An approximate dynamic programming approach to solving a dynamic, stochastic multiple knapsack problem

We model a multiperiod, single resource capacity reservation problem as a dynamic, stochastic, multiple knapsack problem with stochastic dynamic programming. As the state space grows exponentially in the number of knapsacks and the decision set grows exponentially in the number of order arrivals per period, the recursion is computationally intractable for large-scale problems, including those with long horizons. Our goal is to ensure optimal, or near optimal, decisions at time zero when maximizing the net present value of returns from accepted orders, but solving problems with short horizons introduces end-of-study effects which may prohibit finding good solutions at time zero. Thus, we propose an approximation approach which utilizes simulation and deterministic dynamic programming in order to allow for the solution of longer horizon problems and ensure good time zero decisions. Our computational results illustrate the effectiveness of the approximation scheme.     

A dynamic programming approach to solving the assortment planning problem with multiple quality levels

While the assortment planning problem, in which a firm selects a set of products to offer, has been widely studied, several problem instances exist which have not yet been solved to optimality. In particular, we consider an assortment planning problem under a locational choice model for consumer choice with both vertical and horizontal differentiation. We present a combined dynamic programming/line search approach which finds an optimal solution when customer preference for the horizontal attributes are distributed according to a unimodal distribution. The dynamic program makes use of new analytical results, which show that high quality products will be distributed near the mode. This enables significant state reduction and therefore efficient solution times. Efficient computation times allow us to study the solution for a wide range of system parameters and thereby draw several managerial conclusions.     

A neural network approach for solving nonlinear bilevel programming problem

A neural network model is presented for solving nonlinear bilevel programming problem, which is a NP-hard problem. The proposed neural network is proved to be Lyapunov stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem. The asymptotic properties of the neural network are analyzed and the condition for asymptotic stability, solution feasibility and solution optimality are derived. The transient behavior of the neural network is simulated and the validity of the network is verified with numerical examples.     

Using integer programming for balancing return and risk in problems with individual chance constraints

In this paper, we study probabilistically constrained problems involving individual chance constraints, random univariate right-hand sides, and risk tolerances defined as decision variables which affect part of the objective function. Built on the concept of efficient points, we formulate the problems as mixed-integer programs by using binary variables to determine an optimal risk tolerance for each chance constraint. We develop two benchmark approaches, both of which solve chance-constrained programs with fixed risk values in a bisection algorithm or by enumeration. We specify our approaches for a minimum cost flow problem and a network capacity design problem, both of which involve chance constraints for bounding the risk of demand shortages. We test instances with diverse size and complexity of the two network problems, and demonstrate the computational efficacy as well as give managerial insights.     

A new hybrid fuzzy-goal programming scheme for multi-objective topological optimization of static and dynamic structures under multiple loading conditions

This work presents a hybrid fuzzy-goal multi-objective programming scheme for topological optimization of continuum structures, in which both static and dynamic loadings are considered. The proposed methodology fortopological optimization first employs a fuzzy-goal programming scheme at the top level for multi-objective problems with static and dynamic objectives. For the static objective with multi-stiffness cases in the fuzzy-goal formulation, a hybrid approach, involving a hierarchical sequence approach or a hierarchical sequence approach coupled with a compromise programming method, is especially suggested for the statically loaded multi-stiffness structure at the sublevel. Concerning dynamic optimization problems of freevibration cases, nonstructural mass, oscillation of the objective function, and repeated eigenvalues are also discussed. Solid Isotropic Material with Penalization density–stiffness interpolation scheme is used to indicate the dependence ofmaterial modulus upon regularized element densities. The globally convergent version of the method of moving asymptotes and the sequential linear programming method areboth employed as optimizers. Several applications have been applied to demonstrate the validation of the presented methodologies.     

