Multi-period capacitated location with modular equipments

This work deals with a multi-period capacitated location problem inspired by telecommunication access network planning problems, where demands and costs vary from one period to another. On each concentrator site, several capacitated concentrators can be installed at each period. Similarly, several capacitated modules can be installed at each period between each terminal and concentrator sites. We assume that equipments can never be removed.     

Bounds for the single source modular capacitated plant location problem

In this paper, we propose a discrete location problem, which we call the Single Source Modular Capacitated Location Problem (SS-MCLP). The problem consists of finding the location and capacity of the facilities, to serve a set of customers at a minimum total cost. The demand of each customer must be satisfied by one facility only and the capacities of the open facilities must be chosen from a finite and discrete set of allowable capacities. Because the SS-MCLP is a difficult problem, a lagrangean heuristic, enhanced by tabu search or local search was developed in order to obtain good feasible solutions. When needed, the lower bounds are used in order to evaluate the quality of the feasible solutions. Our method was tested computationally on randomly generated test problems some of which are with large dimensions considering the literature related to this type of problem. The computational results obtained were compared with those provided by the commercial software Cplex.     

Assembly line balancing under uncertainty: Robust optimization models and exact solution method

This research deals with line balancing under uncertainty and presents two robust optimization models. Interval uncertainty for operation times was assumed. The methods proposed generate line designs that are protected against this type of disruptions. A decomposition based algorithm was developed and combined with enhancement strategies to solve optimally large scale instances. The efficiency of this algorithm was tested and the experimental results were presented. The theoretical contribution of this paper lies in the novel models proposed and the decomposition based exact algorithm developed. Moreover, it is of practical interest since the production rate of the assembly lines designed with our algorithm will be more reliable as uncertainty is incorporated. Furthermore, this is a pioneering work on robust assembly line balancing and should serve as the basis for a decision support system on this subject.     

A fast hybrid primal heuristic for multiband robust capacitated network design with multiple time periods

We investigate the Robust Multiperiod Network Design Problem, a generalization of the Capacitated Network Design Problem (CNDP) that, besides establishing flow routing and network capacity installation as in a canonical CNDP, also considers a planning horizon made up of multiple time periods and protection against fluctuations in traffic volumes. As a remedy against traffic volume uncertainty, we propose a Robust Optimization model based on Multiband Robustness (Büsing and D’Andreagiovanni, 2012), a refinement of classical Γ-Robustness by Bertsimas and Sim that uses a system of multiple deviation bands.Since the resulting optimization problem may prove very challenging even for instances of moderate size solved by a state-of-the-art optimization solver, we propose a hybrid primal heuristic that combines a randomized fixing strategy inspired by ant colony optimization and an exact large neighbourhood search. Computational experiments on a set of realistic instances from the SNDlib show that our original heuristic can run fast and produce solutions of extremely high quality associated with low optimality gaps.     

Integrated use of fuzzy c-means and convex programming for capacitated multi-facility location problem

In this study a fuzzy c-means clustering algorithm based method is proposed for solving a capacitated multi-facility location problem of known demand points which are served from capacitated supply centres. It involves the integrated use of fuzzy c-means and convex programming. In fuzzy c-means, data points are allowed to belong to several clusters with different degrees of membership. This feature is used here to split demands between supply centers. The cluster number is determined by an incremental method that starts with two and designated when capacity of each cluster is sufficient for its demand. Finally, each group of cluster and each model are solved as a single facility location problem. Then each single facility location problem given by fuzzy c-means is solved by convex programming which optimizes transportation cost is used to fine-tune the facility location. Proposed method is applied to several facility location problems from OR library (Osman & Christofides, 1994) and compared with centre of gravity and particle swarm optimization based algorithms. Numerical results of an asphalt producer’s real-world data in Turkey are reported. Numerical results show that the proposed approach performs better than using original fuzzy c-means, integrated use of fuzzy c-means and center of gravity methods in terms of transportation costs.     

