Integer programming formulations of discrete hub location problems

Survey: Hub location problems: A review of models, classification, solution techniques, and applications

A Bayesian network model for resilience-based supplier selection

Conventionally, vehicle routing problems are defined on a network in which the customer locations and arcs are given. Typically, these arcs somehow represent the distances or expected travel time derived from the underlying road network. When executed, the quality of the solutions obtained from the vehicle routing problem depends largely on the quality of the road network representation. This paper explicitly considers path selection in the road network as an integrated decision in the time-dependent vehicle routing problem, denoted as path flexibility (PF). This means that any arc between two customer nodes has multiple corresponding paths in the road network (geographical graph). Hence, the decisions to make are involving not only the routing decision but also the path selection decision depending upon the departure time at the customers and the congestion levels in the relevant road network. The corresponding routing problem is a time-dependent vehicle routing problem with path flexibility (TDVRP–PF). We formulate the TDVRP–PF models under deterministic and stochastic traffic conditions. We derive important insights, relationships, and solution structures. Based on a representative testbed of instances (inspired on the road network of Beijing), significant savings are obtained in terms of cost and fuel consumption, by explicitly considering path flexibility. Having both path flexibility and time-dependent travel time seems to be a good representation of a wide range of stochasticity and dynamics in the travel time, and path flexibility serves as a natural recourse under stochastic conditions. Exploiting this observation, we employ a Route-Path approximation method generating near-optimal solutions for the TDVRP–PF under stochastic traffic conditions.

Time-dependent vehicle routing problem with path flexibility

Developing framework for reducing purchasing risks associated with suppliers.Combination of grey system theory and uncertainty theory is used.It neither requires any probability distribution nor fuzzy membership function.It selects the most appropriate suppliers and allocates optimal purchase quantity. Supplier selection in supply chain is critical strategic decision for organization's success and has attracted much attention of both academic researchers and practitioners. Supplier selection problem consists of stochastic and recognitive uncertainties. However, the requirement of large sample size and strong subject knowledge to build suitable fuzzy membership function restrict the applicability of probability and fuzzy theories in supplier selection problem. In response, this study proposed a new tool for supplier selection. In this paper, we applied the combination of grey system theory and uncertainty theory which neither requires any probability distribution nor fuzzy membership function. The objective of this paper is to develop framework for reducing the purchasing risks associated with suppliers. The proposed supplier selection method not only selects the most appropriate supplier(s) but also allocate optimal purchase quantity under stochastic and recognitive uncertainties. An example is shown to highlight the procedure of the proposed model at the end of this paper.

Group multi-criteria supplier selection using combined grey systems theory and uncertainty theory

In this paper, we study a resource-constrained project-scheduling problem in which the objective is minimizing total Resource Tardiness Penalty Costs. We assume renewable resources that are limited in number, are restricted to very expensive equipment and machines, therefore they are rented and used in other projects, and are not available in all project periods. In other words, there exists a predefined ready-date as well as a due date for each renewable resource type. In this way, no resource is utilized before its ready date. Nevertheless, resources are allowed to be used after their due date by paying penalty costs depending on the resource type. The objective is to minimize the costs of renewable resource usages. We formulated and mathematically modeled this problem as an integer-Linear programming model. Since our problem is NP-hard and also exact methods are only applicable in small scale, therefore metaheuristic methods are practical approaches for this problem; this means that metaheuristics are better for this problem. In order to authenticate the model and solution algorithm in small scale, we consider a network with low activity, and then solve the model of this network with both exact algorithms and SA-GA-TS metaheuristic algorithms. For more activities, as well as getting closer to the real world, we present a Simulated Annealing Algorithm to solve this problem. In order to examine the performance of this algorithm, data that had been derived from studied literature were used, and their answers were compared with Genetic Algorithm (GA) and Tabu Search Algorithm (TS). Results show that in average, quality of SA answers was better than those of the GA and TS algorithms. In addition, we use relaxation method to achieve an even higher validation for the SA algorithm. Finally all results in this paper indicate that both model and solution algorithm have high validity.

http://www.riejournal.com/article_47958_6c6dd31a2f094c0b2e982c34b603cf6e.pdf

Minimizing Total Resource Tardiness Penalty Costs in the Resource Constrained Project Scheduling Problem with Metaheuristic Algorithms

A significant analytical approach contrived to solve many real-world problems is Goal Programming (GP). In many marketing or decision management problems, the phenomenon of multi-segment aspiration levels and multi-choice goal levels may exist for decision makers. This problem cannot be solved by current GP techniques such as multi-choice goal programming and multi-segment goal programming. This paper provides a new idea to integrate the multi-segment goal programming and multi-choice goal programming in order to solve multi-aspiration problems. Moreover, it develops the concepts of these models significantly for real application; in addition, a real problem is provided to demonstrate usefulness of the proposed model. The results of the problem are analyzed and finally, the conclusion is remarked.

Multi-Aspiration Goal Programming Formulation

Zone pricing is one of the most important pricing policies that are prevalently used by very companies. This paper considers integrating zone pricing and location-routing problems for profit maximization. Hence, a node-based model is proposed as mixed integer nonlinear programming to solve the problem. In order to handle the nonlinearity elements and change the model to a mixed integer linear programming, a piecewise linearization method is employed to approximate the problem. Moreover, we introduce a new heuristic variable neighborhood search (VNS) and tabu search algorithm for large-scale problems. The proposed algorithms consist of four intra-tour and seven inter-tour operators in its local search. Finally, some test instances with 20, 200, 400, and 600 nodes are solved and the results of them confirm the efficiency of the proposed algorithms and comparative superiority of the VNS algorithm over the tabu search algorithm.

The multi-route location-routing problem and zone price decision-making using a tabu and variable neighborhood search algorithm

The simultaneous optimization of multiple responses is an important problem in the design of industrial processes in order to achieve improved quality. In this paper, we present a new metaheuristic approach including Simulated Annealing and Particle Swarm Optimization to optimize all responses simultaneously. For the purpose of illustration and comparison, the proposed approach is applied to two problems taken from the literature. The results of our study show that the proposed approach outperforms the other approaches and can find better solutions. Finally, in both cases, we present the results of a sensitivity analysis incorporating experimental design.

https://aie.ut.ac.ir/article_23322_1533189b6bd6df953c94f62303adb71a.pdf

Hossein Karimi

Papers

Minimizing Total Resource Tardiness Penalty Costs in the Resource Constrained Project Scheduling Problem with Metaheuristic Algorithms

Multi-Aspiration Goal Programming Formulation

The multi-route location-routing problem and zone price decision-making using a tabu and variable neighborhood search algorithm

Metaheuristic Based Multiple Response Process Optimization

Time slot management in selective pickup and delivery problem with mixed time windows