Variable neighborhood search for the bi-objective post-sales network design problem: A fitness landscape analysis approach

Post-sales services are important markets in electronics industry due to their impact on marginal profit, market share, and their ability to retain customers. In this study, designing a multi-product four-layer post-sales reverse logistics network operated by a 3PL is investigated. A bi-objective MILP model is proposed to minimize network design costs as well as total weighted tardiness of returning products to customers. To solve the proposed model, a novel multi-start variable neighborhood search is suggested that incorporates nine neighborhood structures and three new encoding–decoding mechanisms. In particular, a fitness landscape measure is employed to select an effective neighborhood order for the proposed VNS. Extensive computational experiments show the effectiveness of the proposed heuristic and the three encoding–decoding mechanisms. The proposed method finds significantly better Pareto optimal sets in comparison with the original Priority method based on the number and the quality of obtained Pareto optimal solutions. In addition, it shows high efficiency by finding near-optimal solutions for the single objective versions of the problem.     

Location based treatment activities for end of life products network design under uncertainty by a robust multi-objective memetic-based heuristic approach

Rapid growth in world population and recourse limitations necessitate remanufacturing of products and their parts/modules. Managing these processes requires special activities such as inspection, disassembly, and sorting activities known as treatment activities. This paper proposes a capacitated multi-echelon, multi-product reverse logistic network design with fuzzy returned products in which both locations of the treatment activities and facilities are decision variables. As the obtained nonlinear mixed integer programming model is a combinatorial problem, a memetic-based heuristic approach is presented to solve the resulted model. To validate the proposed memetic-based heuristic method, the obtained results are compared with the results of the linear approximation of the model, which is obtained by a commercial optimization package. Moreover, due to inherent uncertainty in return products, demands of these products are considered as uncertain parameters and therefore a fuzzy approach is employed to tackle this matter. In order to deal with the uncertainty, a stochastic simulation approach is employed to defuzzify the demands, where extra costs due to opening new centers or extra transportation costs may be imposed to the system. These costs are considered as penalty in the objective function. To minimize the resulting penalties during simulation's iterations, the average of penalties is added to the objective function of the deterministic model considered as the primary objective function and variance of penalties are considered as the secondary objective function to make a robust solution. The resulted bi-objective model is solved through goal programming method to minimizing the objectives, simultaneously.     

A multi-objective approach for solving the survivable network design problem with simultaneous unicast and anycast flows

In this paper, we consider the survivable network design problem for simultaneous unicast and anycast flow requests. We assume that the network is modeled by a connected and undirected graph. This problem aims at finding a set of connections with a minimized network cost in order to protect the network against any single failure. The cost is computed using the all capacities modular cost (ACMC) model and a set of flow demands. We name it as ACMC-based survivable network design problem (A-SNDP). It is proved that the problem is NP-hard. We introduce a multi-objective approach to solve A-SNDP. The objectives are to minimize the network cost (NCost) and the network failure (NFail). Extensive simulation results on instances of Polska, Germany and Atlanta networks showed the efficiency of the multi-objective approach for solving A-SNDP.     

An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem

The consideration of this paper is given to address the straight and U-shaped assembly line balancing problem. Although many attempts in the literature have been made to develop deterministic version of the assembly line model, the attention is not considerably given to those in uncertain environment. In this paper, a novel bi-objective fuzzy mixed-integer linear programming model (BOFMILP) is developed so that triangular fuzzy numbers (TFNs) are employed in order to represent uncertainty and vagueness associated with the task processing times in the real production systems. In this proposed model, two conflicting objectives (minimizing the number of stations as well as cycle time) are considered simultaneously with respect to set of constraints. For this purpose, an appropriate strategy in which new two-phase interactive fuzzy programming approach is proposed as a solution method to find an efficient compromise solution. Finally, validity of the proposed model as well as its solution approach are evaluated though numerical examples. In addition, a comparison study is conducted over some test problems in order to assess the performance of the proposed solution approach. The results demonstrate that our proposed interactive fuzzy approach not only can be applied in ALBPs but also is capable to handle any practical MOLP models. Moreover, in light of these results, the proposed model may constitute a framework aiming to assist the decision maker (DM) to deal with uncertainty in assembly line problem.     

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.     

