# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

All Issues

## Journal of Industrial & Management Optimization

January 2020 , Volume 16 , Issue 1

Select all articles

Export/Reference:

2020, 16(1): 1-9 doi: 10.3934/jimo.2018136 +[Abstract](3640) +[HTML](1269) +[PDF](344.49KB)
Abstract:

By virtue of the Nesterov's acceleration technique, we establish an accelerated augmented Lagrangian method for solving linearly constrained multi-criteria optimization problem. For this method, we establish its global convergence under suitable condition. Further, we show that its iteration-complexity is \begin{document}$O(1/k^2)$\end{document} which improves the original ALM whose iteration-complexity is \begin{document}$O(1/k)$\end{document}.

2020, 16(1): 11-23 doi: 10.3934/jimo.2018137 +[Abstract](3580) +[HTML](1260) +[PDF](2221.28KB)
Abstract:

Both government and private sector have the characteristic of fairness preference when deciding a suitable concession period for infrastructure projects. The appropriate concession period is helpful to construct the Public-Private-Partnership (PPP) project, to alleviate government's financial burden, and to boast the economic growth. Therefore, this paper aims to develop a decision-making model of concession period with fairness preference based on the two sides' equitable utilities. To better describe decision makers' fair psychology, the Nash bargaining game solution was adopted as a fair reference point. The results show that the concession period with fairness preference will become longer than that without fairness preference. Furthermore, the longer the concession period is, the better construction quality of the infrastructure project (highway) is. So, decision makers with fairness preference tend to make good decisions. In conclusion, the developed decision-making model renders useful references for both government and private sector in negotiating the concession period for infrastructure projects.

2020, 16(1): 25-36 doi: 10.3934/jimo.2018138 +[Abstract](3471) +[HTML](963) +[PDF](414.82KB)
Abstract:

Set optimization is an indispensable part of theory and method of optimization, and has been received wide attentions due to its extensive applications in group decision and group game problems. This paper focus on the continuity of the strict (weak) minimal solution set mapping of parametric set-valued vector optimization problems with the lower set less order relation. We firstly introduce a concept of strict lower level mapping of parametric set-valued vector optimization problems. Moreover, the upper and lower semicontinuity of the strict lower level mapping are obtained under some suitable conditions. Lastly, the sufficient condition for the continuity of the strict minimal solution set mappings of parametric set optimization problems are established by a new proof method, which is different from that in [27,28].

2020, 16(1): 37-53 doi: 10.3934/jimo.2018139 +[Abstract](3251) +[HTML](1076) +[PDF](404.84KB)
Abstract:

In this article, some existence and uniqueness of solutions for a new class of global fractional-order projective dynamical system with delay and perturbation are proved by employing the Krasnoselskii fixed point theorem and the Banach fixed point theorem. Moreover, an approximating algorithm is also provided to find a solution of the global fractional-order projective dynamical system. Finally, an application to the idealized traveler information systems for day-to-day adjustments processes and a numerical example are given.

2020, 16(1): 55-70 doi: 10.3934/jimo.2018140 +[Abstract](3197) +[HTML](1263) +[PDF](403.14KB)
Abstract:

This paper mainly studies the optimality conditions for a class of trilevel optimization problem, of which all levels are nonlinear programs. We firstly transform this problem into an auxiliary bilevel optimization problem by applying KKT approach to the lower-level problem. Then we obtain a necessary optimality condition via the differential calculus of Mordukhovich. Finally, a theorem for existence of optimal solution is derived via Weierstrass Theorem.

2020, 16(1): 71-101 doi: 10.3934/jimo.2018141 +[Abstract](3500) +[HTML](1166) +[PDF](1408.46KB)
Abstract:

This paper investigates the asset liability management problem for an ordinary insurance system incorporating the standard concept of proportional reinsurance coverage in a stochastic interest rate and stochastic volatility framework. The goal of the insurer is to maximize the expectation of the constant relative risk aversion (CRRA) of the terminal value of the wealth, while the goal of the reinsurer is to maximize the expected exponential utility (CARA) of the terminal wealth held by the reinsurer. We assume that the financial market consists of risk-free assets and risky assets, and both the insurer and the reinsurer invest on one risk-free asset and one risky asset. By using the stochastic optimal control method, analytical expressions are derived for the optimal reinsurance control strategy and the optimal investment strategies for both the insurer and the reinsurer in terms of the solutions to the underlying Hamilton-Jacobi-Bellman equations and stochastic differential equations for the wealths. Subsequently, a semi-analytical method has been developed to solve the Hamilton-Jacobi-Bellman equation. Finally, we present numerical examples to illustrate the theoretical results obtained in this paper, followed by sensitivity tests to investigate the impact of reinsurance, risk aversion, and the key parameters on the optimal strategies.