A branch-and-cluster coordination scheme for selecting prison facility sites under uncertainty

A multi-period stochastic model and an algorithmic approach to location of prison facilities under uncertainty are presented and applied to the Chilean prison system. The problem consists of finding locations and sizes of a preset number of new jails and determining where and when to increase the capacity of both new and existing facilities over a time horizon, while minimizing the expected costs of the prison system. Constraints include maximum inmate transfer distances, upper and lower bounds for facility capacities, and scheduling of facility openings and expansion, among others. The uncertainty lies in the future demand for capacity, because of the long time horizon under study and because of the changes in criminal laws, which could strongly modify the historical tendencies of penal population growth. Uncertainty comes from the effects of penal reform in the capacity demand. It is represented in the model through probabilistic scenarios, and the large-scale model is solved via a heuristic mixture of branch-and-fix coordination and branch-and-bound schemes to satisfy the constraints in all scenarios, the so-called branch-and-cluster coordination scheme. We discuss computational experience and compare the results obtained for the minimum expected cost and average scenario strategies. Our results demonstrate that the minimum expected cost solution leads to better solutions than does the average scenario approach. Additionally, the results show that the stochastic algorithmic approach that we propose outperforms the plain use of a state-of-the-art optimization engine, at least for the three versions of the real-life case that have been tested by us.     

A simple and deterministic competitive algorithm for online facility location

This paper presents a deterministic and efficient algorithm for online facility location. The algorithm is based on a simple hierarchical partitioning and is extremely simple to implement. It also applies to a variety of models, i.e., models where the facilities can be placed anywhere in the region, or only at customer sites, or only at fixed locations. The paper shows that the algorithm is O (log n)-competitive under these various models, where n is the total number of customers. It also shows that the algorithm is O (1)-competitive with high probability and for any arrival order when customers are uniformly distributed or when they follow a distribution satisfying a smoothness property. Experimental results for a variety of scenarios indicate that the algorithm behaves extremely well in practice.     

Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty

Model predictive control (MPC) has become one of the most popular control techniques in the process industry mainly because of its ability to deal with multiple-input–multiple-output plants and with constraints. However, in the presence of model uncertainties and disturbances its performance can deteriorate. Therefore, the development of robust MPC techniques has been widely discussed during the last years, but they were rarely, if at all, applied in practice due to the conservativeness or the computational complexity of the approaches. In this paper, we present multi-stage NMPC as a promising robust non-conservative nonlinear model predictive control scheme. The approach is based on the representation of the evolution of the uncertainty by a scenario tree, and leads to a non-conservative robust control of the uncertain plant because the adaptation of future inputs to new information is taken into account. Simulation results show that multi-stage NMPC outperforms standard and min–max NMPC under the presence of uncertainties for a semi-batch polymerization benchmark problem. In addition, the advantages of the approach are illustrated for the case where only noisy measurements are available and the unmeasured states and the uncertainties have to be estimated using an observer. It is shown that better performance can be achieved than by estimating the unknown parameters online and adapting the plant model.     

A bilevel fixed charge location model for facilities under imminent attack

We investigate a bilevel fixed charge facility location problem for a system planner (the defender) who has to provide public service to customers. The defender cannot dictate customer-facility assignments since the customers pick their facility of choice according to its proximity. Thus, each facility must have sufficient capacity installed to accommodate all customers for whom it is the closest one. Facilities can be opened either in the protected or unprotected mode. Protection immunizes against an attacker who is capable of destroying at most r unprotected facilities in the worst-case scenario. Partial protection or interdiction is not possible. The defender selects facility sites from m candidate locations which have different costs. The attacker is assumed to know the unprotected facilities with certainty. He makes his interdiction plan so as to maximize the total post-attack cost incurred by the defender. If a facility has been interdicted, its customers are reallocated to the closest available facilities making capacity expansion necessary. The problem is formulated as a static Stackelberg game between the defender (leader) and the attacker (follower). Two solution methods are proposed. The first is a tabu search heuristic where a hash function calculates and records the hash values of all visited solutions for the purpose of avoiding cycling. The second is a sequential method in which the location and protection decisions are separated. Both methods are tested on 60 randomly generated instances in which m ranges from 10 to 30, and r varies between 1 and 3. The solutions are further validated by means of an exhaustive search algorithm. Test results show that the defender's facility opening plan is sensitive to the protection and distance costs.     

