# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

All Issues

## Journal of Industrial & Management Optimization

April 2018 , Volume 14 , Issue 2

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2018, 14(2): 427-446 doi: 10.3934/jimo.2017054 +[Abstract](5960) +[HTML](1308) +[PDF](911.24KB)
Abstract:

The Ebola virus disease is a severe viral haemorrhagic fever syndrome caused by Ebola virus. This disease is transmitted by direct contact with the body fluids of an infected person and objects contaminated with virus or infected animals, with a death rate close to 90% in humans. Recently, some mathematical models have been presented to analyse the spread of the 2014 Ebola outbreak in West Africa. In this paper, we introduce vaccination of the susceptible population with the aim of controlling the spread of the disease and analyse two optimal control problems related with the transmission of Ebola disease with vaccination. Firstly, we consider the case where the total number of available vaccines in a fixed period of time is limited. Secondly, we analyse the situation where there is a limited supply of vaccines at each instant of time for a fixed interval of time. The optimal control problems have been solved analytically. Finally, we have performed a number of numerical simulations in order to compare the models with vaccination and the model without vaccination, which has recently been shown to fit the real data. Three vaccination scenarios have been considered for our numerical simulations, namely: unlimited supply of vaccines; limited total number of vaccines; and limited supply of vaccines at each instant of time.

2018, 14(2): 447-472 doi: 10.3934/jimo.2017055 +[Abstract](4032) +[HTML](685) +[PDF](1262.8KB)
Abstract:

The urban transport planning process has four main activities: Network design, Timetable construction, Vehicle scheduling and Crew scheduling; each activity has subactivities. In this paper the authors work with the subactivities of timetable construction: minimal frequency calculation and departure time scheduling. The authors propose to solve both subactivities in an integrated way. The developed mathematical model allows multi-period planning and it can also be used for multimodal urban transportation systems. The authors consider demand uncertainty and the authors employ fuzzy programming to solve the problem. The authors formulate the urban transportation timetabling construction problem as a bi-objective problem: to minimize the total operational cost and to maximize the number of multi-period synchronizations. Finally, the authors implemented the SAUGMECON method to solve the problem.

2018, 14(2): 473-496 doi: 10.3934/jimo.2017056 +[Abstract](3977) +[HTML](667) +[PDF](576.14KB)
Abstract:

In this paper, we introduce a novel fully exponentially convergent direct integral pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system. The proposed method combines the superior advantages possessed by the family of pseudospectral methods with the well-conditioning of integral operators through the use of the integral formulation of the distributed parameter system equations, and the spectral accuracy provided by the latest technology of Gegenbauer barycentric quadratures in a fashion that allows us to take advantage of the strengths of these three methodologies. A rigorous error analysis of the method is presented, and a numerical test example is given to show the accuracy and efficiency of the proposed integral pseudospectral method.

Ran Ma and
2018, 14(2): 497-510 doi: 10.3934/jimo.2017057 +[Abstract](4044) +[HTML](669) +[PDF](382.38KB)
Abstract:

We revisit the classical online scheduling problem on parallel machines for minimizing total weighted completion time. In the problem, a set of independent jobs arriving online over time has to be scheduled on identical machines, where the information of each job including its processing time and weight is not known in advance. The goal is to minimize the total weighted completion time of the jobs. For this problem, we propose an improved 2.11-competitive online algorithm based on a kind of waiting strategy.

2018, 14(2): 511-539 doi: 10.3934/jimo.2017058 +[Abstract](4593) +[HTML](969) +[PDF](496.66KB)
Abstract:

Integrated integrated production - distribution planning in traditional forward supply chain has attracted a lot of attention in recent years and its economic advantages are particularly noticeable. However, for closed-loop supply chain, recycling and remanufacturing processes should be taken further into account to the integrated planning. In this paper, we address a planning problem of a multi - echelon decentralized closed-loop supply chain system, which consists of a joint recycling center, multiple manufacturing/remanufacturing factories and multiple distributors decentralized to different regions. For this problem, an integrated recycling-integrated production - distribution multi - level planning model is developed, which considers material flows and decision interactions among members at different echelons in the system, as well as their own operation objectives. And the local interests of members at every echelon would be balanced in order to coordinate the operation of the whole system. According to the characteristics of the planning model, the solution approach is designed by hierarchical iteration strategy based on Self-Adaptive Genetic Algorithm (SAGA). Hierarchical iteration processes, in which SAGA is used to solve every single level model, are corresponding to repeated negotiation behaviors among members at different echelons in closed-loop supply chain. Finally, a numerical example is suggested to demonstrate the applicability and effectiveness of the proposed model and solution approach.

