A multi-dimensional shooting algorithm for the two-facility location–allocation problem with dense demand

We develop an efficient allocation-based solution framework for a class of two-facility location–allocation problems with dense demand data. By formulating the problem as a multi-dimensional boundary value problem, we show that previous results for the discrete demand case can be extended to problems with highly dense demand data. Further, this approach can be generalized to non-convex allocation decisions. This formulation is illustrated for the Euclidean metric case by representing the affine bisector with two points. A specialized multi-dimensional shooting algorithm is presented and illustrated on an example. Comparisons with two alternative methods through a computational study confirm the efficiency of the proposed methodology.     

Discrete approximation heuristics for the capacitated continuous location–allocation problem with probabilistic customer locations

The capacitated continuous location–allocation problem, also called capacitated multisource Weber problem (CMWP), is concerned with locating m facilities in the Euclidean plane, and allocating their capacity to n customers at minimum total cost. The deterministic version of the problem, which assumes that customer locations and demands are known with certainty, is a nonconvex optimization problem. In this work, we focus on a probabilistic extension referred to as the probabilistic CMWP (PCMWP), and consider the situation in which customer locations are randomly distributed according to a bivariate probability distribution. We first formulate the discrete approximation of the problem as a mixed-integer linear programming model in which facilities can be located on a set of candidate points. Then we present three heuristics to solve the problem. Since optimal solutions cannot be found, we assess the performance of the heuristics using the results obtained by an alternate location–allocation heuristic that is originally developed for the deterministic version of the problem and tailored by us for the PCMWP. The new heuristics depend on the evaluation of the expected distances between facilities and customers, which is possible only for a few number of distance function and probability distribution combinations. We therefore propose approximation methods which make the heuristics applicable for any distance function and probability distribution of customer coordinates.     

Uncertain location–allocation decisions for a bi-objective two-stage supply chain network design problem with environmental impacts

In the cases that the historical data of an uncertain event is not available, belief degree-based uncertainty theory is a useful tool to reflect such uncertainty. This study focuses on uncertain bi-objective supply chain network design problem with cost and environmental impacts under uncertainty. As such network may be designed for the first time in a geographical region, this problem is modelled by the concepts of belief degree-based uncertainty theory. This article is almost the first study on belief degree-based uncertain supply chain network design problem with environmental impacts. Two approaches such as expected value model and chance-constrained model are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by some multi-objective optimization approaches of the literature such as TH, Niroomand, MMNV. A deep computational study with several test problems are performed to study the performance of the crisp models and the solution approaches. According to the results, the obtained crisp formulations are highly sensitive to the changes in the value of the cost parameters. On the other hand, Niroomand and MMNV solution approaches perform better than other solution approaches from the solution quality point of view.     

A revised ant algorithm for solving location–allocation problem with risky demand in a multi-echelon supply chain network

This study addresses a capacitated facility location and task allocation problem of a multi-echelon supply chain against risky demands. Two and three-echelon networks are considered to maximize profit. The study represents the problem by a bi-level stochastic programming model. The revised ant algorithm proposed in the study improves the existing ant algorithm by using new design of heuristic desirability and efficient greedy heuristics to solve the problem. A set of computational experiments is reported to not only allow to fine-tune the parameters of the algorithm but also to evaluate its performance for solving the problem proposed. Experiments reveal that the proposed solution algorithm can reach 95–99% of the optimal solution against risky demands while consuming only 1000th of the computational time for large-sized problems as compared to an optimization-based tool.     

A study on facility location–allocation problem in mixed environment of randomness and fuzziness

In logistics system, facility location–allocation problem, which can be used to determine the mode, the structure and the form of the whole logistics system, is a very important decision problem in the logistics network. It involves locating plants and distribution centers, and determining the best strategy for allocation the product from the plants to the distribution centers and from the distribution centers to the customers. Often uncertainty may be associated with demand, supply or various relevant costs. In many cases, randomness and fuzziness simultaneously appear in a system, in order to describe this phenomenon; we introduce the concept of hybrid variable and propose a mixed-integer programming model for random fuzzy facility location–allocation problem. By expected value and chance constraint programming technique, this model is reduced to a deterministic model. Furthermore, a priority-based genetic algorithm is designed for solving the proposed programming model and the efficacy and the efficiency of this method and algorithm are demonstrated by a numerical example. Till now, few has formulated or attacked the FLA problems in the above manner. Furthermore, the techniques illustrated in this paper can easily be applied to other SCN problems. Therefore, these techniques are the appropriate tools to tackle other supply chain network problems in realistic environments.     