Open vehicle routing problem with demand uncertainty and its robust strategies

We investigate the open vehicle routing problem with uncertain demands, where the vehicles do not necessarily return to their original locations after delivering goods to customers. We firstly describe the customer’s demand as specific bounded uncertainty sets with expected demand value and nominal value, and propose the robust optimization model that aim at minimizing transportation costs and unsatisfied demands in the specific bounded uncertainty sets. We propose four robust strategies to cope with the uncertain demand and an improved differential evolution algorithm (IDE) to solve the robust optimization model. Then we analyze the performance of four different robust strategies by considering the extra costs and unmet demand. Finally, the computational experiments indicate that the robust optimization greatly avoid unmet demand while incurring a small extra cost and the optimal return strategy is the best strategy by balancing the trade-off the cost and unmet demand among different robust strategies.     

Optimization under uncertainty with applications to design of truss structures

Many real-world engineering design problems are naturally cast in the form of optimization programs with uncertainty-contaminated data. In this context, a reliable design must be able to cope in some way with the presence of uncertainty. In this paper, we consider two standard philosophies for finding optimal solutions for uncertain convex optimization problems. In the first approach, classical in the stochastic optimization literature, the optimal design should minimize the expected value of the objective function with respect to uncertainty (average approach), while in the second one it should minimize the worst-case objective (worst-case or min–max approach). Both approaches are briefly reviewed in this paper and are shown to lead to exact and numerically efficient solution schemes when the uncertainty enters the data in simple form. For general uncertainty dependence however, the problems are numerically hard. In this paper, we present two techniques based on uncertainty randomization that permit to solve efficiently some suitable probabilistic relaxation of the indicated problems, with full generality with respect to the way in which the uncertainty enters the problem data. In the specific context of truss topology design, uncertainty in the problem arises, for instance, from imprecise knowledge of material characteristics and/or loading configurations. In this paper, we show how reliable structural design can be obtained using the proposed techniques based on the interplay of convex optimization and randomization.     

Robust PID tuning for Smith predictor in the presence of model uncertainty

This paper presents robust PID tuning for the Smith predictor in the presence of model uncertainty. The concept of the equivalent gain plus time delay (EGPTD) is introduced to incorporate robust stability in PID tuning of the Smith predictor. In particular, an application is developed for the robust tuning of the first order plus time delay (FOPTD) system and the second order plus time delay (SOPTD) system because the systems have been used extensively to describe chemical processes. The proposed tuning method can cope with simultaneous uncertainties in all parameters of the model in an efficient manner. Another important and attractive feature of the method is that it can utilize many currently available PID tuning rules. Simulation results are provided to demonstrate the availability of the method.     

A hybridization of an evolutionary algorithm and a parallel branch and bound for solving the capacitated single allocation hub location problem

In this study, we propose a hybrid optimization method, consisting of an evolutionary algorithm (EA) and a branch-and-bound method (BnB) for solving the capacitated single allocation hub location problem (CSAHLP). The EA is designed to explore the solution space and to select promising configurations of hubs (the location part of the problem). Hub configurations produced by the EA are further passed to the BnB search, which works with fixed hubs and allocates the non-hub nodes to located hubs (the allocation part of the problem). The BnB method is implemented using parallelization techniques, which results in short running times. The proposed hybrid algorithm, named EA-BnB, has been tested on the standard Australia Post (AP) hub data sets with up to 300 nodes. The results demonstrate the superiority of our hybrid approach over existing heuristic approaches from the existing literature. The EA-BnB method has reached all the known optimal solutions for AP hub data set and found new, significantly better, solutions on three AP instances with 100 and 200 nodes. Furthermore, the extreme efficiency of the implementation of this hybrid algorithm resulted in short running times, even for the largest AP test instances.     

Robust H∞ control design for systems with structured parameter uncertainty

In a recent paper a unification of the H₂ (LQG) and H_∞ control-design problems was obtained in terms of modified algebraic Riccati equations. In the present paper these results are extended to guarantee robust H₂ and H_∞ performance in the presence of structured real-valued parameter variiations (ΔA, ΔB, ΔC) in the state space model. For design flexibility the paper considers two distinct types of uncertainty bounds for both full- and reduced-order dynamic compensation. An important special case of these results generates H₂/H_∞ controller designs with guaranteed gain margins.     

