in line with the growth of the organization. The case provides an opportunity to understand how different compensation systems are required as company dynamics change.

Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem

Estimation of distribution algorithms (EDAs) have been used to solve numerous hard problems. However, their use with in-group optimization problems has not been discussed extensively in the literature. A well-known in-group optimization problem is the multiple traveling salesmen problem (mTSP), which involves simultaneous assignment and sequencing procedures and are shown in different forms. This paper presents a new algorithm, namedEDAMLA, which is based on self-guided genetic algorithm with a minimum loading assignment (MLA) rule. This strategy uses the transformed-based encoding approach instead of direct encoding. The solution space of the proposed method is onlyn!. We compare the proposed algorithm against the optimal direct encoding technique, the two-part encoding genetic algorithm, and, in experiments on 34 TSP instances drawn from the TSPLIB, find that its solution space isn!n-1m-1. The scale of the experiments exceeded that presented in prior studies. The results show that the proposed algorithm was superior to the two-part encoding genetic algorithm in terms of minimizing the total traveling distance. Notably, the proposed algorithm did not cause a longer traveling distance when the number of salesmen was increased from 3 to 10. The results suggest that EDA researchers should employ the MLA rule instead of direct encoding in their proposed algorithms.

A more compact formulation of the symmetric multiple traveling salesman problem with fixed charges

AbstractThe multiple traveling salesman problem with fixed charges (MTSPF) is an extension of the standard traveling salesman problem (TSP). Previous work by Hong and Padberg showed how to transform to a TSP with n + m + 4 nodes, where m is the number of salesmen. The four extra nodes were included to prevent the transformed problem from escaping part of the fixed costs. This paper shows that two of these nodes can be eliminated without sacrificing the formulation as a TSP. Further, all four extra nodes can be replaced by a pair of simple constraints. All formulations produce equivalent solutions.

A Cutting Planes Algorithm for the m-Salesmen Problem

The existence of reliable and flexible FORTRAN programs for integer linear programming has recently enabled the development of very efficient algorithms for the travelling salesman problem. The main characteristic of these algorithms is the relaxation of most of the constraints of the problem during its solution. The same approach can be used for the solution of the m-salesmen problem in which m salesmen starting from the same city must visit only once n cities at minimum cost. The number of salesmen can be fixed in advance or allowed to vary, upper and lower bounds set on the number of salesmen and even fixed costs associated with the salesmen. The results obtained so far are very encouraging. Problems of up to 100 cities have been solved optimally for the m-travelling salesmen case and other more complex problems are currently under study.