Proposed Solution Methodology Research Articles

A new scheduling technique for the resource–constrained project scheduling problem with discounted cash flows

In this paper, we discuss the resource–constrained project scheduling problem with discounted cash flows. We introduce a new schedule construction technique which moves sets of activities to improve the project net present value and consists of two steps. In particular, the inclusion of individual activities into sets, which are then moved together, is crucial in both steps. The first step groups the activities based on the predecessors and successors in the project network, and adds these activities to a set based on their finish time and cash flow. The second step on the contrary does so based on the neighbouring activities in the schedule, which may but need not include precedence related activities. The proposed scheduling method is implemented in a genetic algorithm metaheuristic and we employ a penalty function to improve the algorithm’s feasibility with respect to a tight deadline. All steps of the proposed solution methodology are tested in detail and an extensive computational experiment shows that our results are competitive with existing work.

Regenerator Location Problem and survivable extensions: A hub covering location perspective

In a telecommunications network the reach of an optical signal is the maximum distance it can traverse before its quality degrades. Regenerators are devices to extend the optical reach. The regenerator placement problem seeks to place the minimum number of regenerators in an optical network so as to facilitate the communication of a signal between any node pair. In this study, the Regenerator Location Problem is revisited from the hub location perspective directing our focus to applications arising in transportation settings. Two new dimensions involving the challenges of survivability are introduced to the problem. Under partial survivability, our designs hedge against failures in the regeneration equipment only, whereas under full survivability failures on any of the network nodes are accounted for by the utilization of extra regeneration equipment. All three variations of the problem are studied in a unifying framework involving the introduction of individual flow-based compact formulations as well as cut formulations and the implementation of branch and cut algorithms based on the cut formulations. Extensive computational experiments are conducted in order to evaluate the performance of the proposed solution methodologies and to gain insights from realistic instances.

A new methodology for analyzing non-Newtonian fluid flow tests

Abstract Conventional treatment of oil flow in porous media assumes that oil is in the typical range of flow velocity and pressure, and it behaves as a Newtonian fluid. This assumption, however, may not be accurate, especially for heavy oil. It is also not accurate in modeling injection behavior for fluids such as fracturing fluids, or polymer fluids for secondary recovery of oil. The literature contains articles that formulated and presented solutions of the posed fluid flow problem. When trying to apply the proposed solution methodology, the limitations of those techniques became apparent. Many authors have already pointed out the inapplicability of the presented techniques and suggested some corrections. Moreover the presented techniques are not valid for non-Newtonian fluids that have a power law index ( n ) greater than 0.6. In this paper we examine the solutions presented in the literature showing their limitations. We will examine the mathematical reasons for the problems and demonstrate rigorously that these (published) analysis techniques are impractical not only for real world problems but also for simulated data. Our in depth analysis explains away the problems analysts have had with the existing methodology. We also present a new reliable methodology for determining reservoir properties. The new methodology was tested on six real field data and two simulated datasets. The examples showed that the previously presented methodologies under-predict the permeability by at least 40%.

Mission Cost and Reliability of 1-out-of-$N$ Warm Standby Systems With Imperfect Switching Mechanisms

In this paper, mission cost and reliability of 1-out-of-N: G nonrepairable warm standby systems with imperfect switching are modeled and analyzed using an iterative method. A general switching structure is considered, which consists of an overall fault detection mechanism (FDM) and a set of individual switches (one for each standby element). The failure of the FDM prevents the replacement of the failed online element by any standby element while the failure of an individual switch only makes the corresponding standby element unavailable. The entire mission fails either when the FDM fails before the failure of the online element during the mission, or when all the system elements have failed or become unavailable before the mission completion. Based on the proposed algorithm for the mission cost and reliability analysis, the optimal element sequencing problem is further formulated and solved for 1-out-of-N: G nonrepairable warm standby systems with nonidentical elements and imperfect switching mechanisms. The objective of the problem is to find the optimal initiation sequence of system elements that can minimize the expected mission cost while providing a certain level of system reliability. Examples are given to illustrate the considered problem and the proposed solution methodology.