Optimal allocation–consumption problem for a portfolio with an illiquid asset

During financial crises investors manage portfolios with low liquidity, where the paper-value of an asset differs from the price proposed by the buyer. We consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. We work in the Merton's optimal consumption framework with continuous time. The liquid part of the investment is described by a standard Black–Scholes market. The illiquid asset is sold at a random moment with prescribed distribution and generates additional liquid wealth dependent on its paper-value. The investor has a hyperbolic absolute risk aversion also denoted as HARA-type utility function, in particular, the logarithmic utility function as a limit case. We study two different distributions of the liquidation time of the illiquid asset – a classical exponential distribution and a more practically relevant Weibull distribution. Under certain conditions we show the smoothness of the viscosity solution and obtain closed formulae relevant for numerics.     

Hierarchical maximal-coverage location–allocation: Case of generalized search-and-rescue

We offer a variant of the maximal covering location problem to locate up to p$p$ signal-receiving stations. The “demands,” called geolocations, to be covered by these stations are distress signals and/or transmissions from any targets. The problem is complicated by several factors. First, to find a signal location, the signal must be received by at least three stations—two lines of bearing for triangulation and a third for accuracy. Second, signal frequencies vary by source and the included stations do not necessarily receive all frequencies. One must decide which listening frequencies are allocated to which stations. Finally, the range or coverage area of a station varies stochastically because of meteorological conditions. This problem is modeled using a multiobjective (or multicriteria) linear integer program (MOLIP), which is an approximation of a highly nonlinear integer program. As a solution algorithm, the MOLIP is converted to a two-stage network-flow formulation that reduces the number of explicitly enumerated integer variables. Non-inferior solutions of the MOLIP are evaluated by a value function, which identifies solutions that are similar to the more accurate nonlinear model. In all case studies, the “best” non-inferior solutions were about one to four standard deviations better than the sample mean of thousands of randomly located receivers with heuristic frequency assignments. We also show that a two-stage network-flow algorithm is a practical solution to an intractable nonlinear integer model. Most importantly, the procedure has been implemented in the field.     

The file allocation problem—A queueing network optimization approach

A set of customers use a connected network of computer installations, each accessing the network from a particular node. These customers share information contained in a set of data files. A typical customer's need is characterized by a request requiring a subset of these files being accessed in a Markovian sequence. The cycle time for this customer is the total time taken on the average to complete his request sequence. The objective is to locate a single copy of each of the files in such a way that a weighted sum of these response times is minimized. The problem is modelled as a Closed Queueing Network optimization problem. Models are developed for both single and multiple chain cases. An incremental analysis approach is used to solve the single chain case. For the multiple chain case, it is shown how this model approximates to a set partitioning problem under certain conditions. Efficient heuristics are developed to solve this partitioning problem. With certain simplifying assumptions, the associated communication problem is then included in the model.     

Solving the multi-compartment capacitated location routing problem with pickup–delivery routes and stochastic demands

This paper considers an advanced capacitated location routing problem in a distribution network with multiple pickup and delivery routes, and each customer placing random multi-item demands on it. The pickup and delivery services need two fleets of vehicles and will form two different sets of routes. However, the unpredictability of variation in the multi-item demands makes the routing of multi-compartment vehicles to accommodate such demands complex. To solve this multifaceted problem, a new process employing the TABU search is proposed in this research study. This proposed approach includes three stages: location selection, customer assignment, and vehicle routing. The innovative concept is to divide all customers into assignment-determined and assignment-undetermined groups in order to narrow down the search area of a solution domain so the TABU search can be more efficient and effective. Two sets of benchmarks are then generated to verify the quality of the proposed method. According to the experiment results, the proposed solution process can both resolve the problems and yield good results in a reasonable amount of computing time. The analysis of the solution process parameters is also provided. In addition, the comparisons between stochastic demand and deterministic demand cases are calculated and discussed as well.     

