A direct heuristic algorithm for linear programming

AnO(n ³) mathematically non-iterative heuristic procedure that needs no artificial variable is presented for solving linear programming problems. An optimality test is included. Numerical experiments depict the utility/scope of such a procedure.     

A matheuristic algorithm for stochastic home health care planning

Efficient human resource planning is the cornerstone of designing an effective home health care system. Human resource planning in home health care system consists of decisions on districting/zoning, staff dimensioning, resource assignment, scheduling, and routing. In this study, a two-stage stochastic mixed integer model is proposed that considers these decisions simultaneously. In the planning phase of a home health care system, the main uncertain parameters are travel and service times. Hence, the proposed model takes into account the uncertainty in travel and service times. Districting and staff dimensioning are defined as the first stage decisions, and assignment, scheduling, and routing are considered as the second stage decisions. A novel algorithm is developed for solving the proposed model. The algorithm consists of four phases and relies on a matheuristic-based method that calls on various mixed integer models. In addition, an algorithm based on the progressive hedging and Frank and Wolf algorithms is developed to reduce the computational time of the second phase of the proposed matheuristic algorithm. The efficiency and accuracy of the proposed algorithm are tested through several numerical experiments. The results prove the ability of the algorithm to solve large instances.     

A planning and routing model for patient transportation in health care

In this paper, a problem concerning both the planning of health care services and the routing of vehicles, for patients transportation is addressed. An integrated approach, based on the column generation technique, is proposed to solve the planning and routing problem. Preliminary results on real data show the effectiveness of the proposed approach.     

A heuristic approach for big bucket multi-level production planning problems

Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper, we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates high quality lower bounds using strong formulations, and its simple scheme allows it to be easily implemented in the Xpress-Mosel modeling language. Extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic, particularly for challenging problems.     

A hybrid heuristic algorithm for the open-pit-mining operational planning problem

This paper deals with the Open-Pit-Mining Operational Planning problem with dynamic truck allocation. The objective is to optimize mineral extraction in the mines by minimizing the number of mining trucks used to meet production goals and quality requirements. According to the literature, this problem is NP-hard, so a heuristic strategy is justified. We present a hybrid algorithm that combines characteristics of two metaheuristics: Greedy Randomized Adaptive Search Procedures and General Variable Neighborhood Search. The proposed algorithm was tested using a set of real-data problems and the results were validated by running the CPLEX optimizer with the same data. This solver used a mixed integer programming model also developed in this work. The computational experiments show that the proposed algorithm is very competitive, finding near optimal solutions (with a gap of less than 1%) in most instances, demanding short computing times.     

A heuristic algorithm for a production planning problem in an assembly system

This paper focuses on a production planning problem in an assembly system operating on a make-to-order basis. Due dates are considered as constraints in the problem, that is, tardiness is not allowed. The objective of the problem is to minimise holding costs for final product inventory as well as work-in-process inventory. A non-linear mathematical model is presented and a heuristic algorithm is developed using a solution property and a network model for defining solutions of the problem. A series of computational tests were done to compare the algorithm with a commercial planning/scheduling software and backward finite-loading methods that employ various priority rules. The results showed that the suggested algorithm outperformed the others.     

Optimizing heuristic search in forest planning

Heuristic search methods are being used more and more in forest planning since the current formulations of exact methods such as linear programming are not suitable to all today's planning problems. A practical problem with most heuristics is that their performance greatly depends on the parameters that guide their search process. The effect of parameters is hard to know without extensive tests, but these tests cannot be conducted in forest planning practice, because of lacking time and experience. This study presented a method that uses Hooke and Jeeves direct search to optimize the parameters of a heuristic, taking into account the allowed computing time. The method was used to optimize three local-improvement heuristics in a non-spatial and a spatial forest planning problem, and with a short and long computing time. The heuristics were simulated annealing, threshold accepting, and tabu search, all of which are used in forestry. The results were logical and showed that while the optimal values of some parameters were rather constant the others were sensitive to problem type, allowed computing time, or problem size. The objective function value of the forest planning problem was not sensitive to small changes in the parameters of the heuristics. However, because computing time was very sensitive to many parameters, there was not much freedom to set the parameters if both the quality of the solution and speed of the algorithm had to be maintained.     

