Integrated dynamic single-facility location and inventory planning problems

We consider the dynamic facility location problem with generalized modular capacities, a multiperiod facility location problem in which the costs for capacity changes may differ for all pairs of capacity levels. The problem embeds a complex cost structure and generalizes several existing facility location problems, such as those that allow temporary facility closing or capacity expansion and reduction. As the model may become very large, general-purpose mixed-integer programming (MIP) solvers are limited to solving instances of small to medium size. In this paper, we extend the generalized model to the case of multiple commodities. We propose Lagrangian heuristics, based on subgradient and bundle methods, to find good quality solutions for large-scale instances with up to 250 facility locations and 1,000 customers. To improve the final solution quality, a restricted MIP model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian-based heuristics provide highly reliable results for all problem variants considered. They produce good quality solutions in short computing times even for instances where state-of-the-art MIP solvers do not find feasible solutions. The strength of the formulation also allows the method to provide tight bounds on the optimal value. Data and the online appendix are available at https://doi.org/10.1287/ijoc.2016.0738 .

This paper introduces a variant of the dynamic Facility Location Problem with modular capacities. Inspired by the challenges faced by cellular telecommunication networks, the problem seeks to optimize the placement and equipment of facilities to meet the fluctuating demand of clients while minimizing installation and operational costs. Selected facilities must provide coverage to the whole considered area. In addition, clients must be served by the active facility that provides the best quality of service. We propose two integer linear programming formulations and analyze their theoretical properties in terms of lower bound. Furthermore, we propose a reinforcement for one formulation and valid inequalities. To evaluate the performance of the proposed formulations, we performed computational experiments with a commercial solver on instances with up to 20 candidate sites and 60 clients. The formulations proved to be very sensitive to the size of the instances. The analysis, both theoretical and numerical, provides meaningful insights on the formulations performance, and it constitutes a key starting point for developing further approaches, either exact methods or heuristics.

The design of logistic distribution systems is one of the most critical and strategic issues in industrial facility management. The aim of this study is to develop and apply innovative mixed integer programming optimization models to design and manage dynamic (i.e. multi-period) multi-stage and multi-commodity location allocation problems (LAP). LAP belong to the NP-hard complexity class of decision problems, and the generic occurrence requires simultaneous determination of the number of logistic facilities (e.g. production plants, warehousing systems, distribution centres), their locations, and assignment of customer demand to them. The proposed models use a mixed integer linear programming solver to find solutions in complex industrial applications even when several entities are involved (production plants, distribution centres, customers, etc.). Lastly, the application of the proposed models to a significant case study is presented and discussed.

The economics of the thermohaline circulation—A problem with multiple thresholds of unknown locations

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical dynamic programming (DP) algorithms guarantee optimal solutions, but scale badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP), which aims to combine the strengths of learned neural heuristics with those of DP algorithms. DPDP prioritizes and restricts the DP state space using a policy derived from a deep neural network, which is trained to predict edges from example solutions. We evaluate our framework on the travelling salesman problem (TSP), the vehicle routing problem (VRP) and TSP with time windows (TSPTW) and show that the neural policy improves the performance of (restricted) DP algorithms, making them competitive to strong alternatives such as LKH, while also outperforming most other ‘neural approaches’ for solving TSPs, VRPs and TSPTWs with 100 nodes.KeywordsDynamic ProgrammingDeep LearningVehicle Routing

Multi-class hazmat distribution network design with inventory and superimposed risks

Dynamic facility location problems consider situations where it is important to decide not only where but also when to open (or close) facilities, given a planning time horizon. Considering explicitly multiple time periods is especially important if assignment costs are expected to change significantly in the future and relocating facilities is expensive. The majority of models presented in the literature considers binary decision variables that define whether facilities are open in a given time period. In addition, if a facility is first opened at some time period then clients can usually be assigned to it from that period forward, without any guarantee that the facility will be operational at the planned time period. In this paper, a new mathematical model is presented where uncertainty in the setup time of facilities is explicitly considered. This means that the decision maker is only capable of deciding where to locate facilities and when to begin all the necessary works to get the facilities operational, but the time elapsed until opening the facility is not known for sure. A primal-dual heuristic is also developed for this problem and its performance is compared with the performance of a commercial exact solver.

A variable-scale dynamic clustering method

Approximation algorithms for the dynamic k-level facility location problems

Research on dynamic and stochastic vehicle routing problems received increasing interest in the last decade. It considers a novel problem class, aiming at an appropriate handling of dynamic events combined with the incorporation of stochastic information about possible future events. This survey summarises the recent literature in this area. Besides, the classification according to the available stochastic information, a new classification based on the point in time where substantial computational effort for determining decisions or decision policies arises, is introduced. Furthermore, the difference in solution quality is analysed between approaches which consider either purely dynamic or stochastic problems compared to those which consider both, stochastic and dynamic aspects. A graphical representation demonstrates the strength of the reviewed approaches incorporating dynamic and stochastic information. The survey also gives an overview on the intensity of research for the different problem classes and its benefit in recent years. Finally, guidelines and promising directions for further research are presented.