Bi-objective vibration damping optimization for congested location–pricing problem

This paper presents a bi-objective mathematical programming model for the restricted facility location problem, under a congestion and pricing policy. Motivated by various applications such as locating server on internet mirror sites and communication networks, this research investigates congested systems with immobile servers and stochastic demand as M/M/m/k queues. For this problem, we consider two simultaneous perspectives; (1) customers who desire to limit waiting time for service and (2) service providers who intend to increase profits. We formulate a bi-objective facility location problem with two objective functions: (i) maximizing total profit of the whole system and (ii) minimizing the sum of waiting time in queues; the model type is mixed-integer nonlinear. Then, a multi-objective optimization algorithm based on vibration theory (so-called multi-objective vibration damping optimization (MOVDO)), is developed to solve the model. Moreover, the Taguchi method is also implemented, using a response metric to tune the parameters. The results are analyzed and compared with a non-dominated sorting genetic algorithm (NSGA-II) as a well-developed multi-objective evolutionary optimization algorithm. Computational results demonstrate the efficiency of the proposed MOVDO to solve large-scale problems.     

Formulations and relaxations for a multi-echelon capacitated location–distribution problem

We consider a multi-echelon location–distribution problem arising from an actual application in fast delivery service. We present and compare two formulations for this problem: an arc-based model and a path-based model. We show that the linear programming (LP) relaxation of the path-based model provides a better bound than the LP relaxation of the arc-based model. We also compare the so-called binary relaxations of the models, which are obtained by relaxing the integrality constraints for the general integer variables, but not for the 0–1 variables. We show that the binary relaxations of the two models always provide the same bound, but that the path-based binary relaxation appears preferable from a computational point of view, since it can be reformulated as an equivalent simple plant location problem (SPLP), for which several efficient algorithms exist. We also show that the LP relaxation of this SPLP reformulation provides a better bound than the LP relaxation of the path-based model.     

The integrated production–inventory–distribution–routing problem

The integration of production and distribution decisions presents a challenging problem for manufacturers trying to optimize their supply chain. At the planning level, the immediate goal is to coordinate production, inventory, and delivery to meet customer demand so that the corresponding costs are minimized. Achieving this goal provides the foundations for streamlining the logistics network and for integrating other operational and financial components of the system. In this paper, a model is presented that includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of vehicles for making the deliveries. Demand can be satisfied from either inventory held at the customer sites or from daily product distribution. In the most restrictive case, a vehicle routing problem must be solved for each time period. The decision to visit a customer on a particular day could be to restock inventory, meet that day’s demand or both. In a less restrictive case, the routing component of the model is replaced with an allocation component only. A procedure centering on reactive tabu search is developed for solving the full problem. After a solution is found, path relinking is applied to improve the results. A novel feature of the methodology is the use of an allocation model in the form of a mixed integer program to find good feasible solutions that serve as starting points for the tabu search. Lower bounds on the optimum are obtained by solving a modified version of the allocation model. Computational testing on a set of 90 benchmark instances with up to 200 customers and 20 time periods demonstrates the effectiveness of the approach. In all cases, improvements ranging from 10–20% were realized when compared to those obtained from an existing greedy randomized adaptive search procedure (GRASP). This often came at a three- to five-fold increase in runtime, however.     

Burglars blocked by barriers? The impact of physical and social barriers on residential burglars' target location choices in China

Based on an offender spatial decision-making perspective, this burglary target location choice study aims to understand how physical and social barriers affect why residential burglars commit their crimes at particular locations in a major Chinese city. Using data on 3860 residential burglaries committed by 3772 burglars between January 2012 and June 2016 in ZG city, China, conditional logit (discrete choice) models were estimated to assess residential burglars' target location choice preferences. Three types of physical barriers were distinguished: major roads with access control, major roads without access control, and major rivers. Social barriers were constructed based on the Hukou system to reflect how local and nonlocal residents live segregated lives. Results show that residential burglars are less likely to target areas for which they have to cross a physical barrier and even less likely to do so if they have to cross multiple rivers. Local burglars are more likely to target communities with a majority of local residents than communities with a majority nonlocal population or a mixed community. Such a social barrier was less pronounced for nonlocal burglars. These findings add new insight that physical and social barriers affect, to various degrees, where residential burglars in China commit their crimes.     

FA–QABC–MRTA: a solution for solving the multi-robot task allocation problem

Intelligent Service Robotics - The problem of task allocation in a multi-robot system is the situation where we have a set of tasks and a number of robots; then each task is assigned to the...     

