heuristic algorithm

Nurses’ scheduling problems have attracted a significant amount of healthcare research, indicating the importance of these issues. In this paper, it has tried to present a multi-objective model for the assignment of nurses and anesthesiologists to surgical teams, considering frequency and fairness in allocating time to staff members. Since idle time is inevitable, we seek to divide idle time equally among staff. In addition, the break time of each staff member have an almost regular frequency during the shift. Minimizing overtime costs and maximizing attention to the willingness of surgical staff members to work overtime are other objectives of the problem. Three metaheuristic algorithms NSGA-II, MOPSO, and SPEA-II used to solve the presented model. A hybrid multi-objective genetic algorithm based on variable neighborhood search is also presented. The comparison of the solutions of 4 algorithms shows that the proposed hybrid algorithm has a significant superiority compared to other algorithms in terms of the average value of the solution, the quality of the Pareto solution set, and execution time. The presented model is compared with the real data of the surgical department of elective patients of a government hospital in Qazvin province. The obtained results show that the presented model has significantly created equality in the amount of working time of nurses and anesthesiologists in the elective surgery department. It has also spread the idle time of each staff member during the work shift, which has caused different time breaks for each one.

Due to the many applications of the travelling salesman problem, solving this problem has been considered by many researchers. One of the subsets of the travelling salesman problem is the metric travelling salesman problem in which a triangular inequality is observed. This is a crucial problem in combinatorial optimization as it is used as a standard problem as a basis for proving complexity or providing solutions to other problems in this class. The solution is used usually in logistics, manufacturing and other areas for cost minimization. Since this is an NP-hard problem, heuristic and meta-heuristic algorithms seek near-optimal solutions in polynomial time as numerical solutions. For this purpose, in this paper, a heuristic algorithm based on the minimum spanning tree is presented to solve this problem. Then, by generating 20 instances, the efficiency of the proposed algorithm was compared with one of the most famous algorithms for solving the travelling salesman problem, namely the nearest neighbour algorithm and the ant colony optimization algorithm. The results show that the proposed algorithm has good convergence to the optimal solution. In general, the proposed algorithm has a balance between runtime and the solution found compared to the other two algorithms. So the nearest neighbour algorithm has a very good runtime to reach the solution but did not have the necessary convergence to the optimal solution, and vice versa, the ant colony algorithm converges very well to the optimal solution, but, its runtime solution is very longer than the proposed algorithm.

This paper considers a customer order scheduling (COS) problem in which each customer requests a variety of products processed in a two-machine flow shop. A sequence-independent attached setup for each machine is needed before processing each product lot. We assume that customer orders are satisfied by the job-based processing approach in which the same products from different customer orders form a product lot (job). Each customer order for a product is processed as a sublot (a batch of identical items) of the product lot by applying the lot streaming (LS) idea in scheduling. We assume that all sublots of the same product must be processed together by the same machine without intermingling the sublots of other products. The completion time of a customer order is the completion time of the product processed as the last product in that order. All products in a customer order are delivered in a single shipment to the customer when the processing of all the products in that customer order is completed. We aim to find an optimal schedule with a product lots sequence and the sequence of the sublots in each job to minimize the sum of completion times of the customer orders. We have developed a mixed-integer linear programming (MILP) model and a multi-phase heuristic algorithm for solving the problem. The results of our computational experiments show that our model can solve the small-sized problem instances optimally. However, our heuristic algorithm finds optimal or near-optimal solutions for the medium- and large-sized problem instances in a short time.