2020, 16(1): 103-115 doi: 10.3934/jimo.2018142 +[Abstract](4511) +[HTML](1296) +[PDF](494.81KB)
Abstract:

Cuckoo Search (CS) is a recently proposed metaheuristic algorithm to solve optimization problems. For improving its performance both on the efficiency of searching and the speed of convergence, we proposed an improved Cuckoo Search algorithm based on the teaching-learning strategy (TLCS). For a better balance between intensification and diversification, both a dynamic weight factor and an out-of-bound project strategies are also introduced into TLCS. The results of numerical experiment demonstrate that our improved TLCS performs better than the basic CS and other two improved CS methods appearing in literatures.

2020, 16(1): 117-140 doi: 10.3934/jimo.2018143 +[Abstract](5723) +[HTML](1372) +[PDF](699.99KB)
Abstract:

The newsvendor problem is a classical task in inventory management. The present paper considers a two-period newsvendor problem where demand of different periods is interdependent (not independent), and seeks to follow this approach to develop a two-period newsvendor problem with unsatisfied demand or unsold quantity. Concerning the complexity of solution of multiple integrals, the problem is assessed for only two periods. In the course of a numerical solution, the probability distribution function of demand pertaining to each period is assumed to be given (in the form of a bivariate normal distribution). The optimal solution is presented in the form of the initial inventory level that maximizes the expected profit. Finally, all model parameters are subjected to a sensitivity analysis. This model can be used in a number of applications, such as procurement of raw materials in projects (e.g., construction, bridge-building and molding) where demand of different periods is interdependent. Proposed model takes into account interdependent demand oughts to provide a better solution than a model based on independent demand.

2020, 16(1): 141-167 doi: 10.3934/jimo.2018144 +[Abstract](4167) +[HTML](1683) +[PDF](650.43KB)
Abstract:

It is important to adopt precisely the optimum level of preservation technology for deteriorating products, as with every passing day, a larger number of items deteriorate and cause an economic loss. For earning more profit, industries have a tendency to add more preservatives for long lifetime of products. However, realizing the health issues, there is a boundary that no manufacturer can add huge amount of preservatives for infinite lifetime of products. The correlation between the long lifetime along with the price of the product is introduced in this model to show the benefit of the optimum level of investment in preservation technology. To maintain the environmental sustainability, the deteriorated items, which can no longer be preserved by adding preservatives anywhere, are disposed with proper protection. The objective of the study is to obtain profit to show the application through a non-linear mathematical. The model is solved through Kuhn-Tucker and an algorithm. Robustness of the model is verified through numerical experiments and sensitivity analysis. Some comparative analyses are provided, which support the adoption of preservation technology for deteriorating products. Numerical studies proved that the profit increases significantly with the application of proposed preservation technology. Some important managerial insights are provided to help the decision makers while implementing the proposed model in real-world situations.

2020, 16(1): 169-187 doi: 10.3934/jimo.2018145 +[Abstract](2753) +[HTML](1019) +[PDF](466.52KB)
Abstract:

The present paper studies a new class of problems of optimal control theory with differential inclusions described by fourth order Sturm-Liouville type differential operators (SLDOs). Then, there arises a rather complicated problem with simultaneous determination of the SLDOs with variable coefficients and a Mayer functional depending of high order derivatives of searched functions. The sufficient conditions, containing both the Euler-Lagrange and Hamiltonian type inclusions and "transversality" conditions are derived. Formulation of the transversality conditions at the endpoints \begin{document}$t = 0$\end{document} and \begin{document}$t = 1$\end{document} of the considered time interval plays a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions. The main idea of the proof of optimality conditions of Mayer problem for differential inclusions with fourth order SLDO is the use of locally-adjoint mappings. The method is demonstrated in detail as an example for the semilinear optimal control problem, for which the Weierstrass-Pontryagin maximum principle is obtained.

2020, 16(1): 189-205 doi: 10.3934/jimo.2018146 +[Abstract](3793) +[HTML](1342) +[PDF](594.73KB)
Abstract:

This paper solves a new model of preventive maintenance scheduling with novel methodology. The aim of solving this problem is to determine the period for which bag filter should be taken off line for planned preventive maintenance over a specific time horizon and maintain a certain level of reliability with minimal maintenance cost. A mathematical programming method (Benders' decomposition) and a metaheuristic algorithm are presented to provide solutions. The obtained objective value from Benders' decomposition method is considered as the stopping criterion in the metaheuristic algorithm. To demonstrate the significance and originality of the proposed model and the efficiency of the algorithms, computational analysis is provided to realistic bag filters system in the cement factory. The obtained result is a schedule that allows the cement factory to consider the preventive maintenance for bag filters over the time horizon.