A compromised large-scale neighborhood search heuristic for capacitated air cargo loading planning

Cost effectiveness is central to the air freight forwarders. In this work, we study how an air freight forwarder should plan its cargo loading in order to minimize the total freight cost given a limited number of rented containers. To solve the problem efficiently for practical implementation, we propose a new large-scale neighborhood search heuristic. The proposed large-scale neighborhood relaxes the subset-disjoint restriction made in the existing literature; the relaxation risks a possibility of infeasible exchanges while at the same time it avoids the potentially large amount of checking effort required to enforce the subset-disjoint restriction. An efficient procedure is then used to search for improvement in the neighborhood. We have also proposed a subproblem to address the difficulties caused by the fixed charges. The compromised large-scale neighborhood (CLSN) search heuristic has shown stably superior performance when compared with the traditional large-scale neighborhood search and the mixed integer programming model.     

A new heuristic and an exact approach for a production planning problem

Central European Journal of Operations Research - We deal with a very complex and hard scheduling problem. Two types of products are processed by a heterogeneous resource set, where resources have...     

Mid-term and short-term planning support for home health care services

In this paper we are looking at routing and scheduling problems arising in the context of home health care services. Many small companies are working in this sector in Germany and planning is still done manually, resulting in long planning times and relatively inflexible solutions.     

A heuristic algorithm for the hospital health examination scheduling problem

This study considers the problem of health examination scheduling. Depending on their gender, age, and special requirements, health examinees select one of the health examination packages offered by a health examination center. The health examination center must schedule all the examinees, working to minimize examinee/doctor waiting time and respect time and resource constraints, while also taking other limitations, such as the sequence and continuity of the examination procedures, into consideration. The Binary integer programming (BIP) model is one popular way to solve this health examination scheduling problem. However, as the number of examinees and health examination procedures increase, solving BIP models becomes more and more difficult, if not impossible. This study proposes health examination scheduling algorithm (HESA), a heuristic algorithm designed to solve the health examination scheduling problem efficiently and effectively. HESA has two primary objectives: minimizing examinee waiting time and minimizing doctor waiting time. To minimize examinee waiting time, HESA schedules the various parts of each examinee’s checkup for times when the examinee is available, taking the sequence of the examination procedures and the availability of the resources required into account. To minimize doctor waiting time, HESA focuses on doctors instead of examinees, assigning waiting examinees to a doctor as soon as one becomes available. Both complexity analysis and computational analyses have shown that HESA is very efficient in solving the health examination scheduling problem. In addition to the theoretical results, the results of HESA’s application to the concrete health examination scheduling problems of two large hospitals in Taiwan are also reported.     

Forecasting transport requirements for district primary health care in Ghana: A simulation study

In rural planning in developing countries, random factors such as vehicle breakdown, weather conditions and staff availability are particularly important. These can be dealt with specially well by simulation. Transportation is also particularly important in rural areas. This paper presents a simulation study of transport requirements for a rural primary health care scheme in Ghana where the random factors are unavailability of vehicles due to repairs and unavailability of health specialists and drivers for work due to holidays, etc. The analysis gives a quick method of calculating the expected number of jobs that can be done for given numbers of vehicles, levels of availability etc. The simulation gives the corresponding probability distribution. The analysis also indicates which random factor has most effect on limiting the number of jobs that can be done. Policy conclusions are drawn regarding the number of vehicles per district and the payment of incentives to staff for good attendance.     