An interactive possibilistic programming approach for a multi-objective closed-loop supply chain network under uncertainty

In this article, we first propose a closed-loop supply chain network design that integrates network design decisions in both forward and reverse supply chain networks into a unified structure as well as incorporates the tactical decisions with strategic ones (e.g., facility location and supplier selection) at each period. To do so, various conflicting objectives and constraints are simultaneously taken into account in the presence of some uncertain parameters, such as cost coefficients and customer demands. Then, we propose a novel interactive possibilistic approach based on the well-known STEP method to solve the multi-objective mixed-integer linear programming model. To validate the presented model and solution method, a numerical test is accomplished through the application of the proposed possibilistic-STEM algorithm. The computational results demonstrate suitability of the presented model and solution method.     

Cooperative network design: A Nash bargaining solution approach

The Network Design problem has received increasing attention in recent years. Previous works have addressed this problem considering almost exclusively networks designed by selfish users, which can be consistently suboptimal. This paper addresses the network design issue using cooperative game theory, which permits to study ways to enforce and sustain cooperation among users. Both the Nash bargaining solution and the Shapley value are widely applicable concepts for solving these games. However, the Shapley value presents several drawbacks in this context.For this reason, we solve the cooperative network design game using the Nash bargaining solution (NBS) concept. More specifically, we extend the NBS approach to the case of multiple players and give an explicit expression for users’ cost allocations. We further provide a distributed algorithm for computing the Nash bargaining solution. Then, we compare the NBS to the Shapley value and the Nash equilibrium solution in several network scenarios, including real ISP topologies, showing its advantages and appealing properties in terms of cost allocation to users and computation time to obtain the solution.Numerical results demonstrate that the proposed Nash bargaining solution approach permits to allocate costs fairly to users in a reasonable computation time, thus representing a very effective framework for the design of efficient and stable networks.     

On the wireless local area network design problem with performance guarantees

In this paper, we propose a model for the wireless local area network (WLAN) design problem with performance guarantees. This problem consists of selecting the location of the access points (APs) as well as the power and the channel of each AP. The performance guarantees we refer to are coverage and minimum bandwidth guarantees. Since this problem is -hard, we propose a tabu search algorithm to find solutions for real-size instances of the problem. Finally, numerical results are presented. The results show that good solutions can be found with the proposed algorithm in a reasonable amount of time.     

A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning

In this study a hybrid (including qualitative and quantitative objectives) fuzzy multi objective nonlinear programming (H-FMONLP) model with different goal priorities will be developed for aggregate production planning (APP) problem in a fuzzy environment. Using an interactive decision making process the proposed model tries to minimize total production costs, carrying and back ordering costs and costs of changes in workforce level (quantitative objectives) and maximize total customer satisfaction (qualitative objective) with regarding the inventory level, demand, labor level, machines capacity and warehouse space. A real-world industrial case study demonstrates applicability of proposed model to practical APP decision problems. GENOCOP III (Genetic Algorithm for Numerical Optimization of Constrained Problems) has been used to solve final crisp nonlinear programming problem.     

A cooperative negotiation embedded NSGA-II for solving an integrated product family and supply chain design problem with remanufacturing consideration

Product family design is a popular approach adopted by manufacturers to increase their product varieties in order to satisfy the needs of various markets. In recent years, because of increasing environmental concerns in societies and strict regulations of environmental protection, quite a number of manufacturers adopted remanufacturing strategy in their product development in response to the challenges. Remanufacturing of used products unavoidably involves a closed-loop supply chain system. To achieve the best outcomes, the supply chain design should be considered in product family design process. In this research, a multi-objective optimization model of integrated product family and closed loop supply chain design is formulated based on a cooperative game model for minimizing manufacturer’s total cost and maximize suppliers’ total payoffs. Since the optimization problem could be a large- scale one and involves mixed continuous-discrete variables, a new version of nondominated sorting genetic algorithm-II (NSGA-II), namely cooperative negotiation embedded NSGA-II (NSGA-CO), is proposed to solve the optimization model. Simulation tests are conducted to validate the effectiveness of the proposed NSGA-CO. The test results indicate that the proposed NSGA-CO outperforms NSGA-II in solving various scale of multi-objective optimization problems in terms of convergence. With the formulated optimization model and the proposed NSGA-CO, a case study of integrated product family and supply chain design is conducted to investigate the effects of environmental penalty, quantity of demand and marginal cost of remanufacturing on used product return rate, manufacturers’ and suppliers’ profits and joint payoff.     