2018, 14(2): 541-559 doi: 10.3934/jimo.2017059 +[Abstract](4215) +[HTML](862) +[PDF](489.52KB)
Abstract:

We consider the framework of the classical Markowitz mean-variance (MV) model when multiple solutions exist, among which the sparse solutions are stable and cost-efficient. We study a two - phase stochastic linear complementarity approach. This approach stabilizes the optimization problem, finds the sparse asset allocation that saves the transaction cost, and results in the solution set of the Markowitz problem. We apply the sample average approximation (SAA) method to the two - phase optimization approach and give detailed convergence analysis. We implement this methodology on the data sets of Standard and Poor 500 index (S & P 500), real data of Hong Kong and China market stocks (HKCHN) and Fama & French 48 industry sectors (FF48). With mock investment in training data, we construct portfolios, test them in the out-of-sample data and find their Sharpe ratios outperform the \begin{document} $\ell_1$ \end{document} penalty regularized portfolios, \begin{document} $\ell_p$ \end{document} penalty regularized portfolios, cardinality constrained portfolios, and \begin{document} $1/N$ \end{document} investment strategy. Moreover, we show the advantage of our approach in the risk management by using the criteria of standard deviation (STD), Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).

2018, 14(2): 561-582 doi: 10.3934/jimo.2017060 +[Abstract](5234) +[HTML](974) +[PDF](744.77KB)
Abstract:

The single window concept refers to systems that allow organizations to provide one-stop services to users. This paper describes a model for the design of a single window system in the context of e-government. The model determines which government service procedures should be incorporated into the system, which technology should be used to execute each procedure and the time in the planning horizon at which technology upgrades and incorporation processes should take place, while maximizing the total social benefit associated with these decisions. The proposed model, a mixed integer linear program, is applied to the particular problem faced by the government of Chile a few years ago. The solution generated by the model for this instance is compared to that obtained through the Chilean government's own method for prioritizing the inclusion of procedures into its single window system. When the proposed model was limited to choosing 60 procedures, the number chosen by the Chilean government's method, the solution produced 1.6 times more benefits. With the limit on the number of procedures removed but considering a budget constraint, the model chose 111 procedures that generated 1.85 times more social benefits than those procedures chosen using the government's method.

2018, 14(2): 583-596 doi: 10.3934/jimo.2017061 +[Abstract](4592) +[HTML](644) +[PDF](374.23KB)
Abstract:

This paper deals with the exponential stabilization problem by means of memory state feedback controller for linear singular positive systems with delay. By using system decomposition approach, singular systems theory and Lyapunov function method, we obtain new delay-dependent sufficient conditions for designing such controllers. The conditions are given in terms of standard linear programming (LP) problems, which can be solved by LP optimal toolbox. A numerical example is given to illustrate the effectiveness of the proposed method.

2018, 14(2): 597-611 doi: 10.3934/jimo.2017062 +[Abstract](4131) +[HTML](698) +[PDF](1033.43KB)
Abstract:

In this paper, we propose a robust local image statistic based on optimized direction, by which we can distinguish image details and edges from impulse noise effectively. Therefore it can identify noisy pixels more accurately. Meanwhile, we combine it with the edge-preserving regularization to remove random-valued impulse noise in the cause of precise estimated value. Simulation results show that our method can preserve edges and details efficiently even at high noise levels.

2018, 14(2): 613-623 doi: 10.3934/jimo.2017063 +[Abstract](3656) +[HTML](744) +[PDF](319.55KB)
Abstract:

This paper was motivated by a practical optimization problem formulated at the Erdenet Mining Corporation (Mongolia). By solving an identification problem for a chosen design of experiment we developed a quadratic model that quite adequately represents the experimental data. The problem obtained turned out to be the indefinite quadratic program, which we solved by applying the global search theory for a d.c. programming developed by A.S. Strekalovsky [13]-[15]. According to this d.c. optimization theory, we performed a local search that takes into account the structure of the problem in question, and constructed procedures of escaping critical points provided by the local search. The algorithms proposed for d.c. programming were verified using a set of test problems as well as a copper content maximization problem arising at the mining factory.

2018, 14(2): 625-636 doi: 10.3934/jimo.2017064 +[Abstract](3768) +[HTML](609) +[PDF](371.47KB)
Abstract:

Quadratic programs with complementarity constraints (QPCC) are NP-hard due to the nonconvexity of complementarity relation between the pairs of nonnegative variables. Most of the existing solvers are capable of solving QPCC by finding stationary solutions, which are not able to be verified as global or local optimal ones. In this paper, we aim to globally solve QPCC by a branch-and-bound algorithm, in which the doubly nonnegative (DNN) relaxation in each node is efficiently solved via an augmented Lagrangian method. The method is practically efficient due to the fact that the augmented Lagrangian function can be decomposed into two easy-to-solve subproblems. Computational results demonstrate the effectiveness of the proposed algorithm, with a particular highlight in only a few nodes for some instances.

