Bottleneck Transportation Problem Research Articles

A Ratio-Based approach to identifying the most basic feasible solution to bottleneck transportation problems

A Ratio-Based approach to identifying the most basic feasible solution to bottleneck transportation problems

Enhanced grouping league championship and optics inspired optimization algorithms for scheduling a batch processing machine with job conflicts and non-identical job sizes

This research aims to address scheduling of a single batch processing machine, where jobs are in different sizes and have a conflicting nature with each other, in the sense that two conflicting jobs cannot share the same batch and hence, cannot be processed simultaneously by the machine. The problem is referred to as SBMC. After formulating the problem, a strong lower bound procedure is developed by transforming a relaxed version of the scheduling problem to the multiple bottleneck transportation problem (MTP) with conflicts. An efficient Lagrangian relaxation procedure is proposed, which takes advantage of decomposable nature of the relaxed problem, to attain a lower bound for MTP which in essence is a lower bound for SBMC. To solve the problem, two metaheuristic algorithms, namely the League Championship Algorithm (LCA) and Optic Inspired Optimization (OIO), are adapted and fundamentally modified to match the problem unique structure (i.e., the grouping structure) and accordingly the grouping version of these algorithms is developed. The effectiveness of the lower bound procedure, as well as algorithms, are evaluated through extensive computational experiments. To show they perform efficiently in running times and effective in finding near-optimal bounds for most of the problem instances, we generate 20 different classes of problems according to variability in job sizes, number of jobs and density of incompatibility matrix. Then, we make comparison with two of extensively used algorithms from literature, SA and GA. Our proposed algorithms obtain solutions with objective values less than 6% gap from the lower bound and outperform SA and GA algorithms, especially for large instances. Moreover, values of the lower bound procedure lie within less than 4% of objective values provided by CPLEX.

Optimal Solutions of the Fuzzy Multi Index Bi-criteria Fixed Charge Bottleneck Transportation Problem

In this paper, fuzzy multi index bi-criteria fixed charge bottleneck transportation problem (FMIBCFCBTP) is considered and for the first time all parameters are taken as trapezoidal fuzzy numbers. An algorithm is developed to find fuzzy time-cost trade-off pairs of FMIBCFCBTP. A numerical example is given to explain the proposed algorithm.

Bottleneck transportation problem with a fuzzy random constraint

Bottleneck transportation problem with a fuzzy random constraint

The bottleneck transportation problem with auxiliary resources

In this paper, we introduce a new extension of the bottleneck transportation problem where additionally auxiliary resources are needed to support the transports. A single commodity has to be sent from supply to demand nodes such that the total demand is satisfied and the time at which all units of the commodity have arrived at the demand nodes is minimized. We show that already the problem with a single demand node and a single auxiliary resource is NP-hard and consider some polynomially solvable special cases.

Risk-control approach for bottleneck transportation problem with randomness and fuzziness

Solving transportation problems is essential in engineering and supply chain management, where profitability depends on optimal traffic flow. This study proposes risk-control approaches for two bottleneck transportation problems with random variables and preference levels to objective functions with risk parameters. Each proposed model is formulated as a multiobjective programming problem using robust-based optimization derived from stochastic chance constraints. Since it is impossible to obtain a transportation pattern that optimizes all objective functions, our proposed models are numerically solved by introducing an aggregation function for the multiobjective problem. An exact algorithm that performs deterministic equivalent transformations and introduces auxiliary problems is also developed.

Bottleneck flows in unit capacity networks

The bottleneck network flow problem (BNFP) is a generalization of several well-studied bottleneck problems such as the bottleneck transportation problem (BTP), bottleneck assignment problem (BAP), bottleneck path problem (BPP), and so on. The BNFP can easily be solved as a sequence of O ( log n ) maximum flow problems on almost unit capacity networks. We observe that this algorithm runs in O ( min { m 3 / 2 , n 2 / 3 m } log n ) time by showing that the maximum flow problem on an almost unit capacity graph can be solved in O ( min { m 3 / 2 , n 2 / 3 m } ) time. We then propose a faster algorithm to solve the unit capacity BNFP in O ( min { m ( n log n ) 2 / 3 , m 3 / 2 log n } ) time, an improvement by a factor of at least log n 3 . For dense graphs, the improvement is by a factor of log n . On unit capacity simple graphs, we show that BNFP can be solved in O ( m n log n ) time, an improvement by a factor of log n . As a consequence we have an O ( m n log n ) algorithm for the BTP with unit arc capacities.

The Constrained Bottleneck Transportation Problem

Two classes of the bottleneck transportation problem with an additional budget constraint are introduced. An exact approach was proposed to solve both problem classes with proofs of correctness and complexity. Moreover, the approach was extended to solve a class of multi-commodity transportation network with a special case of the multi-period constrained bottleneck assignment problem.

A linear-time algorithm for the bottleneck transportation problem with a fixed number of sources

We investigate a special case of the bottleneck transportation problem where the number s of sources is bounded by a constant and not part of the input. For the subcase s=2, a best-possible linear-time algorithm has been derived by Varadarajan [Oper. Res. Lett. 10 (1991) 525–529]. In this note we show that for any fixed number s⩾1, the bottleneck transportation problem with s sources can be solved in linear-time. The algorithm is conceptually simple, and easy to implement.

An extension to the single bottleneck transportation problem

Abstract In the existing models of bottleneck transportation problem (BTP), the transport time along a given path is taken as a fixed charge. In most practical situations, however, the transport time usually varies with the amount of transport. In order to make up this defect, an extended BTP model is built in which transport time tij is determined by a function of the amount to be transported rather than a constant. A heuristic recursive algorithm is proposed for the solution of the model. Furthermore, a special case of the model (that the supplies at sources are sufficient) is studied and a set of formulae of optimal solution are derived.