Location equilibria for a continuous competitive facility location problem under delivered pricing

The problem of finding location equilibria of a location-price game where firms first select their locations and then set delivered prices in order to maximise their profits is investigated. Assuming that firms set the equilibrium prices in the second stage, the game can be reduced to a location game for which a global minimiser of the social cost is a location equilibrium, provided that the demand is completely inelastic and the marginal production cost is constant. When the set of feasible locations is a region of the plane the minimisation of the social cost becomes a hard-to-solve global optimisation problem. We propose an exact interval branch-and-bound algorithm suitable for small and medium size problems and an alternating Weiszfeld-like heuristic for larger instances. The latter approach is based on a new iterative formula for which the validity of the descent property is proved. The proposed heuristic performs extremely well against the exact method when tested on small to medium size instances while requiring a tiny fraction of its computational time.     

Emergency facility location under random network damage: Insights from the Istanbul case

Damage to infrastructure, especially to highways and roads, adversely affects accessibility to disaster areas. Predicting accessibility to demand points from the supply points by a systematic model would lead to more effective emergency facility location decisions. To this effect, we model the spatial impact of the disaster on network links by random failures with dependency such that failure of a link induces failure of nearby links that are structurally more vulnerable. For each demand point, a set of alternative paths is generated from each potential supply point so that the shortest surviving path will be used for relief transportation after the disaster. The objective is to maximize the expected demand coverage within a specified distance over all possible network realizations. To overcome the computational difficulty caused by extremely large number of possible outcomes, we propose a tabu search heuristic that evaluates candidate solutions over a sample of network scenarios. The scenario generation algorithm that represents the proposed distance and vulnerability based failure model is the main contribution of our study. The tabu search algorithm is applied to Istanbul earthquake preparedness case with a detailed analysis comparing solutions found in no link failure, independent link failure, and dependent link failure cases. The results show that incorporating dependent link failures to the model improves the covered demand percentages significantly.     

Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty

Measuring and controlling emissions across the logistics network is an important challenge for today’s firms according to increasing concern about the environmental impact of business activities. This paper proposes a bi-objective credibility-based fuzzy mathematical programming model for designing the strategic configuration of a green logistics network under uncertain conditions. The model aims to minimize the environmental impacts and the total costs of network establishment simultaneously for the sake of providing a sensible balance between them. A popular but credible environmental impact assessment index, i.e., CO₂ equivalent index is used to model the environmental impact across the concerned logistics network. Since transportation mode and production technology play important roles on the concerned objectives, the proposed model integrates their respective decisions with those of strategic network design ones. In addition, to solve the proposed bi-objective fuzzy optimization model, an interactive fuzzy solution approach based upon credibility measure is developed. An industrial case study is also provided to show the applicability of the proposed model as well as the usefulness of its solution method.     

Comparing Robust Decision-Making and Dynamic Adaptive Policy Pathways for model-based decision support under deep uncertainty

A variety of model-based approaches for supporting decision-making under deep uncertainty have been suggested, but they are rarely compared and contrasted. In this paper, we compare Robust Decision-Making with Dynamic Adaptive Policy Pathways. We apply both to a hypothetical case inspired by a river reach in the Rhine Delta of the Netherlands, and compare them with respect to the required tooling, the resulting decision relevant insights, and the resulting plans. The results indicate that the two approaches are complementary. Robust Decision-Making offers insights into conditions under which problems occur, and makes trade-offs transparent. The Dynamic Adaptive Policy Pathways approach emphasizes dynamic adaptation over time, and thus offers a natural way for handling the vulnerabilities identified through Robust Decision-Making. The application also makes clear that the analytical process of Robust Decision-Making is path-dependent and open ended: an analyst has to make many choices, for which Robust Decision-Making offers no direct guidance.     

A facility location model for logistics systems including reverse flows: The case of remanufacturing activities

After a brief introduction to the basic concepts of reverse logistics, we present a two-level location problem with three types of facility to be located in a specific reverse logistics system, named a Remanufacturing Network (RMN). For this problem, we propose a 0–1 mixed integer programming model, in which we simultaneously consider “forward” and “reverse” flows and their mutual interactions. An algorithm based on Lagrangian heuristics is developed and the model is tested on data adapted from classical test problems.