2018, 14(2): 637-646 doi: 10.3934/jimo.2017065 +[Abstract](3284) +[HTML](656) +[PDF](331.97KB)
Abstract:

This paper focuses on solving normalized stationary points of a class of equilibrium problem with equilibrium constraints (EPEC). We show that, under some kind of separability assumption, normalized C-/M-/S-stationary points of EPEC are actually C-/M-/S-stationary points of an associated mathematical program with equilibrium constraints (MPEC), which implies that we can solve MPEC to obtain normalized stationary points of EPEC. In addition, we demonstrate the proposed approach on competition of manufacturers for similar products in the same city.

2018, 14(2): 647-652 doi: 10.3934/jimo.2017066 +[Abstract](3299) +[HTML](696) +[PDF](270.25KB)
Abstract:

Using the data of stock returns and the variations of quarterly institutional ownership around Secondary Equity Offerings (SEOs) in China from 2004 to 2008, we verify that institutional investors are smart in selecting stocks. Sorting the SEOs samples into two groups according to whether there is an increase or decrease in institutional ownership, we find no significant difference in stock returns between the two groups before SEOs, but higher returns among the group with increases in institutional ownership over 1 month, 3 month, 6 month, 9 month, 12 month and 18 month periods, respectively. This result indicates the evidence of the stronger stock selection ability of institutional investors.

2018, 14(2): 653-671 doi: 10.3934/jimo.2017067 +[Abstract](3997) +[HTML](656) +[PDF](470.22KB)
Abstract:

We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions for the solutions of the regular-singular control problem. Finally we apply the maximum principles to solve the investment and dividend problem of an insurer.

2018, 14(2): 673-686 doi: 10.3934/jimo.2017068 +[Abstract](3406) +[HTML](738) +[PDF](422.78KB)
Abstract:

In this study, the stability problem of descriptor second-order systems is considered. Lyapunov equations for stability of second-order systemsare established by using Lyapunov method. The existence of solutions for Lyapunov equations are discussed and linear matrixinequality condition for stability of second-order systems aregiven. Then, based on the feasible solutions of the linear matrixinequality, all parametric solutions of Lyapunov equations are derived.Furthermore, the results of Lyapunov equations and linear matrixinequality condition for stability of second-ordersystems are extended to high-order systems. Finally, illustratingexamples are provided to show the effectiveness of the proposed method.

2018, 14(2): 687-705 doi: 10.3934/jimo.2017069 +[Abstract](3570) +[HTML](642) +[PDF](387.94KB)
Abstract:

This paper integrates the prospect theory with two-product ordering problem and adopts Bayesian forecasting model under Brownian motion to propose a loss-averse two-product ordering model with demand information updating in a two-echelon inventory system. We also derive all psychological perceived revenue functions for sixteen supply-demand cases as well as the expected value functions and prospect value function for the loss-averse retailer. To solve this model, a Monte Carlo algorithm is presented to estimate the high dimensional integrals with curved polyhedral integral region of unknown volume. Numerical results show that the optimal order quantities of both high-risk product and low-risk product vary across different psychological reference points, which are also affected by information updating, and the loss-averse retailer benefits considerably from information updating. All results suggest that our model provides a better description of the retailer$'$s actual ordering behavior than existing models.

2018, 14(2): 707-718 doi: 10.3934/jimo.2017070 +[Abstract](3420) +[HTML](667) +[PDF](196.33KB)
Abstract:

In this paper, an adaptive trust region algorithm in which the trust region radius converges to zero is presented for solving large-residual nonsmooth least squares problems. This algorithm uses the smoothing technique of the approximation function, and it combines an adaptive trust region radius. Moreover, this algorithm differs from the existing methods for solving nonsmooth equations through use of the approximation function of second-order information, which improves the convergence rate for large-residual nonsmooth least squares problems. Under some suitable conditions, the global and local superlinear convergences of the proposed method are proven. The preliminary numerical results indicate that the proposed algorithm is effective and suitable for solving large-residual nonsmooth least squares problems.

2018, 14(2): 719-729 doi: 10.3934/jimo.2017071 +[Abstract](3608) +[HTML](720) +[PDF](520.97KB)
Abstract:

In this paper, we propose a new multitask feature selection model based on least absolute deviations. However, due to the inherent nonsmoothness of \begin{document}$l_1$\end{document} norm, optimizing this model is challenging. To tackle this problem efficiently, we introduce an alternating iterative optimization algorithm. Moreover, under some mild conditions, its global convergence result could be established. Experimental results and comparison with the state-of-the-art algorithm SLEP show the efficiency and effectiveness of the proposed approach in solving multitask learning problems.