Hybrid special class for solving differential-algebraic equations

This paper introduces three classes of hybrid methods to solve systems of differential algebraic equations (DAEs). These classes are based on a free parameter class of linear multistep method (LMM). Two classes contain one step point and one stage point (off-step point) of the first derivative of the solution. The third one contains two step points and one stage point of the first derivative of the solution. Parameters are selected to improve the absolute stability regions. The proposed solution methodologies have larger stability regions compared to the backward differentiation formulae (BDF), the extended backward differentiation formulae (EBDF), and the Hybrid extended backward differentiation formulae (HEBDF). The constructed first class is A?stable of the orders 2 to 5, and A(?)?stable of the orders 6 to 11. The second class is A?stable of the orders 2 to 5 and A(?)?stable of the orders 6 to 10. The last class is A?stable of the orders 3 to 4 and A(?)?stable of the orders 5 to 9. The A? stable methods of the three classes are L?stable. Numerical tests are conducted to validate the performance of the proposed technique.

The robust crew pairing problem: model and solution methodology

We present a new robust formulation for the crew pairing problem where flight and connection times are random and vary within an interval. The model protects against infeasibility with a specified level of uncertainty and minimizes crew cost in the worst case. The resulting robust terms in the objective function and in the resource constraints are nonlinear. We apply Lagrangian relaxation to separate the nonlinear terms in the subproblem leading to a new robust formulation of the shortest path problem with resource constraints. We show that the nonlinear subproblem can be solved as a series of linear auxiliary problems. The proposed solution methodology was successful to solve industry instances in very competitive times and led to more robust crew pairing solutions as shown by simulation experiments.

Efficient DG‐like formulation equipped with curved boundary edges for solving elasto‐acoustic scattering problems

SUMMARYA Discontinuous Galerkin (DG)‐based approach is proposed for computing the scattered field from an elastic bounded object immersed in an infinite homogeneous fluid medium. The proposed method possesses two distinctive features. First, it employs higher‐order polynomial‐shape functions needed to address the high‐frequency propagation regime. Second, it is equipped with curved boundary edges to provide an accurate representation of the fluid–structure interface. The most salient benefits resulting from the latter feature, as demonstrated by the numerical investigation, are the following: (i) an improvement by—at least—two orders of magnitude on the relative error and (ii) the disappearance of spurious resonance frequencies in the surrounding fluid medium. In addition, the reported numerical results reveal that when using cubic polynomials with less than three elements per wavelength, the proposed DG method computes the scattered field with a relative error below 1% for an elastic scatterer of about 30 wavelengths. This observation highlights the potential of the proposed solution methodology for efficiently solving mid‐frequency to high‐frequency elasto‐acoustic scattering problems. Copyright © 2014 John Wiley & Sons, Ltd.

Minimum Mission Cost Cold-Standby Sequencing in Non-Repairable Multi-Phase Systems

This paper considers the optimal cold standby element sequencing problem (SESP) for 1-out-of- n: G heterogeneous non-repairable cold-standby systems that accomplish multi-phase missions. Given a fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected mission cost while providing a desired level of system reliability. It is assumed that during different mission phases the elements are exposed to different stresses, which affects their time-to-failure distributions. The startup and exploitation costs of system elements are also phase dependent. We suggest an algorithm for evaluating the mission reliability and expected mission cost based on a discrete approximation of time-to-failure distributions of the system elements. A genetic algorithm is used as an optimization tool for solving the formulated SESP for multi-phase cold-standby systems. Examples are given to illustrate the considered problem and the proposed solution methodology.

