Scheduling aerial resource operations for the extinction of large-scale wildfires

The significant increase in large-scale wildfire events in recent decades, caused primarily by climate change, has resulted in a growing number of aerial resources being used in suppression efforts. Present-day management lacks efficient and scalable algorithms for complex aerial resource allocation and scheduling for the extinction of such fires, which is crucial to ensuring safety while maximizing the efficiency of operations. In this work, we present a Mixed Integer Linear Programming (MILP) optimization model tailored to large-scale wildfires for the daily scheduling of aerial operations. The main objective is to achieve a prioritized target water flow over all areas of operation and all time periods. Minimal target completion across individual areas and time periods and total water output are also maximized as secondary and ternary objectives, respectively. An efficient and scalable multi-start heuristic, combining a randomized greedy approach with simulated annealing employing large neighborhood search techniques, is proposed for larger instances. A diverse set of problem instances is generated with varying sizes and extinction strategies to test the approaches. Results indicate that the heuristic can achieve (near)-optimal solutions for smaller instances solvable by the MILP, and gives solutions approaching target water flows for larger problem sizes. The algorithm is parallelizable and has been shown to give promising results in a small number of iterations, making it applicable for both night-before planning and, more time-sensitive, early-morning scheduling.     

A multi-depot dial-a-ride problem with heterogeneous vehicles and compatibility constraints in healthcare

In this paper, a multi-depot dial-a-ride problem arising from a real-world healthcare application is addressed, concerning the non-emergency transportation of patients. The problem presents several constraints and features, such as heterogeneous vehicles, vehicle–patient compatibility constraints, quality of service requirements, patients׳ preferences, tariffs depending on the vehicles׳ waiting. Variable Neighborhood Search and Tabu Search algorithms are proposed able to tackle all the characteristics of the problem. A Mixed Integer Linear Programming formulation is also presented. Computational results on large real-world and random instances based on real data show the effectiveness of the proposed approaches.     

Robust multi-sensor scheduling for multi-site surveillance

This paper presents mathematical programming techniques for solving a class of multi-sensor scheduling problems. Robust optimization problems are formulated for both deterministic and stochastic cases using linear 0–1 programming techniques. Equivalent formulations are developed in terms of cardinality constraints. We conducted numerical case studies and analyzed the performance of optimization solvers on the considered problem instances.     

Subcontracting price schemes for order acceptance and scheduling

In this paper we study subcontracting price schemes between a subcontractor and a firm that are engaged in subcontracting of heterogeneous orders with distinct due dates, revenues, and processing times. We assume that the subcontractor proposes the subcontracting pricing and the firm follows by determining the subcontracted orders by solving its order acceptance and scheduling problem. When the subcontractor adopts a linear pricing scheme, we find the firm׳s optimal decisions and develop an algorithm to derive the subcontractor׳s own optimal pricing. We then design a fixed pricing with transfer payment scheme and a quantity discount pricing scheme to coordinate the firm׳s and subcontractor׳s decisions. We examine if the subcontractor can make a higher profit using either of these schemes than the linear pricing scheme, and if they will induce the firm to make decisions that lead to system-wide optimal outcomes.     

Incorporating balance concerns in resource allocation decisions: A bi-criteria modelling approach

We consider resource allocation problems where inputs are allocated to different entities such as activities, projects or departments. In such problems a common goal is achieving a desired balance in the allocation over different categories of the entities. We propose a bi-criteria framework for trading balance off against efficiency. We define and categorise indicators based on balance distribution and propose formulations and solution algorithms which provide insight into the balance-efficiency tradeoff. We illustrate our models by applying them to the data of a portfolio selection problem faced by a science funding agency and to randomly generated large-sized problem instances to demonstrate computational feasibility.     

A NOTE ON USER SOLUTION STRATEGY FOR MIXED-INTEGER LINEAR PROGRAMMING MODELS

Large-scale mixed-integer linear programming (MILP) models may easily prove extraordinarily difficult to solve, even with efficient commercially implemented MILP solution codes. Drawing on experience gained in solving and analyzing three intertemporal investment planning MILP models for electric power supply, this note offers several practical suggestions for reducing computer solution times for general production-allocation MILP models. Solution time reduction stems from judicious use of the powerful computational capabilities of existing commercial linear programming codes in conjunction with information known or to be learned by the practitioner about the model's structure.     