2018, 14(2): 731-742 doi: 10.3934/jimo.2017072 +[Abstract](4000) +[HTML](739) +[PDF](440.13KB)
Abstract:

We extend stochastic newsvendor games with information lag by including dynamic retail prices, and we characterize their equilibria. We show that the equilibrium wholesale price is a nonincreasing function of the demand, while the retailer's output increases with demand until we recover the usual equilibrium. In particular, it is then optimal for retailer and wholesaler to have demand at least equal to some threshold level, beyond which the retailer's output tends to an upper bound which is absent in fixed retail price models. When demand is given by a delayed Ornstein-Uhlenbeck process and price is an affine function of output, we numerically compute the equilibrium output and we show that the lagged case can be seen as a smoothing of the no lag case.

2018, 14(2): 743-757 doi: 10.3934/jimo.2017073 +[Abstract](3768) +[HTML](667) +[PDF](375.6KB)
Abstract:

This paper considers a multi-server polling system with batch service of an unlimited size, i.e., the so called "Israeli queue" with multi-server, where the service rate of each server switches between a low and a high value depending on the number of groups standing in front of the servers upon its service completion. By means of matrix geometric method and LU-type RG factorization of the infinitesimal generator in irreducible QBD process, the explicit closed-form of rate matrix $R$ and the steady state distribution of the queue length are respectively derived. In terms of the results, some stationary performance measures are obtained. In addition, some numerical examples are presented.

2018, 14(2): 759-784 doi: 10.3934/jimo.2017074 +[Abstract](4265) +[HTML](689) +[PDF](692.64KB)
Abstract:

We study a multi-objective access point dispersion problem, where the conflicting objectives of maximizing the distance and maximizing the connectivity between the agents are considered with explicit coverage (or Quality of Service) constraints. We model the problem first as a multi-objective model, and then, we consider the constrained single objective alternatives, which we propose to solve using three approaches: The first approach is an optimal tree search algorithm, where bounds are used to prune the search tree. The second approach is a beam search heuristic, which is also used to provide lower bound for the first approach. The third approach is a straightforward integer programming approach. We present an illustrative application of our solution approaches in a real wireless mesh network deployment problem.

Yigui Ou and
2018, 14(2): 785-801 doi: 10.3934/jimo.2017075 +[Abstract](4086) +[HTML](761) +[PDF](431.62KB)
Abstract:

This paper presents a nonmonotone scaled memoryless BFGS preconditioned conjugate gradient algorithm for solving nonsmooth convex optimization problems, which combines the idea of scaled memoryless BFGS preconditioned conjugate gradient method with the nonmonotone technique and the Moreau-Yosida regularization. The proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. Under mild conditions, the global convergence of the proposed method is established. Preliminary numerical results and related comparisons show that the proposed method can be applied to solve large scale nonsmooth convex optimization problems.

2018, 14(2): 803-815 doi: 10.3934/jimo.2017076 +[Abstract](3505) +[HTML](645) +[PDF](340.06KB)
Abstract:

This paper investigates multi-machine scheduling problems with interval constrained actual processing times. The actual processing time of each job is assumed to be restricted in a given interval otherwise the extra earliness or tardiness time should be used to patch up the flaw of job. The objectives are to find the optimal job sequence to minimize the total load of machines, the number of exceeding-interval jobs and the makespan of job schedule, respectively. This paper shows that both of the total load minimization problem and the exceeding job number minimization problem are polynomially solvable. For the makespan minimization problem, this paper proves that it is NP-hard, and proposes a fully polynomial time approximation scheme (FPTAS) for the case with two parallel machines.

2018, 14(2): 817-831 doi: 10.3934/jimo.2017077 +[Abstract](4293) +[HTML](715) +[PDF](433.29KB)
Abstract:

The retrieval of parameters related to an environmental model is explored. We address computational challenges occurring due to a significant numerical difference of up to two orders of magnitude between the two model parameters we aim to retrieve. First, the corresponding optimization problem is poorly scaled, causing minimization algorithms to perform poorly (see Gill et al., practical optimization, AP, 1981,401pp). This issue is addressed by proper rescaling. Difficulties also arise from the presence of strong nonlinearity and ill-posedness which means that the parameters do not converge to a single deterministic set of values, but rather there exists a range of parameter combinations that produce the same model behavior. We address these computational issues by the addition of a regularization term in the cost function. All these computational approaches are addressed in the framework of variational adjoint data assimilation. The used observational data are derived from numerical simulation results located at only two spatial points. The effect of different initial guess values of parameters on retrieval results is also considered. As indicated by results of numerical experiments, the method presented in this paper achieves a near perfect parameter identification, and overcomes the indefiniteness that may occur in inversion process even in the case of noisy input data.

2018  Impact Factor: 1.025