Balancing user preferences for aircraft schedule recovery during irregular operations

In this paper, the irregular operations problem is approached for the first time in a way that allows an airline to provide for schedule recovery with minimal deviations from the original aircraft routings. A network model with side constraints is presented in which delays and cancellations are used to deal with aircraft shortages in a way that ensures a significant portion of the original aircraft routings remain intact. The model is flexible, allowing user preferences in the objective, and thereby reflecting the immediate concerns of the decision-maker in the recovery schedule. The model can be tailored by airline operations personnel to emphasize differing solution characteristics. Fleet data provided by Continental Airlines are used to demonstrate the approach. Extensive testing indicates that optimal or near-optimal solutions are routinely obtained from the LP relaxation of the network formulation. When integrality is not achieved, a rounding heuristic is provided that finds feasible solutions within a small fraction of the optimum.     

A comparison of stochastic programming and bi-objective optimisation approaches to robust airline crew scheduling

A prominent problem in airline crew scheduling is the pairings or Tour-of-Duty planning problem. The objective is to determine a set of pairings (or Tours-of-Duty) for a crew group to minimise the planned cost of operating a schedule of flights. However, due to unforeseen events the performance in operation can differ considerably from planning, sometimes causing significant additional recovery costs. In recent years there has been a growing interest in robust crew scheduling. Here, the aim is to find solutions that are “cheap” in terms of planned cost as well as being robust, meaning that they are less likely to be disrupted in case of delays. Taking the stochastic nature of delays into account, Yen and Birge (Transp Sci 40:3–14, 2006) formulate the problem as a two-stage stochastic integer programme and develop an algorithm to solve this problem. Based on the contradictory nature of the goals, Ehrgott and Ryan (J Multi-Criteria Decis Anal 11:139–150, 2002) formulate a bi-objective set partitioning model and employ elastic constraint scalarisation to enable the solution by set partitioning algorithms commercially used in crew scheduling software. In this study, we compare the two solution approaches. We improve the algorithm of Yen and Birge (Transp Sci 40:3–14, 2006) and implement both methods with a commercial crew scheduling software. The results of both methods are compared with respect to characteristics of robust solutions, such as the number of aircraft changes for crew. We also conduct experiments to simulate the performance of the obtained solutions. All experiments are performed using actual schedule data from Air New Zealand.     

Integrated fleet assignment and aircraft routing based on delay propagation

Airlines’ expensive resources, especially aircraft, are to be optimally scheduled to cover flights of timetables. However, the irregular flight, due to bad weather, mechanical fault and so on, is inevitable. Moreover, flight delays become more severe with the rapid development of the air transport industry in China and have huge irregular flight cost. In order to alleviate flight delays impact on the flight plan, we present a double objective multi-commodity network flow model of flight delay propagation-based aircraft scheduling and minimize the total delay propagation and airline operation cost as the optimization objective. Branch-and-price solution and column generation algorithm are used to solve the problem. Computational results obtained by using data from a major domestic airline show that our approach can reduce delay propagation significantly, thus improving on-time performance and robustness of aircraft scheduling, and decreasing the total cost simultaneously.     

Air cargo scheduling: integrated models and solution procedures

Designing a profitable flight schedule is a highly complex planning problem. Both passenger and cargo airlines usually follow a decomposition approach and break this problem into several subproblems which are then solved consecutively and iteratively using specific but isolated models. At cargo airlines, the four major interdependent decision problems are flight selection, fleet assignment, rotation planning, and cargo routing. In our research, we have developed a planning approach which differs from other OR-based planning approaches in two aspects. The approach is based on integrated models and it is based on the pragmatic planning paradigm to optimally modify an existing schedule. For this purpose, the planner has to identify mandatory and optional flights. Then the planning goal is to identify the best combination of optional flights to be included into the schedule. Our integrated planning models comprise several additional important planning aspects for cargo airlines such as available capacities on external flights (e.g. belly capacities from passenger flights or road-feeder services), cargo handling costs and constraints, and aircraft maintenance regulations. There are two main aspects which we present in this paper. First, we describe the planning problem and the specific planning paradigm, develop a set of complex mixed-integer programs representing the different subproblems, and finally present integrated problem formulations as well as several model extensions. Thereafter, we develop a branch and price and cut approach for solving the mathematical programs and present extensive computational results obtained for a set of generated yet highly practical problem instances for different types of carriers. The results show that our approach is able to find high quality solutions to problem instances of realistic size and complexity within reasonable time.     