A location–inventory supply chain problem: Reformulation and piecewise linearization

In this paper, we study a two-echelon inventory management problem with multiple warehouses and retailers. The problem is a natural extension to the well-known one-warehouse multi-retailer inventory problem. The problem is formulated as a mixed integer non-linear program such that its continuous relaxation is non-convex. We propose an equivalent formulation with fewer non-linear terms in the objective function so that the continuous relaxation of the new model is a convex optimization problem. We use piecewise linearization to transform the resulting MINLP to a mixed integer program and we solve it using CPLEX. Through numerical experiments, we compare the solutions obtained by solving the new formulation using CPLEX with two previously published Lagrangian relaxation based heuristics to solve the original mixed integer non-linear program. We demonstrate that the new approach is capable of providing almost the same solutions without the need of using specialized algorithms. This important contribution further implies that additional variants of the problem, such as multiple products, capacitated warehouses and routing, can be added to result in a problem that will again be solvable by commercial optimization software, while the respective Lagrangian heuristics will fail to solve such variants or extended problems.     

Multi-objective mitigation budget allocation problem and solution approaches: The case of İstanbul

İstanbul is the financial, commercial, industrial, cultural and educational center of Turkey. However, İstanbul is also an earthquake-prone city that has experienced many earthquakes throughout its history; and it is threatened with a high probability of a devastating earthquake in the next 30 years. In this study, we propose three financial allocation strategies and their multi-objective models related to building reinforcement, with the purpose of reducing the risk of disaster in Istanbul. The study aims to answer three important questions: (1) How should the mitigation budget be distributed among Istanbul’s districts? (2) Which building types should be mitigated, and how? (3) Can Pareto-efficient solutions be sorted? Pareto-efficient solutions for all of the proposed models were obtained and analyzed. The proposed superefficiency model has the ability to rank the Pareto-optimal solutions.     

A simple and effective evolutionary algorithm for the capacitated location–routing problem

This paper proposes a hybrid genetic algorithm (GA) to solve the capacitated location–routing problem. The proposed algorithm follows the standard GA framework using local search procedures in the mutation phase. Computational evaluation was carried out on three sets of benchmark instances from the literature. Results show that, although relatively simple, the proposed algorithm is effective, providing competitive results for benchmark instances within reasonable computing time.     

Modelling and solving grid resource allocation problem with network resources for workflow applications

A problem of allocating resources of a grid to workflow applications is considered. The problem consists, generally, in allocating distributed grid resources to tasks of a workflow in such a way that the resource demands of each task are satisfied. Grid resources are divided into computational resources and network resources. Computational tasks and transmission tasks of a workflow are distinguished. We present a model of the problem, and an algorithm for finding feasible resource allocations. A numerical example is included, showing the importance of the resource allocation phase on a grid. Some conclusions and directions for future research are given.     

The min–max split delivery multi-depot vehicle routing problem with minimum service time requirement

The min–max Split Delivery Multi-Depot Vehicle Routing Problem with Minimum Service Time Requirement (min–max SDMDVRP-MSTR) is a variant of the Multi-Depot Vehicle Routing Problem. Each customer requires a specified amount of service time. The service time can be split among vehicles as long as each vehicle spends a minimum amount of service time at a customer. The objective is to minimize the duration of the longest route (where duration is the sum of travel and service times).We develop a heuristic (denoted by MDS) that solves the min–max SDMDVRP-MSTR in three stages: (1) initialize a feasible solution without splits; (2) improve the longest routes by splitting service times; (3) ensure all minimum service time requirements are satisfied. The first stage of MDS is compared to an existing heuristic to solve the min–max Multi-Depot Vehicle Routing Problem on 43 benchmark instances. MDS produces 37 best-known solutions. We also demonstrate the effectiveness of MDS on 21 new instances whose (near) optimal solutions can be estimated based on geometry. Finally, we investigate the savings from split service and the split patterns as we vary the required service times, the average number of customers per route, and the minimum service time requirement.     

The Deutsch–Jozsa problem: de-quantisation and entanglement

The Deutsch–Jozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : {0, 1} ⁿ → {0, 1} and suppose we have a black-box to compute f. The Deutsch–Jozsa problem is to determine if f is constant (i.e. f(x) = const, "x ? {0,1}ⁿf(x) = \hbox {const, } \forall x \in \{0,1\}^n) or if f is balanced (i.e. f(x) = 0 for exactly half the possible input strings x ? {0,1}ⁿx \in \{0,1\}^n) using as few calls to the black-box computing f as is possible, assuming f is guaranteed to be constant or balanced. Classically it appears that this requires at least 2 ⁿ⁻¹ + 1 black-box calls in the worst case, but the well known quantum solution solves the problem with probability one in exactly one black-box call. It has been found that in some cases the algorithm can be de-quantised into an equivalent classical, deterministic solution. We explore the ability to extend this de-quantisation to further cases, and examine with more detail when de-quantisation is possible, both with respect to the Deutsch–Jozsa problem, as well as in more general cases.