Consideration of environmental and social issues in addition to economic ones is a critical strategy that companies pay special attention to designing their supply chain. A resilient system prevents organizations from being surprised by catastrophic disruptions and critical conditions and eliminates high unwanted costs. In this study, a mixed-integer mathematical programming model is proposed to design a sustainable and resilient closed-loop supply chain network. Since suppliers are the most important external players, the slightest probability of disruptions can have a significant impact on chain performance. Accordingly, applying efficient strategies can be very helpful for coping with them. Also, because of the uncertain nature of some input parameters, the P-robust optimization method has been used to tackle them. An efficient algorithm has been carried out beside a heuristic method based on the strategic variables relaxation to solve the model. A case study of a lighting projectors industry has been conducted to evaluate the efficiency of the proposed approach. Finally, sensitivity analysis is performed on critical parameters of the problem. By solving the example, it is seen that 3 primary suppliers and 3 backups are selection, and 3 production centers, 2 collection centers and 1 repair, recycling and disposal centers have been established. The value of the economic objective function is equal to 565.857552 monetary units (MU). The CL-SCN environmental score is 658.07, while it is 608.93 in the social dimension. Eventually, the value of the final multi-objective function is equal to 0.658.

This paper proposes a truck scheduling model in a cross dock system under multi-period, multi-commodity condition with fixed outbound departures. In an operational truck scheduling problem, outbound trucks leave the cross dock terminals at predetermined times and delayed loads are kept as inventory that are sent at the next period (a time slot in a day). The proposed model optimizes the inbound truck scheduling problem through the minimizing cross dock operational costs. An accelerated Benders decomposition technique based on Covering Cut Bundle (CCB) strategy and a heuristic approach are developed to solve the model. Finally, numerical analysis introduces the sensitivity of the input parameters to the objective value.

Facility layout problems have been generally solved either hierarchically or integrated into other phases of plant design. In this paper, a hybrid method is introduced so that clustering and facilities layout can be simultaneously optimized. Each cluster is formed by a group of connected facilities and selection of the most appropriate cluster configuration is aimed. Since exact method by MIP is limited to small problems, a heuristic algorithm including constructive and improving phases is developed. In order to enhance the performance of the algorithm, systematic generation of intersection points inside available area together with shaking, split groups and Tabu list techniques are used.Then, two different examples are presented and the comparison of the results supports the merit of the proposed algorithm. For further validation, 18 test problems are solved both by the proposed algorithm and MIP by CPLEX. Comparison of the results reveals that for up to 13 facilities, the best solutions of the algorithm are equal to optimum solution of MIP but achieved in shorter times. For larger problems with higher number of facilities, even though processing times for MIP is much longer, in almost all cases, it cannot produce the best solutions of the proposed algorithm.

The aim of a multi-mode resource-constrained project scheduling problem (MRCPSP) is to assign resource(s) with the restricted capacity to an execution mode of activities by considering relationship constraints, to achieve pre-determined objective(s). These goals vary with managers or decision makers of any organization who should determine suitable objective(s) considering organization strategies. We also introduce the preemptive extension of the problem which allows activity splitting. In this paper the preemption multi-mode resource-constrained project scheduling problem (P-MMRCPSP) with Minimum makespan and the maximization of net present value (NPV) has been considered. Since the considered model is NP-Hard, The performance of our proposed model is evaluated by comparison with two well-known algorithms; non-dominated sorting genetic algorithm (NSGA II), multi-objective imperialist competitive algorithm (MOICA). These metaheuristics have been compared on the basis of a computational experiment performed on a set of instances obtained from standard test problems constructed by the ProGen project generator, where, additionally, cash flows were generated randomly with the uniform distribution. Since the effectiveness of most meta-heuristic algorithms significantly depends on choosing the proper parameters. A Taguchi experimental design method (DOE) was applied to set and estimate the proper values of GAs parameters for improving their performances. The computational results show that the proposed MOICA outperforms the NSGA-II.

From the most important issues in the design of large logistics network in times of crisis are providing a timely quick reaction for treating of injured people and the rapid distribution of medicines and medical equipment. In this paper, a multi-objective model is presented that aims to determine the location of transfer points and hospitals to provide timely quick reaction for treating injured people as well as to determine unreliable and reliable depots for the distribution of medicines and medical equipment. Given that the dynamic nature of the great crises, the parameters of the model has considered as uncertain and dynamic. To solve the model, the hybrid meta-heuristic algorithm is proposed which is composed of simulated annealing algorithm and CPLEX. By comparing the results can be seen that the proposed meta-heuristic hybrid algorithm is efficient.