A shelf-space optimization model when demand is stochastic and space-elastic

The more customer demand is impulse-driven, the more it is space-dependent and the more it is subject to variation. We investigate the corresponding problem of retail shelf-space planning when demand is stochastic and sensitive to the number and position of facings. We develop a model to maximize a retailer׳s profit by selecting the number of facings and their shelf position under the assumption of limited space. The model is particularly applicable to promotional or temporary products.We develop the first optimization model and solution approach that takes stochastic demand into account, since the current literature applies deterministic models for shelf-space planning. By the means of an innovative modeling approach for the case with space- and positioning effects and the conversion of our problem into a mixed-integer problem, we obtain optimal results within very short run times for large-scale instances relevant in practice. Furthermore, we develop a solution approach to account for cross-space elasticity, and solve it using an own heuristic, which efficiently yields near-optimal results. We demonstrate that correctly considering space elasticity and demand variation is essential. The corresponding impacts on profits and solution structures become even more significant when space elasticity and stochastic demand interact, resulting in up to 5% higher profits and up to 80% differences in solution structures, if both effects are correctly accounted for. We develop an efficient modeling approach, compare the model results with approaches applied in practice and derive rules-of-thumb for planners.     

Revised GRASP with path-relinking for the linear ordering problem

The linear ordering problem (LOP) is an NP\mathcal{NP}-hard combinatorial optimization problem with a wide range of applications in economics, archaeology, the social sciences, scheduling, and biology. It has, however, drawn little attention compared to other closely related problems such as the quadratic assignment problem and the traveling salesman problem. Due to its computational complexity, it is essential in practice to develop solution approaches to rapidly search for solution of high-quality. In this paper we propose a new algorithm based on a greedy randomized adaptive search procedure (GRASP) to efficiently solve the LOP. The algorithm is integrated with a Path-Relinking (PR) procedure and a new local search scheme. We tested our implementation on the set of 49 real-world instances of input-output tables (LOLIB instances) proposed in Reinelt (Linear ordering library (LOLIB) 2002). In addition, we tested a set of 30 large randomly-generated instances proposed in Mitchell (Computational experience with an interior point cutting plane algorithm, Tech. rep., Mathematical Sciences, Rensellaer Polytechnic Institute, Troy, NY 12180-3590, USA 1997). Most of the LOLIB instances were solved to optimality within 0.87 seconds on average. The average gap for the randomly-generated instances was 0.0173% with an average running time of 21.98 seconds. The results indicate the efficiency and high-quality of the proposed heuristic procedure.     

Aircraft routing and crew pairing: Updated algorithms at Air France

Aircraft routing and crew pairing problems aim at building the sequences of flight legs operated respectively by airplanes and by crews of an airline. Given their impact on airlines operating costs, both have been extensively studied for decades. Our goal is to provide reliable and easy to maintain frameworks for both problems at Air France. We propose simple approaches to deal with Air France current setting. For routing, we introduce an exact compact IP formulation that can be solved to optimality by current MIP solvers in at most a few minutes even on Air France largest instances. Regarding crew pairing, we provide a methodology to model the column generation pricing subproblem within a new resource constrained shortest path framework recently introduced by the first author. This new framework, which can be used as a black-box, leverages on bounds to discard partial solutions and speed-up the resolution. The resulting approach enables to solve to optimality Air France largest instances. Recent literature has focused on integrating aircraft routing and crew pairing problems. As a side result, we are able to solve to near optimality large industrial instances of the integrated problem by combining the aforementioned algorithms within a simple cut generating method.     

A heuristic framework for the bi-objective enhanced index tracking problem

The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation.     