Column generation based heuristic for tactical planning in multi-period vehicle routing

The periodic vehicle routing problem (PVRP) consists in establishing a planning of visits to clients over a given time horizon so as to satisfy some service level while optimizing the routes used in each time period. The tactical planning model considered here restricts its attention to scheduling visits and assigning them to vehicles while leaving sequencing decisions for an underlying operational model. The objective is twofold: to optimize regional compactness of the routes in a desire to specialize routes to restricted geographical area and to balance the workload evenly between vehicles. Approximate solutions are constructed using a truncated column generation procedure followed by a rounding heuristic. This mathematical programming based procedure can deal with problems with 50–80 customers over five working days which is the range of size of most PVRP instances treated in the literature with meta-heuristics. The paper highlights the importance of alternative optimization criteria not accounted for in standard operational models and provides insights on the implementation of a column generation based rounding heuristic.     

Lagrangean heuristic for primary routes assignment in survivable connection-oriented networks

Our discussion in this article centers on the application of a Lagrangean relaxation and a subgradient optimization technique to the problem of primary route assignment (PRA) in survivable connection-oriented networks. The PRA problem consists in a static optimization of primary routes minimizing the Lost Flow in Node (LFN) function. The major contribution of this work is a combination of the Lagrangean relaxation with other heuristic algorithms. We evaluate the performance of the proposed Lagrangean-based heuristic by making a comparison with their counterparts including evolutionary algorithm and GRASP using various network topologies and demand patterns. The results of simulation tests show that the new algorithm provides sub-optimal results, which are better than other heuristics.     

A heuristic for the long-term electricity generation planning problem using the Bloom and Gallant formulation

Long-term power planning is a stochastic problem often confronted by electrical utilities in liberalized markets. One can model it for profit maximization—using market-price estimation functions for each interval—by posing it as a quadratic programming problem with some linear equalities and an exponential number of load-matching linear inequality constraints.     

A tabu search heuristic for the dynamic transportation of patients between care units

The problem studied in this paper stems from a real application to the transportation of patients in the Hospital Complex of Tours (France). The ambulance central station of the Hospital Complex has to plan the transportation demands between care units which require a vehicle. Some demands are known in advance and the others arise dynamically. Each demand requires a specific type of vehicle and a vehicle can transport only one person at a time. The demands can be subcontracted to a private company which implies high cost. Moreover, transportations are subject to particular constraints, among them priority of urgent demands, disinfection of a vehicle after the transportation of a patient with contagious disease and respect of the type of vehicle needed. These characteristics involve a distinction between the vehicles and the crews during the modeling phase. We propose a modeling for solving this difficult problem and a tabu search algorithm inspired by Gendreau et al. (1999). This method supports an adaptive memory and a tabu search procedure. Computational experiments on a real-life instance and on randomly generated instances show that the method can provide high-quality solutions for this dynamic problem with a short computation time.     

A fuzzy goal programming and meta heuristic algorithms for solving integrated production: distribution planning problem

Integrated production–distribution planning is one of the most important issues in supply chain management (SCM). We consider a supply chain (SC) network to consist of a manufacturer, with multiple plants, products, distribution centers (DCs), retailers and customers. A multi-objective linear programming problem for integrating production–distribution, which considers various simultaneously conflicting objectives, is developed. The decision maker’s imprecise aspiration levels of goals are incorporated into the model using a fuzzy goal programming approach. Due to complexity of the considered problem we propose three meta-heuristics to tackle the problem. A simple genetic algorithm and a particle swarm optimization (PSO) algorithm with a new fitness function, and an improved hybrid genetic algorithm are developed. In order to show the efficiency of the proposed methods, two classes of problems are considered and their instances are solved using all methods. The obtained results show that the improved hybrid genetic algorithm gives us the best solutions in a reasonable computational time.     

A model and two heuristic approaches for a forage harvester planning problem: a case study

This work considers a decision problem about orders of owners and routes of smallholdings for a harvester in an agricultural cooperative in which each owner has a proposal about the instant time in which he would like that the machine starts the activity in his land and the different smallholdings of each owner should be processed as a block. A binary linear programming model is introduced in order to reducing costs. Solving the model for actual size instances is computationally burdensome. Hence, we introduce and implement two heuristic algorithms to reduce the computational time. The heuristics are applied to the real case of the cooperative “Os Irmandiños” with a large number of owners and smallholdings. The numerical results show that the heuristics can solve large instances effectively with reasonable computational effort.