Covering models have found many applications in a wide variety of real-world problems; nevertheless, some assumptions of covering models are not realistic enough. Accordingly, a general approach would not be able to answer the needs of encountering varied aspects of real-world considerations. Assumptions like the unavailability of servers, uncertainty, and evaluating more factors at the same time, are a sort of assumptions, with which covering models are always faced; however, these models are not able to find any answers for them. Therefore, how to deal with these sorts of assumptions has been always a big question. In this research, for facing unavailability and uncertainty in input data, backup covering and interval full-ranking model were addressed, respectively. Furthermore, by combining backup covering and interval full-ranking models (also conceptions), not only time was saved and more factors like efficiency and cost were simultaneously evaluated, but also covering considerations were reachable in real aspects.

This paper considers the reliable multi-product multi-vehicle multi-type link logistics network design problem (RMLNDP) with system disruptions, which is concerned with facilities locating, transshipment links constructing, and also allocating them to the customers in order to satisfy their demand on minimum expected total cost (including locating costs, link constructing costs, and also expected transshipment costs in normal and disruption conditions). The motivating application of this class of problem is in multi-product, multi-vehicle, and multi-type link logistics network design regarding to system disruptions simultaneously. In fact, the decision makers in this area are not only concerned with the facility locating costs, link constructing costs, and logistical costs of the system but also by focusing on the several system disruptions states in order to be able to provide a reliable sustainable multi configuration logistic network system. All of the facility location plan, link construction plan and also link transshipment plan of the demands in the problem must be efficiently determined while considering the several system disruptions. The problem was modeled as a MIP. Also, a hybrid heuristic, based on LP relaxation approach, is proposed. Computational experiments illustrate that the provided algorithm will able to substantially outperform the proposed integer programming model in terms of both finding and verifying the efficient optimal (or near optimal) solution at a reasonable processing time.

In this paper, a heuristic algorithm is proposed in order to solve a nonlinear lexicography goal programming (NLGP) by using an efficient initial point. Some numerical experiments showed that the search quality by the proposed heuristic in a multiple objectives problem depends on the initial point features, so in the proposed approach the initial point is retrieved by Data Envelopment Analysis to be selected as an efficient solution. There are some weaknesses in classic NLGP algorithm that lead to trapping into the local optimum, so a simulated annealing concept is implemented during the searching stage to increase the diversity of search in the solution space. Some numerical examples with different sizes were generated and comparison of results confirms that the proposed solution heuristic is more efficient than the classic approach. Moreover the proposed approach was extended for cases with ordinal weights of inputs or outputs. The computational experiments for 5 numerical instances and the statistical analysis indicate that the proposed heuristic algorithm is a robust procedure to find better preferred solution comparing to the classic NLGP.

In this paper, a novel mathematical model for a preemption multi-mode multi-objective resource-constrained project scheduling problem with distinct due dates and positive and negative cash flows is presented. Although optimization of bi-objective problems with due dates is an essential feature of real projects, little effort has been made in studying the P-MMRCPSP while due dates are included in the activities. This paper tries to bridge this gap by studying tardiness MMRCPSP, in which the objective is to minimize total weighted tardiness and to maximize the net present value (NPV). In order to solve the given problem, we introduced a Non-dominated Ranking Genetic Algorithm (NRGA) and Non-Dominated Sort Genetic Algorithm (NSGA-II). Since the effectiveness of most meta-heuristic algorithms significantly depends on choosing the proper parameters. A Taguchi experimental design method was applied to set and estimate the proper values of GAs parameters for improving their performances. To prove the efficiency of our proposed meta-heuristic algorithms, a number of test problems taken from the project scheduling problem library (PSPLIB) were solved. The computational results show that the proposed NSGA-II outperforms the NRGA.