A network optimization-based approach for crowd management in large public gatherings

Effective crowd management during large public gatherings is necessary to enable pedestrians' access to and from the venue and to ensure their safety. This paper proposes a network optimization-based methodology to support such efficient crowd movement during large events. Specifically, a bi-level integer program is presented that, at the upper-level, seeks a reconfiguration of the physical layout that will minimize total travel time incurred by system users (e.g. evacuees) given utility maximizing route decisions that are taken by individuals in response to physical offerings in terms of infrastructure at the lower-level. The lower-level formulation seeks a pure-strategy Nash equilibrium that respects collective behavior in crowds. A Multi-start Tabu Search with Sequential Quadratic Programming procedure is proposed for its solution. Numerical experiments on a hypothetical network were conducted to illustrate the proposed solution methodology and the insights it provides.

Finding Pattern Configurations for Bank Cheque Printing

The problem we address in this paper arises in large-scale manufacturing of bank cheques. Due to security reasons, the cheques must be printed on special (expensive) paper. The first step in the printing process is to prepare the plates that will be used by the composing machine. If the imprint (image) of a particular cheque is on a plate, each time the composing machine uses this plate a new cheque of this type is produced. Each plate has a predefined number of positions to be impressed. Due to delivery due dates, there is an additional constraint requiring each cheque not to be present in more than a predefined number of different plates. There are two different production costs that have to be considered: overproduction costs and printing costs. Each overproduced cheque can be either destroyed or stored in a proper location under surveillance. Both these alternatives have a huge environmental impact, indeed, on the one hand, paper waste is produced, while, on the other hand there is a huge energy consumption. The problem consists in defining the pattern (i.e. the configuration of cheque images) of each plate to be used and the corresponding frequency, such that total costs are minimized.We study this real world problem that is strictly related to the cutting stock problem with pattern minimization. Such a problem is addressed actually by a large cheque manufacturer in Southern part of Italy. We define a very efficient heuristic to solve it. The proposed solution methodology is currently used by the above mentioned manufacturer to define the cheque allocation of the plates.

Closed loop supply chain network design and optimisation using fuzzy mixed integer linear programming model

Owing to the revolution in sustainable and green manufacturing the production planning and network design of closed loop supply chain concept has got the attention of researchers and managers. In this paper, a multi-product, multi-facility capacitated closed-loop supply chain framework is proposed in an uncertain environment including reuse, refurbish, recycle and disposal of parts. The uncertainty related to demand, fraction of parts recovered for different product recovery processes, product acquisition cost, purchasing cost, transportation cost, processing, and set-up cost is handled with fuzzy numbers. A fuzzy mixed integer linear programming model is proposed to decide optimally the location and allocation of parts at each facility and number of parts to be purchased from external suppliers in order to maximise the profit of organisation. The proposed solution methodology is able to generate a balanced solution between the feasibility degree and degree of satisfaction of the decision maker. The proposed model has been tested with an illustrative example.

Sequencing Optimization in k-out-of-n Cold-Standby Systems Considering Mission Cost

The k-out-of-n: G heterogeneous cold-standby system structure is a widely used fault-tolerant system design method, where the sequence in which the different system elements are initiated can greatly affect the system reliability and mission cost. This paper considers the optimal standby element sequencing problem (SESP) for such systems. Given the desired cold-standby redundancy level and fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected system mission cost while meeting a certain level of system reliability constraint. Based on a discrete approximation of time-to-failure distributions of the system elements, the system reliability and expected mission cost are evaluated simultaneously using a numerical method. A genetic algorithm is used as an optimization tool for solving the formulated SESP problem for k-out-of-n: G heterogeneous cold-standby systems. Examples are given to illustrate the considered problem and the proposed solution methodology.

Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems

It is well recognized that using the hot standby redundancy provides fast restoration in the case of failures. However the redundant elements are exposed to working stresses before they are used, which reduces the overall system reliability. Moreover, the cost of maintaining the hot redundant elements in the operational state is usually much greater than the cost of keeping them in the cold standby mode. Therefore, there exists a tradeoff between the cost of losses associated with the restoration delays and the operation cost of standby elements. Such a trade-off can be obtained by designing both hot and cold redundancy types into the same system. Thus a new optimization problem arises for the standby system design. The problem, referred to in this work as optimal standby element distributing and sequencing problem (SE-DSP) is to distribute a fixed set of elements between cold and hot standby groups and select the element initiation sequence so as to minimize the expected mission operation cost of the system while providing a desired level of system reliability. This paper first formulates and solves the SE-DSP problem for 1-out-of-N: G heterogeneous non-repairable standby systems. A numerical method is proposed for evaluating the system reliability and expected mission cost simultaneously. This method is based on discrete approximation of time-to-failure distributions of the system elements. A genetic algorithm is used as an optimization tool for solving the formulated optimization problem. Examples are given to illustrate the considered problem and the proposed solution methodology.

Multi-objective preventive maintenance and replacement scheduling in a manufacturing system using goal programming

This research presents a new multi-objective nonlinear mixed-integer optimization model to determine Pareto-optimal preventive maintenance and replacement schedules for a repairable multi-workstation manufacturing system with increasing rate of occurrence of failure. The operational planning horizon is segmented into discrete and equally-sized periods and in each period three possible maintenance actions (repair, replacement, or do nothing) have been considered for each workstation. The optimal maintenance decisions for each workstation in each period are investigated such that the objectives and the requirements of the system can be achieved. Total operational costs, overall reliability and the system availability are incorporated as the objective functions and the multi-objective model is solved using a hybrid Monte Carlo simulation and goal programming procedure to obtain set of non-dominated schedules. The effectiveness and feasibility of the proposed solution methodology are demonstrated in a manufacturing setting and the computational performance of method in obtaining Pareto-optimal solutions is evaluated. Such a modeling approach and the proposed solution algorithm could be useful for maintenance planners and engineers tasked with the problem of developing optimal maintenance plans for complex productions systems.

Studies on controllability of directed networks with extremal optimization

Almost all natural, social and man-made-engineered systems can be represented by a complex network to describe their dynamic behaviors. To make a real-world complex network controllable with its desired topology, the study on network controllability has been one of the most critical and attractive subjects for both network and control communities. In this paper, based on a given directed–weighted network with both state and control nodes, a novel optimization tool with extremal dynamics to generate an optimal network topology with minimum control nodes and complete controllability under Kalman’s rank condition has been developed. The experimental results on a number of popular benchmark networks show the proposed tool is effective to identify the minimum control nodes which are sufficient to guide the whole network’s dynamics and provide the evolution of network topology during the optimization process. We also find the conclusion: “the sparse networks need more control nodes than the dense, and the homogeneous networks need fewer control nodes compared to the heterogeneous” (Liu et al., 2011 [18]), is also applicable to network complete controllability. These findings help us to understand the network dynamics and make a real-world network under the desired control. Moreover, compared with the relevant research results on structural controllability with minimum driver nodes, the proposed solution methodology may also be applied to other constrained network optimization problems beyond complete controllability with minimum control nodes.

A robust linear-pressure analog for the analysis of natural gas transportation networks

Reliable analysis of transportation networks is crucial for design and planning purposes. A pipeline network system could range from simple to very sophisticated and complex arrangement: from a single pipe transporting fluid from a place to another or elaborated as an interconnected set of fluid networks for intra-state or international transportation. As the complexity of the network system grows, the solution for the network model complicates further. For a natural gas network system, the resulting set of fluid flow governing equations is highly non-linear. In such situations, the customary method employed for the solution of a set of non-linear equations is the multivariable Newton–Raphson method despite its potentially negative drawbacks. Newton–Raphson solution protocols demand a good initialization (i.e., a good initial “guess” of the actual solution) for satisfactory performance because convergence is only guaranteed to occur within a potentially narrow neighborhood around the solution vector. This prerequisite can become fairly restrictive for the solution of large gas network systems, where estimations of “good” initial gas load and nodal values across the domain can defy intuition. In addition, some Newton–Raphson formulations require pre-defining flow loops within a network system prior to attempting a solution, which proves to be a challenging task in an extensive network. We propose an alternate, simple yet elegant method to address the aforementioned problems. The proposed solution methodology retains most advantages of the Newton-nodal method while removing the need for initial guesses and eliminating the need for expensive Jacobian formulations and associated derivative calculations. The resulting linear-pressure analog model is robust, reliable and its execution and convergence is independent of user-defined initial guesses for nodal pressures and flow rates. This allows the simulation study of a steady-state gas network system to be efficiently and straight-forwardly conducted.

