On the truck dispatching problem

This article considers the minmax version of the m-Traveling Salesman Problem in which the objective is to minimize the length of the longest route. Tabu search heuristics and exact search schemes are developed. Problems involving up to 50 vertices are solved to optimality. (A)

The m-traveling salesman problem with minmax objective

An assignment problem (AP) usually deals with how a set of persons/tasks can be assigned to a set of tasks/persons on a one-to-one basis in an optimal manner. It has been observed that balancing among the persons and jobs in several real-world situations is very hard, thus such scenarios can be seen as unbalanced assignment models (UAP) being a lack of workforce. The solution techniques presented in the literature for solving UAP’s depend on the assumption to allocate some of the tasks to fictitious persons; those tasks assigned to dummy persons are ignored at the end. However, some situations in which it is inevitable to assign more tasks to a single person. This paper addresses a practical variant of UAP called k-cardinality unbalanced assignment problem (k-UAP), in which only of persons are asked to perform jobs and all the persons should perform at least one and at most jobs. The k-UAP aims to determine the optimal assignment between persons and jobs. To tackle this problem optimally, an enumerative Lexi-search algorithm (LSA) is proposed. A comparative study is carried out to measure the efficiency of the proposed algorithm. The computational results indicate that the suggested LSA is having the great capability of solving the smaller and moderate instances optimally.

/pdf/an-exact-algorithm-for-constrained-k-cardinality-unbalanced-mua0fqk4.pdf

An exact algorithm for constrained k-cardinality unbalanced assignment problem

A practical distribution system that arises in the context of delivering liquefied petroleum gas (LPG) through cylinders is considered in this study. To meet all the challenging constraints, the model is explicitly considered as a simultaneous pickup and delivery single commodity truncated vehicle routing problem with the homogeneous fleet of vehicles. The aim of this problem is to find the optimal routes for the set of vehicles locating at the distributing agency (DA), which offers simultaneous pickup and delivery operations over single commodity (i.e. LPG cylinders) to a fixed subset (need not serve all delivery centers) of delivery centers at rural level. The model is designed using zero-one integer linear programming. For proper treatment of the present model, an exact Lexi-search algorithm (LSA) has been developed. A comparative study is performed between the LSA and existing results for the relaxed version of the present model. Further, the efficiency of the LSA is tested through numerical experiments over small and medium CVRP benchmark test instances. The extensive computational results have shown that the LSA is productive and revealed that the real solutions have more consistent than the integral solutions in the presence of truncation constraint.

/pdf/designing-optimal-route-for-the-distribution-chain-of-a-2xhqrav84h.pdf

Designing optimal route for the distribution chain of a rural LPG delivery system

Bangladesh is blessed with various agro-based natural resources like Date sap, extracted from date trees. As this date sap is found in rural areas in large quantities annually but a very small fraction is converted into some value-added delicious foods at a domestic level while a large portion is left underutilized due to negligence, improper collection, and preservation system from the industry level. The processed delicious foods have conspicuous demand in the national market due to their nutritious value and the growth of the national economy. Despite its economic importance, very little researches have been conducted in this field for its industrial processing. So, this research implies to improve this straggled sector providing much attention for collecting raw sap from source and processing into value-added products from industrial level cost-effectively. The key objectives of this paper are to determine optimal facility location for processing date sap and set vehicle routes that can pick up date sap from source to processing plant simultaneously curtailing operational transportation costs. Initially, a Mixed Integer Linear Programming (MILP) model is introduced to determine optimal facility location. Besides, the Large Neighborhood Search (LNS) algorithm has been used to find the optimal set of vehicle routes. This paper outlines a summary of final results that Jessore (A south-western city in Bangladesh) is an optimal plant location and 10 vehicles are necessary for covering 15 areas which ultimately optimize the total supply time, respecting constraints concerning routing, timing, capacity, and supply as well transportation costs.

http://www.journal-aprie.com/article_132553_829f99e0372752c492c1f77f4b400e96.pdf

Determining optimal production plant location and vehicle route in upstream supply chain network for date sap processing industry

. thors; licensee Growing Science, Canada 2018 by the au ©

/pdf/an-open-close-multiple-travelling-salesman-problem-with-13lekmvx08.pdf

An open close multiple travelling salesman problem with single depot

This paper deals with the bi-criteria travelling salesman subtour problem with time threshold (BTSSP-T), which comes from the family of the travelling salesman problem (TSP) and is NP-hard in the strong sense. The problem arises in several application domains, mainly in routing and scheduling contexts. Here, the model focuses on two criteria: total travel distance and gains attained. The BTSSP-T aims to determine a subtour that starts and ends at the same city and visits a subset of cities at a minimum travel distance with maximum gains, such that the time spent on the tour does not exceed the predefined time threshold. A zero-one integer-programming problem is adopted to formulate this model with all practical constraints, and it includes a finite set of feasible solutions (one for each tour). Two algorithms, namely, the Lexi-Search Algorithm (LSA) and the Tabu Search (TS) algorithm have been developed to solve the BTSSP-T problem. The proposed LSA implicitly enumerates the feasible patterns and provides an efficient solution with backtracking, whereas the TS, which is metaheuristic, will give the better approximate solution. A numerical example is demonstrated in order to understand the search mechanism of the LSA. Numerical experiments are carried out in the MATLAB environment, on the different benchmark instances available in the TSPLIB domain as well as on randomly generated test instances. The experimental results show that the proposed LSA works better than the TS algorithm in terms of solution quality and, computationally, both LSA and TS are competitive.

Bi-criteria travelling salesman subtour problem with time threshold

In open travelling salesman subset-tour problem (OTSSP), the salesman needs to traverse a set of k (≤n) out of n cities and after visiting the last city, the salesman does not necessarily return to the central depot. The goal is to minimize the overall traversal distance of covering k cities. The OTSSP model comprises two types of problems such as subset selection and permutation of the cities. Firstly, the problem of selection takes place as the salesman’s tours do not contain all the cities. On the other hand, the next problem is about to determine the optimal sequence of the cities from the selected subset of cities. To deal with this problem efficiently, a hybrid nearest neighbor technique based crossover-free Genetic algorithm (GA) with complex mutation strategies is proposed. To the best of the author’s knowledge, this is the first hybrid GA for the OTSSP. As there are no existing studies on OTSSP yet, benchmark instances are not available for OTSSP. For computational experiments, a set of test instances is created by using TSPLIB. The extensive computational results show that the proposed algorithm is having great potential in achieving better results for the OTSSP. Our proposed GA being the first evolutionary-based algorithm that will help as the baseline for future research on OTSSP.

/pdf/solving-open-travelling-salesman-subset-tour-problem-through-39jgrk8s5x.pdf

Jayanth Kumar Thenepalle

Papers

An exact algorithm for constrained k-cardinality unbalanced assignment problem

Designing optimal route for the distribution chain of a rural LPG delivery system

An open close multiple travelling salesman problem with single depot

Bi-criteria travelling salesman subtour problem with time threshold

Solving open travelling salesman subset-tour problem through a hybrid genetic algorithm