An optimization model for assigning through flights

Non-stop flights are the first choice for passengers traveling from one city to another. In the absence of such flights, passengers must take connecting services (or connections) with two or more flights. A through flight is a type of connection that uses the same aircraft for the flights involved, which enables connecting passengers to remain onboard rather than deplaning to locate their departure gates at busy airports. The convenience of through flights gives them a marketing advantage over regular connections. For this reason, airline schedulers invest significant effort in building profitable through flights into the flight schedule. We have developed an optimization model for United Airlines for constructing the set of through flights that maximizes the through revenue for a schedule. The model eliminates the manual effort involved in assigning through flights and enhances the network contribution by at least ten million dollars annually.     

Sequencing n Products Involving m Independent Jobs on m Machines

This article considers the problem of scheduling n products over m distinct machines. Every product consists of a set of jobs, each requiring a known processing time on a designated machine. There are no precedence constraints, and simultaneous processing of jobs requiring different machines within a product is allowed. The object of scheduling is to minimize a regular measure of performance associated with the products. It is shown that there exists an optimal schedule with the “no passing property.” Branch and bound routines are developed for finding the optimal solution for the two measures of performance: (1) total penalty cost; and (2) sum of product completion times. Comparisons between the optimal solution and solutions obtained using dispatching rules are given in the penalty cost case.     

Project scheduling algorithms for re-layout projects

The most common type of facility layout project is re-layout, which involves rearranging existing equipment in a facility. Project schedule development is an often overlooked yet critical portion of a facility re-layout project. When developing a re-layout project schedule, departments cannot be moved into their final locations until all previous occupants have moved. By incurring the cost of moving departments to temporary locations, it is possible to reduce the overall project duration. A two-criteria mixed-integer programming model is developed that finds the schedule minimizing department move costs subject to precedence constraints. An efficient algorithm uses this model to find all non-dominated time and cost solutions to the re-layout problem. Modifications to the basic model and algorithm handle resource constraints and turnaround space constraints. The algorithm and its modifications are demonstrated on an actual re-layout project.     

Project scheduling algorithms for re-layout projects

The most common type of facility layout project is re-layout, which involves rearranging existing equipment in a facility. Project schedule development is an often overlooked yet critical portion of a facility re-layout project. When developing a re-layout project schedule, departments cannot be moved into their final locations until all previous occupants have moved. By incurring the cost of moving departments to temporary locations, it is possible to reduce the overall project duration. A two-criteria mixed-integer programming model is developed that finds the schedule minimizing department move costs subject to precedence constraints. An efficient algorithm uses this model to find all non-dominated time and cost solutions to the re-layout problem. Modifications to the basic model and algorithm handle resource constraints and turnaround space constraints. The algorithm and its modifications are demonstrated on an actual re-layout project.     

Optimal scheduling of logistical support for an emergency roadway repair work schedule

The completion of every disaster rescue task performed by repair work teams relies on the in-time supply of materials to the rescue workers. Up to now, logistical support planning for emergency repair work in Taiwan has been done manually, which is neither effective nor efficient. To remedy the problem, this study presents a logistical support scheduling model for the given emergency repair work schedule. The objective is to minimize the short-term operating cost subject to time constraints and other related operating constraints. This model is formulated as an integer multiple-commodity network flow problem which is characterized as NP-hard. A heuristic algorithm, based on the problem decomposition and variable fixing techniques, is also proposed to efficiently solve this problem. Computational tests are performed using data from Taiwan's 1999 Chi-Chi earthquake. The results show that the model and the solution algorithm would be useful for the logistical support scheduling.     

Capacitated lot-sizing with sequence dependent setup costs

In this paper we consider a single-stage system where a number of different items have to be manufactured on one machine. Expenditures for the setups depend on the sequence in which items are scheduled on the machine. Holding costs are incurred for holding items in inventory. The demand of the items has to be satisfied without delay, i.e. shortages are not allowed. The objective is to compute a schedule such that the sum of holding and setup costs is minimized with respect to capacity constraints. For this problem which we call capacitated lot-sizing problem with sequence dependent setup costs (CLSD) we formulate a new model. The main differences between the new model and the discrete lot-sizing problem with sequence dependent setup costs (DLSDSD), introduced by Fleischmann, is that continuous lot-sizes are allowed and the setup state can be preserved over idle time. For the solution of the new model we present a heuristic which applies a priority rule. Since the priority values are affected by two significant parameters, we perform a local search in the parameter space to obtain low cost solutions. The solution quality is analyzed by a computational study. The comparison with optimal solutions of small instances shows that the solution quality of our heuristic is acceptable. The Fleischmann approach for the DLSPSD computes upper bounds for our new problem. On the basis of larger instances we show that our heuristic is more efficient to solve the CLSD.     