In this paper, we consider a class of optimal control problems in which the system is to be determined in an optimal way. This class of problems involves the choice of a fixed number of switching time points which divide the system’s time horizon into a number of time periods. For each of these time periods, a subsystem is selected, from a finite number of given candidate subsystems, to run during that time periods. The choice of the switching points and the selection of the subsystems are carried out in such a way that a given cost functional is minimized. We consider only problems involving ordinary differential equations over a finite time horizon. A computational method is developed for solving these problems. In our method, the candidate subsystems are combined into a single system by considering their ‘linear combination’. By introducing suitable constraints on the coefficients of the linear combination and using a time rescaling technique, the original problem is transformed into an equivalent optimal control problem with system parameters. An algorithm is proposed for solving this transformed problem and the required gradient formulae are derived. To show the effectiveness of the method, a numerical example is solved.

A fuzzy programming approach for dynamic virtual hub location problem

Problem solving is one of the major paradigms in Artificial Intelligence research in which an intelligent task to automate is interpreted as a series of problems to be solved. Various problem solving techniques have been spawned in the field of AI, mostly by concentrating on a certain reasoning approach to tackle a particular class of problems. For instance, theorem proving, constraint solving and machine learning provide powerful techniques for solving AI problems. In all these approaches, background knowledge needs to be provided, from which the system will infer new knowledge. Often, however, in real world scenarios, there may not be enough background information for any single solver to solve the problem. In these situations, some researches have demonstrated the benefits of using combined reasoning, i.e., a reasoning process which employs various, often disparate, problem solving techniques in concert, in order to solve a given task. The systems that engage such reasoning processes are called combined reasoning systems. Their power draws upon disparate techniques they employ. As such, combined reasoning systems are supposed to be more capable than their constituents. In this thesis we mainly focus on using a combined reasoning approach in solving a type of problems that cannot be solved by any of the aforementioned standalone systems. We refer to this type as investigation problem which models to some extent a generic situation which might arise in, say, medical diagnosis or the solving of a crime. That is, there are a number of possible diagnoses/suspects (candidates), and the problem is to use the facts of the case to rank them in terms of their likelihood of being the cause of the illness/guilty of the crime. Such ranking often leads to further medical tests/police enquiries focusing on the most likely candidates, which will bring to light further information about the current case. We use the term dynamic investigation problems to describe a series of such problems to be solved. Solving each problem entails using the facts of the case, coupled with prior knowledge about the domain to narrow down the candidates to just one. However, when there is no upright solution due to lack of some essential information, additional relevant information can often be found in related past cases thereby irregularities can be observed and utilized. Hence, dynamic investigation problems are hybrid machine-learning/constraint solving problems, and as such are more realistic and of interest to the wider AI community. In this thesis we focus on formal definition, exploration, generation and solution of “Dynamic Investigation Problems”, and we develop a framework which performs “Investigative Reasoning”, that is a framework in which a combination of reasoning techniques are incorporated in order to tackle dynamic investigation problems.

In this paper a memetic algorithm integrating genetic procedures and local search, able to solve capacitated and uncapacitated dynamic location problems, is described. These problems are characterized by explicitly considering the possibility of a facility being opened, closed and reopened more than once during the planning horizon. It is also possible to explicitly consider different open and reopen fixed costs. The problems can be of single or multi-level nature. The computational results obtained show that the algorithm is capable of finding good quality solutions, but at the cost of large computational times, when compared with dedicated primal-dual heuristics and even with a general solver. Some changes are proposed to tackle this disadvantage.

Recently, Multitask learning, which can cope with several tasks, has attracted much attention. Multitask Reinforcement Learning introduced by Tanaka et al is a problem class where number of problem instances of Markov Decision Processes sampled from the same probability distributions is sequentially given to reinforcement learning agents. The purpose of solving this problem is to realize adaptive agents for newly given environments by using knowledge acquired from past experience. Evolutionary Algorithms are often used to solve reinforcement learning problems if problem classes are quite different with Markov Decision Processes or state-action space is quite huge. From the viewpoint of Evolutionary Algorithms studies, the Multitask Reinforcement Learning problems are regarded as dynamic problems whose fitness landscape has changed temporally. In this paper, a memory-based Evolutionary Programming which is suitable for Multitask Reinforcement Learning problems is proposed.