Governance Considerations for Seeker–Solver Relationships: A Knowledge‐Based Perspective in Crowdsourcing for Innovation Contests

The need to solve innovation problems and insource knowledge has led to an increasing number of organizations engaging in crowdsourcing activities and subsequently establishing working relationships with winning solution providers. Using a knowledge‐based view and the problem‐solving perspective, we develop a theoretical framework suggesting how specific innovation problem attributes (i.e. the decomposability, formulation and search space of the problem) influence the governance decision (unilateral vs. bilateral) of seekers to manage the relationship with winning solvers. We empirically analyse the framework using 582 challenges broadcast on the NineSigma crowdsourcing platform. Our results indicate that problem attributes – the formulation and search space of the problem – have a positive effect on seekers’ preference towards unilateral governance structures. However, we did not find any empirical confirmation of the effect that the decomposability of the innovation problem has on seekers’ preference towards unilateral governance structures. This study offers several contributions to the crowdsourcing literature, and also has important implications for managers of organizations aiming to insource knowledge through crowdsourcing for innovation contests.     

Exact and heuristic methods for a class of selective newsvendor problems with normally distributed demands

In this paper we study a class of selective newsvendor problems, where a decision maker has a set of raw materials each of which can be customized shortly before satisfying demand. The goal is then to select which subset of customizations maximizes expected profit. We show that certain multi-period and multi-product selective newsvendor problems fall within our problem class. Under the assumption that the demands are independent and normally, but not necessarily identically, distributed we show that some problem instances from our class can be solved efficiently using an attractive sorting property that was also established in the literature for some related problems. For our general model we use the KKT conditions to develop an exact algorithm that is efficient in the number of raw materials. In addition, we develop a class of heuristic algorithms. In a numerical study, we compare the performance of the algorithms, and the heuristics are shown to have excellent performance and running times as compared to available commercial solvers.     

Strong formulation for the spot 5 daily photograph scheduling problem

Earth observation satellites, such as the SPOT 5, take photographs of the earth according to consumers’ demands. Obtaining a good schedule for the photographs is a combinatorial optimization problem known in the literature as the daily photograph scheduling problem (DPSP). The DPSP consists of selecting a subset of photographs, from a set of candidates, to different cameras, maximizing a profit function and satisfying a large number of constraints. Commercial solvers, with standard integer programming formulations, are not able to solve some DPSP real instances available in the literature. In this paper we present a strengthened formulation for the DPSP, based on valid inequalities arising in node packing and 3-regular independence system polyhedra. This formulation was able, with a commercial solver, to solve to optimality all those instances in a short computation time.     

Problem Formulation and Solution Mechanisms: A Behavioral Study of Humanitarian Transportation Planning

When dealing with urgent, ill‐defined problems, such as rapidly evolving emergency situations, operations managers have little time for problem formulation or solution. While the mechanisms by which humans formulate and solve problems have been described, mechanisms for rapid, concurrent formulating and solving are not well understood. This study investigates these mechanisms through a field study of transportation planning in a humanitarian response setting. The findings show that the problem is solved through greedy search and formulated through sensemaking, in which search enables updates to an evolving problem formulation, and the formulation directs and limits the search process. This study explores the implications of these findings for the development of better problem formulation processes and problem‐solving strategies for urgent and ill‐defined operations management problems.     

求解不允许卖空证券组合前沿的区间搜索方法

综合分析了不允许卖空时证券组合前沿的构成和性质 ,在此基础上给出了求解不允许卖空时证券组合前沿的区间搜索方法 .应用该方法可以方便迅速地求出带有大型协方差矩阵的非负证券组合前沿及构成前沿的全部抛物的解析式 .对于大型证券组合优化问题的求解以及最优证券组合选择理论和方法的实用化具有重要的理论意义和实用价值     

Scheduling internal audit activities: a stochastic combinatorial optimization problem

The problem of finding the optimal timing of audit activities within an organisation has been addressed by many researchers. We propose a stochastic programming formulation with Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) certainty-equivalent models. In experiments neither approach dominates the other. However, the CP approach is orders of magnitude faster for large audit times, and almost as fast as the MILP approach for small audit times. This work generalises a previous approach by relaxing the assumption of instantaneous audits, and by prohibiting concurrent auditing.     