Integrated multi-factory production and distribution scheduling applying vehicle routing approach

This paper introduces a new integrated multi-factory production and distribution scheduling problem in supply chain management. This supply chain consists of a number of factories joined together in a network configuration. The factories produce intermediate or finished products and supply them to other factories or to end customers that are distributed in various geographical zones. The problem consists of finding a production schedule together with a vehicle routing solution simultaneously to minimise the sum of tardiness cost and transportation cost. A mixed-integer programming model is developed to tackle the small-sized problems using CPLEX, optimally. Due to the NP-hardness, to deal with medium- and large-sized instances, this paper develops a novel Improved Imperialist Competitive Algorithm (IICA) employing a local search based on simulated annealing algorithm. Performance of the proposed IICA is compared with the optimal solution and also with four variants of population-based metaheuristics: Imperialist Competitive Algorithm, Genetic Algorithm, Particle Swarm Optimisation (PSO), and Improved PSO. Based on the computational results, it is statistically shown that quality of the IICA’s solutions is the same as optimal ones solving small problems. It also outperforms other algorithms in finding near-optimal solutions dealing with medium and large instances in a reasonably short running time.     

An automated approach for planning mass tactical airborne operations

This paper develops an automated approach to plan for mass tactical airborne operations. This proposed tool enables the user to properly load aircraft according to the mission and user specifications, so that the minimum amount of time is required to seize all assigned objectives. The methodology is based on a hybrid approach in which the first portion is a mathematical model that provides the optimal manifest under “perfect conditions”. This mathematical model is represented by a transportation network, and can be optimized using a transportation algorithm. The optimum solution from the mathematical model is input to a simulation model that introduces the inherent variability induced by wind conditions, drift, aircraft location and speed, and delays between jumper exit times. The simulation returns the expected, best, and worst arrival times to the assigned objectives. This hybrid approach allows a large problem to be solved efficiently with a great deal of time saving.     

Flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints

The purpose of this research is to solve flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints in the operations. We first formulate the problem as a Mixed-Integer Linear Program (MILP). The MILP can be used to compute optimal solutions for small-sized problems. We also developed a heuristic algorithm that can obtain a good solution for the problem regardless of its size. Moreover, we have developed a representation and schedule builder that always produces a legal and feasible solution for the problem, and developed genetic and tabu search algorithms based on the proposed schedule builder. The results of the computational experiments show that the developed meta-heuristics are very effective.     

A Compromise Programming to Task Assignment Problem in Software Development Project

The scheduling process that aims to assign tasks to members is a difficult job in project management. It plays a prerequisite role in determining the project’s quality and sometimes winning the bidding process. This study aims to propose an approach based on multi-objective combinatorial optimization to do this automatically. The generated schedule directs the project to be completed with the shortest critical path, at the minimum cost, while maintaining its quality. There are several real-world business constraints related to human resources, the similarity of the tasks added to the optimization model, and the literature’s traditional rules. To support the decision-maker to evaluate different decision strategies, we use compromise programming to transform multi-objective optimization (MOP) into a single-objective problem. We designed a genetic algorithm scheme to solve the transformed problem. The proposed method allows the incorporation of the model as a navigator for search agents in the optimal solution search process by transferring the objective function to the agents’ fitness function. The optimizer can effectively find compromise solutions even if the user may or may not assign a priority to particular objectives. These are achieved through a combination of non-preference and preference approaches. The experimental results show that the proposed method worked well on the tested dataset.     

A new intelligent approach for air traffic control using gravitational search algorithm

Aircraft landing planning (ALP) is one of the most important challenging problems in the domain of air traffic control (ATC). Solving this NP-hard problem is a valuable aid in organizing air traffic in terminal control area (TCA), which itself leads to a decrease in aircraft fuel consumption, costs of airlines, and workload undertaken by air traffic controllers. In the present paper, the ALP problem is dealt with by applying effective rich knowledge to the optimization process (to remove obvious non-optimal solutions), and the first use of Gravitational Search Algorithm (GSA) in resolving such a case. In this regard, while the specific regulations for safe separation have been observed, the optimal landing time, the optimal runway, and the order of consecutive landings have been determined so that the main goal (minimizing total flight delays) would be best met. Results of simulations show that this approach, compared to previous ones, which are based on Genetic and Bionomic algorithms, GLS, and Scatter search method, considerably decreases total flight delays. Attaining zero in the total flight delays in three scenarios with real data shows that the suggested intelligent approach is more decisive than others in finding an optimal solution.     