On the hop-constrained survivable network design problem with reliable edges

In this paper, we study the hop-constrained survivable network design problem with reliable edges. Given a graph with non-negative edge costs and node pairs Q, the hop-constrained survivable network design problem consists of constructing a minimum cost set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. In addition, we consider here a subset of reliable edges that are not subject to failure. We study two variants: a static problem where the reliability of edges is given, and an upgrading problem where edges can be upgraded to the reliable status at a given cost. We adapt for the two variants an extended formulation proposed in Botton, Fortz, Gouveia, Poss (2011) [1] for the case without reliable edges. As before, we use Benders decomposition to accelerate the solving process. Our computational results indicate that these two variants appear to be more difficult to solve than the original problem (without reliable edges). We conclude with an economical analysis which evaluates the incentive of using reliable edges in the network.     

A knowledge-based approach to the local area network design problem

Computer networks are an essential tool for people in business, industries, government, and schools. With the rapid rate of change in network technology and products, and the emergence of highly sophisticated network users, network design has become an increasingly complex task. Although the computer society aims at agreeing to a series of international standards for describing network architectures, the design of a computer network remains an ill-structured problem that lends itself perfectly to expert systems solutions. We propose an expert system that is able to design local area networks meeting the requirements specified by the user. Rules and guidelines pertaining to local area network design are formulated and incorporated into the knowledge base. The system is built on an object-oriented paradigm. The object-oriented approach and the hierarchical rule structure paradigm are discussed. We also employ the blackboard technique through which rules can access dynamic objects conveniently.     

Supply chain network design under uncertainty with new insights from contracts

In this paper, the classical problem of supply chain network design is reconsidered to emphasize the rolc of contracts in uncertain environments. The supply chain addressed consists of four layers： suppliers, manufacturers, warehouses, and customers acting within a single period. The single owner of the manufacturing plants signs a contract with each of the suppliers to satisfy demand from downstream. Available contracts consist of long-term and option contracts, and unmet demand is satisfied by purchasing from the spot market. In this supply chain, customer demand, supplier capacity, plants and warehouses, transportation costs, and spot prices are uncertain. Two models are proposed here： a risk-neutral two-stage stochastic model and a risk-averse model that considers risk measures. A solution strategy based on sample average approximation is then proposed to handle large scale problems. Extensive computational studies prove the important role of contracts in the design process, especially a portfolio of contracts. For instance, we show that long-term contract alone has similar impacts to having no contracts, and that option contract alone gives inferior results to a combination of option and long-term contracts. We also show that the proposed solution methodology is able to obtain good quality solutions for large scale problems.     

Optimal design and verification of temporal and spatial filters using second-order cone programming approach

11 Introduction The filters are widely used in many applications of signal processing. Filter design is an important research problem in many diverse application areas. The filters we usually refer to are temporal filters, which pass the frequency components of interest and attenuate the others. A spatial filter passes the signal radiating from a specific location and attenuates signals from other locations. Beamformer that widely used in radar, sonar,and wireless communications is a kind of …     

Supply chain network design under oligopolistic price and service level competition with foresight

In this paper a new bi-level model for designing the network structure of a competitive supply chain (SC) is presented with anticipating variable prices and service levels competition in markets under stochastic price and service level dependent elastic demands with the presence of existing, external rivals. The network structure of the new entrant SC would be designed under the limited production capacity of its producers in a way to maximize its future capturable profit in the competitive markets. The network of the new SC is assumed to be set “once and for all” but further price and service level adjustments are possible. Outer part of this bi-level model deals with strategic decisions of SC network design. Given the SC network structure assigned by the outer model in each iteration, the inner equilibrium model determines the equilibrium retail prices and service levels. Finally, we illustrate the model through several numerical examples.