Reliable design of a closed loop supply chain network under uncertainty: An interval fuzzy possibilistic chance-constrained model

This article seeks to offer a systematic approach to establishing a reliable network of facilities in closed loop supply chains (CLSCs) under uncertainties. Facilities that are located in this article concurrently satisfy both traditional objective functions and reliability considerations in CLSC network designs. To attack this problem, a novel mathematical model is developed that integrates the network design decisions in both forward and reverse supply chain networks. The model also utilizes an effective reliability approach to find a robust network design. In order to make the results of this article more realistic, a CLSC for a case study in the iron and steel industry has been explored. The considered CLSC is multi-echelon, multi-facility, multi-product and multi-supplier. Furthermore, multiple facilities exist in the reverse logistics network leading to high complexities. Since the collection centres play an important role in this network, the reliability concept of these facilities is taken into consideration. To solve the proposed model, a novel interactive hybrid solution methodology is developed by combining a number of efficient solution approaches from the recent literature. The proposed solution methodology is a bi-objective interval fuzzy possibilistic chance-constraint mixed integer linear programming (BOIFPCCMILP). Finally, computational experiments are provided to demonstrate the applicability and suitability of the proposed model in a supply chain environment and to help decision makers facilitate their analyses.

Cold-standby sequencing optimization considering mission cost

This paper considers the optimal standby component sequencing problem (SESP) for 1-out-of-N: G heterogeneous cold-standby systems. Given the desired cold-standby redundancy level and a fixed set of components, the objective of the optimal system operation scheduling is to select the initiation sequence of the system components so as to minimize the expected mission cost of the system. Based on a discrete approximation of time-to-failure distributions of the system components, the mission reliability and expected mission cost are simultaneously evaluated using the universal generating function technique. A genetic algorithm is used as an optimization tool for solving the formulated SESP problem for the 1-out-of-N: G heterogeneous cold-standby systems. Several examples are given to illustrate the considered problem and the proposed solution methodology.

Novel bi-level hierarchical production planning in hybrid MTS/MTO production contexts

A hybrid make-to-stock (MTS)/make-to-order (MTO) production strategy is one of the most appealing production strategies that has recently been investigated by academics and practitioners. In this paper, a hierarchical production planning (HPP) structure is developed in hybrid MTS/MTO production contexts for the first time. The proposed structure includes mid-term and short-term production planning levels by proposing a systematic and integrated approach towards tactical and operational issues. To cope with the problem, diverse novel modules are developed at each level and then they are interrelated from a hierarchical point of view. Moreover, a hybrid meta-heuristic algorithm is developed to tackle the computational complexity of a scheduling task. Finally, numerical experiments validate the proposed solution methodology.

A novel hybrid method for supply chain optimization with capacity constraint and shipping option

In a modern market, supply chain network design is considered as a strategic decision that provides the proper platform for cost management and increases the competitive edge of enterprise. In a five-tier supply chain, there are several facilities such as suppliers, manufacturers, warehouses, distribution centers, and retailers or customers. For product transportation from one facility to another, different types of options may be used. These options have variety price and the manager should do the best assignment to reduce the total cost. In this paper, we formulated an integer programming model for a five-tier supply chain with capacitated facility and multiple transportation option with fixed lead time. We also proposed a novel meta-heuristic solution methodology that combines the Taguchi's feature with artificial immune approach in order to solve the proposed model. The performance of the proposed solution methodology has been examined against a set of numeric instances and the obtained results are compared with those provided by hybrid genetic algorithm and Taguchi and artificial immune system. Results indicate that this methodology can make better results than previous solutions effectively.