An efficient technique to solve combined economic and emission dispatch problem using modified Ant colony optimization

Economic load dispatch is one of the vital purposes in electrical power system operation, management and planning. Economic dispatch problem is one of the most important problems in electric power system operation. In large scale system, the problem is more complex and difficult to find out optimal solution because it is nonlinear function and it contains number of local optimal. Combined economic emission dispatch (CEED) problem is to schedule the committed generating units outputs to meet the required load demand at minimum operating cost with minimum emission simultaneously. The main aim of economic load dispatch is to reduce the total production cost of the generating system and at the same time the necessary equality and inequality constraints should also be fulfilled. This leads to the development of CEED techniques. There are various techniques proposed by several researchers to solve CEED problem based on optimization techniques. But still some problems such as slower convergence and higher computational complexity exist in using the optimization techniques such as GA for solving CEED problem. This paper proposes an efficient and reliable technique for combined fuel cost economic optimization and emission dispatch using the Modified Ant Colony Optimization algorithm (MACO) to produce better optimal solution. The simulation results reveal the significant performance of the proposed MACO approach.     

On discrete lot streaming in no-wait flow shops

Lot streaming is the process of splitting a job or lot to allow overlapping between successive operations in a multistage production system. This use of transfer lots usually results in a substantially shorter makespan for the corresponding schedule. In this paper, we study the discrete lot streaming problem for a single job in no-wait flow shops. We present a new linear programming formulation for the problem. We show that the optimal solutions are the same for the m ×2 case with or without no-wait constraints. We also present a fast, polynomial-time solution method for this case. For the general case, we prove that any solution which is 'close' to the continuous optimal solution will be a good approximation for the discrete problem. This property allows us to present two quickly obtainable approximations of very good quality.     

Methodology for the optimal component selection of electronic devices under reliability and cost constraints

The objective of this paper is to present an efficient computational methodology for the reliability optimization of electronic devices under cost constraints. The system modeling for calculating the reliability indices of the electronic devices is based on Bayesian networks using the fault tree approach, in order to overcome the limitations of the series–parallel topology of the reliability block diagrams. Furthermore, the Bayesian network modeling for the reliability analysis provides greater flexibility for representing multiple failure modes and dependent failure events, and simplifies fault diagnosis and reliability allocation. The optimal selection of components is obtained using the simulated annealing algorithm, which has proved to be highly efficient in complex optimization problems where gradient‐based methods can not be applied. The reliability modeling and optimization methodology was implemented into a computer program in Matlab using a Bayesian network toolbox. The methodology was applied for the optimal selection of components for an electrical switch of power installations under reliability and cost constraints. The full enumeration of the solution space was calculated in order to demonstrate the efficiency of the proposed optimization algorithm. The results obtained are excellent since a near optimum solution was found in a small fraction of the time needed for the complete enumeration (3%). All the optimum solutions found during consecutive runs of the optimization algorithm lay in the top 0.3% of the solutions that satisfy the reliability and cost constraints. Copyright © 2007 John Wiley & Sons, Ltd.     

Economic-emission load dispatch using binary successive approximation-based evolutionary search

A novel binary successive approximation-based evolutionary search strategy has been proposed to solve the economic-emission load dispatch problem by searching the generation pattern of committed units. Inequality constraints are taken care of during the search of a generation pattern. To meet the demand, a slack generator is introduced to compensate the perturbation of unmet load during the search. To determine the trade-off relationship between conflicting objectives in the non-inferior domain, the weighting method is exploited. Once the trade-off has been obtained, fuzzy set theory helps the decision maker to choose the optimal operating point over the trade-off curve and adjust the generation schedule in the most preferred manner. Generally the weights are regulated in a systematic manner, which is a time-consuming process. To reduce the time to arrive at the best compromising solutions, the weight pattern assigned to objectives are searched for more significant digits in a fixed number of iterations. Performance of the algorithm is investigated on economic load dispatch problems of different sizes and complexity having non-convex cost curves where conventional gradient-based methods are inapplicable. This technique has emerged as the useful optimisation tool for handling network losses, ramp rate limits, valve point loading and prohibited zone avoidance into account to determine the global optimal dispatch solution as well as optimal operating point in the noninferior domain for any number of the goals. The method is applied on various test systems and better results are achieved with reference to emission (Kg/h), however when compared with other techniques, the proposed method has lower performance with reference to losses (MW) and cost ($/h).     

Multiple machine JIT scheduling: a tabu search approach

This paper presents an approach to solving the multiple machine, non-preemptive, earliness-tardiness scheduling problem with unequal due dates in a flow shop with machine tiers (FMT). In this variant of the flow shop problem, machines are arranged in tiers or groups, and the jobs must visit one machine in each tier. The processing times, machine assignments, and due dates are deterministic and known in advance. The objective is to find a permutation schedule that minimizes the total deviation of each job from its due date. A tabu search (TS) meta-heuristic combined with an LP evaluation function is applied to solve this problem and results are compared to optimal permutation solutions for small problems and the earliest due date schedule for large problems. Several neighborhood generation methods and two diversification strategies are examined to determine their effect on solution quality. Results show that the TS method works well for this problem. TS found the optimal solution in all but one of the small problem instances and improved the earliest due date solutions for larger instances where no optimal solutions could be found.