A Stochastic Bottleneck Transportation Problem

In this paper, a stochastic bottleneck transportation problem, which aims at minimizing the transportation time target subject to a chance constraint, is formulated and an algorithm based on a parametric programming approach is developed to solve it. Further, assuming the transportation costs to be deterministic, a trade-off analysis between the transportation time target and the total cost is given. In addition, methods are developed which give the whole spectrum of optimal solutions to the problems mentioned above. The algorithms are illustrated by numerical examples. The computational complexity of the algorithms is also discussed.

An instant solution of the 2 × n bottleneck transportation problem

This paper provides an instant method to solve the 2 × n bottleneck transportation problem. It also compares the optimal solution structure of the bottleneck and the classical transportation models.

The multiple bottleneck transportation problem

An extension to the Bottleneck Transportation Problem (BTP) is considered wherein a bottleneck is computed for each demand point. Due to the existence of local optima, solution procedures that have been developed for BTP do not readily apply to the Multiple Bottleneck Problem (MTP). An effective solution technique that uses Lagrangean relaxation methods is described and tested. One of the keys to the algorithm is a unique “double bounding” technique derived from the special structure of MTP.

An optimal algorithm for 2 × n bottleneck transportation problems

Bottleneck transportation problems differ from the standard transportation problems only in their objective function which is expressed as the maximum cost of shipping a commodity instead of as the sum of shipping costs. In this paper, we present a linear and hence an optimal algorithm for 2 × n bottleneck transportation problems.

Algorithms for the minimax transportation problem

AbstractIn this paper, we consider a variant of the classical transportation problem as well as of the bottleneck transportation problem, which we call the minimax transportation problem. The problem considered is to determine a feasible flow xij from a set of origins I to a set of destinations J for which max(i,j)εIxJ{cijxij} is minimum. In this paper, we develop a parametric algorithm and a primal‐dual algorithm to solve this problem. The parametric algorithm solves a transportation problem with parametric upper bounds and the primal‐dual algorithm solves a sequence of related maximum flow problems. The primal‐dual algorithm is shown to be polynomially bounded. Numerical investigations with both the algorithms are described in detail. The primal‐dual algorithm is found to be computationally superior to the parametric algorithm and it can solve problems up to 1000 origins, 1000 destinations and 10,000 arcs in less than 1 minute on a DEC 10 computer system. The optimum solution of the minimax transportation problem may be noninteger. We also suggest a polynomial algorithm to convert this solution into an integer optimum solution.

One-parametric bottleneck transportation problems

We discuss the bottleneck transportation problem with one nonlinear parameter in the bottleneck objective function. A finite sequence of feasible basic solutions which are optimal in subsequent closed parameter-intervals is generated using a primal method for the nonparametric subproblems. The best among three primal codes for solving these subproblems is selected on extensive computational comparisons. We discuss computational experience with the sequential method for the case of linear and quadratic dependence on one parameter. Observed computational behaviour is O((n ·m)α), with α⩽2.

A study of the bottleneck single source transportation problem

Given a set of users with known demands, a set of suppliers with known supplies and known costs of shipping between suppliers and users, the Bottleneck Single Source Transportation is that of assigning the users to the suppliers so that the following conditions are satisfied: 1. (i) the demand of each user is satisfied by a single supplier; 2. (ii) the amount supplied by each supplier does not exceed its capacity; 3. (iii) the maximum cost of supplying any user by its unique supplier is minimal. Applications of this problem include: voter redistricting, shipping perishable goods, assignment of city blocks to emergency facilities and others. We first discuss a heuristic method which tries to find a feasible solution by assigning the users in order of decreasing demand to the suppliers according to certain orders. In our experience on randomly generated problems, the heuristic was able to find a good and frequently an optimal feasible solution, most of the time. If the heuristic fails to find a solution, or finds a solution which is not known to be optimal, then a branch and bound algorithm, using ordinary bottleneck transportation problems as relaxations, is employed to find the optimum single source solution. Computational experience on some randomly generated problems up to 100 × 400 is presented which indicates that these problems can be solved in less than 2 min. Also several small problems with real data were solved; in all but one of these problems the heuristic succeeded in finding an optimal solution.

Minimizing Overshipments In Bottleneck Transportation Problems

AbstractBottleneck transportation problems usually arise in connection with perishable comnjodities that have to be distributed as quickly as possible. A new approach is given that often permits the acceleration of the distribution. This reduction of the classical bottleneck time is obtained by allowing certain overshipments in the network. A primal algorithm will be given that determines completely the bottleneck time overshipment function. The technique will include capacity restrictions, and will also yield an efficient solution procedure for the classical bottleneck problem and for overshipment problems.

An efficient primal approach to bottleneck transportation problems

AbstractThis article addresses bottleneck linear programming problems and in particular capacitated and constrained bottleneck transportation problems. A pseudopricing procedure based on the poly‐ω procedure is used to facilitate the primal simplex procedure. This process allows the recent computational developments such as the Extended Threaded Index Method to be applied to bottleneck transportation problems. The impact on problem solution times is illustrated by computational testing and comparison with other current methods.

On three basic methods for solving bottleneck transportation problems

For solving transportation problems essentially three types of methods are known: primal methods, the Hungarian method and the shortest augmenting path method. In this paper we present the specialization of these approaches to the bottleneck transportation problem and report some computational experience.