Job-shop scheduling-joint consideration of production,transport, and storage/retrieval systems

This paper proposes a new problem by integrating the job shop scheduling, the part feeding, and the automated storage and retrieval problems. These three problems are intertwined and the performance of each of these problems influences and is influenced by the performance of the other problems. We consider a manufacturing environment composed of a set of machines (production system) connected by a transport system and a storage/retrieval system. Jobs are retrieved from storage and delivered to a load/unload area (LU) by the automated storage retrieval system. Then they are transported to and between the machines where their operations are processed on by the transport system. Once all operations of a job are processed, the job is taken back to the LU and then returned to the storage cell. We propose a mixed-integer linear programming (MILP) model that can be solved to optimality for small-sized instances. We also propose a hybrid simulated annealing (HSA) algorithm to find good quality solutions for larger instances. The HSA incorporates a late acceptance hill-climbing algorithm and a multistart strategy to promote both intensification and exploration while decreasing computational requirements. To compute the optimality gap of the HSA solutions, we derive a very fast lower bounding procedure. Computational experiments are conducted on two sets of instances that we also propose. The computational results show the effectiveness of the MILP on small-sized instances as well as the effectiveness, efficiency, and robustness of the HSA on medium and large-sized instances. Furthermore, the computational experiments clearly shown that importance of optimizing the three problems simultaneous. Finally, the importance and relevance of including the storage/retrieval activities are empirically demonstrated as ignoring them leads to wrong and misleading results.

     

A genetic algorithm-based decomposition approach to solve an integrated equipment-workforce-service planning problem

We develop a new genetic algorithm to solve an integrated Equipment-Workforce-Service Planning problem, which features extremely large scales and complex constraints. Compared with the canonical genetic algorithm, the new algorithm is innovative in four respects: (1) The new algorithm addresses epistasis of genes by decomposing the problem variables into evolutionary variables, which evolve with the genetic operators, and the optimization variables, which are derived by solving corresponding optimization problems. (2) The new algorithm introduces the concept of Capacity Threshold and calculates the Set of Efficient and Valid Equipment Assignments to preclude unpromising solution spaces, which allows the algorithm to search much narrowed but promising solution spaces in a more efficient way. (3) The new algorithm modifies the traditional genetic crossover and mutation operators to incorporate the gene dependency in the evolutionary procedure. (4) The new algorithm proposes a new genetic operator, self-evolution, to simulate the growth procedure of an individual in nature and use it for guided improvements of individuals. The new genetic algorithm design is proven very effective and robust in various numerical tests, compared to the integer programming algorithm and the canonical genetic algorithm. When the integer programming algorithm is unable to solve the large-scale problem instances or cannot provide good solutions in acceptable times, and the canonical genetic algorithm is incapable of handling the complex constraints of these instances, the new genetic algorithm obtains the optimal or close-to-optimal solutions within seconds for instances as large as 84 million integer variables and 82 thousand constraints.     

Solving the maximum vertex weight clique problem via binary quadratic programming

In recent years, the general binary quadratic programming (BQP) model has been widely applied to solve a number of combinatorial optimization problems. In this paper, we recast the maximum vertex weight clique problem (MVWCP) into this model which is then solved by a probabilistic tabu search algorithm designed for the BQP. Experimental results on 80 challenging DIMACS-W and 40 BHOSLIB-W benchmark instances demonstrate that this general approach is viable for solving the MVWCP problem.     

Pareto mimic algorithm: An approach to the team orienteering problem

The team orienteering problem is an important variant of the vehicle routing problem. In this paper, a new algorithm, called Pareto mimic algorithm, is proposed to deal with it. This algorithm maintains a population of incumbent solutions which are updated using Pareto dominance. It uses a new operator, called mimic operator, to generate a new solution by imitating an incumbent solution. Furthermore, to improve the quality of a solution, it employs an operator, called swallow operator which attempts to swallow (or insert) an infeasible node and then repair the resulting infeasible solution. A comparative study supports the effectiveness of the proposed algorithm, especially, our algorithm can quickly find new better results for several large-scale instances. We also demonstrate that Pareto mimic algorithm can be generalized to solve other routing problems, e.g., the capacitated vehicle routing problem.