2020, 16(1): 207-230 doi: 10.3934/jimo.2018147 +[Abstract](3949) +[HTML](1447) +[PDF](537.75KB)
Abstract:

This paper extends the existing dynamic consumption-investment problem to the case with more general discount functions under the robust framework. The decision-maker is ambiguity-averse and invests her wealth in a risk-free asset and a risky asset. Since non-exponential discounting is considered in our model, our optimization problem is time inconsistent. By solving the extended Hamilton-Jacobi-Bellman equations, the corresponding optimal consumption-investment strategies for sophisticated and naive investors under power and logarithmic utility functions are derived explicitly. Our model and results extend some existing ones and derive some interesting phenomena.

2020, 16(1): 231-244 doi: 10.3934/jimo.2018148 +[Abstract](3680) +[HTML](1021) +[PDF](343.83KB)
Abstract:

This paper addresses single machine and flowshop machines with the learning phenomenon. The learning phenomenon means that the actual jobs processing time of a job is a non-increasing function of the sum of processing times of jobs already processed. Under single machine, some properties firstly are presented to solve the objectives of minimizing the makespan problem, the total (weighted) completion time problem, the maximum lateness problem and the total tardiness problem. We show that minimizing the makespan problem and the total completion time problem can be solved in polynomial time. For the weighted completion time problem, the maximum lateness problem and the total tardiness problem, we give heuristic algorithm based on the corresponding optimal schedule and analyze the worst case error bound. Furthermore, we also show that the three problems are polynomially solvable under certain conditions. Under flowshop machines, we finally show that the makespan problem and the total completion time problem under more specialized proportional job processing times can be solved in polynomial time.

2020, 16(1): 245-260 doi: 10.3934/jimo.2018149 +[Abstract](4082) +[HTML](1170) +[PDF](573.71KB)
Abstract:

In this paper, we develop a three-term Polak-Ribière-Polyak conjugate gradient method, in which the search direction is close to the direction in the memoryless BFGS quasi-Newton method. The new scheme reduces to the standard Polak-Ribière-Polyak method when an exact line search is used. For any line search, the method satisfies the sufficient descent condition \begin{document}$g_{k}^{T}d_{k}≤ -{(1-\frac{1}{4}(1+\overline{t})^2})\|g_k\|^2$\end{document}, where \begin{document}$\overline{t}∈[0,1)$\end{document} is a constant. The global convergence results of the new algorithm are established with suitable line search methods. Numerical results show that the proposed method is efficient for the unconstrained problems in the CUTEr library.

2020, 16(1): 261-287 doi: 10.3934/jimo.2018151 +[Abstract](3270) +[HTML](1260) +[PDF](503.37KB)
Abstract:

This paper considers a two-echelon supply chain with one supplier and one retailer. The retailer holds private information on the stochastic demand, and the supplier knows neither the market information nor its prior distribution. Two decision making criteria based on the generalized lexicographic preference are proposed to the supplier: the profit criterion and the regret criterion. Our analyses show that the profit criterion always coordinates the supply chain, while the regret criterion does not. If the market state is low, the profit criterion generates higher profit for the supplier than the regret criterion does, and vise versa. In both criteria, we show that the supplier's regret is bounded by both the range of the market state and the volatility of the demand. We further show that, the supplier should cooperate with the retailer with full demand information if the differences between market states are large enough, while selling the product by himself is better if the differences between market states are small enough.

2020, 16(1): 289-307 doi: 10.3934/jimo.2018152 +[Abstract](3392) +[HTML](1125) +[PDF](596.7KB)
Abstract:

This paper considers price and modularity of competition between two firms with deterministic demand, in which demand is dependent on both the prices and the modularity levels determined by two firms. Bertrand competition and Stackelberg competition are formulated to derive the equilibrium solutions analytically. Because of the complexity, an intensive numerical study is conducted to investigate the impact of the sensitive parameters on equilibrium prices and modularity levels, as well as optimal profits of the two firms. An important and interesting finding is that optimal profits of the two firms under both types of competition are decreasing with the modularity cost when the price and modularity sensitivities are low, where both firms are worse-off due to decrease of the modularity levels; but they are increasing when the price and modularity sensitivities are high, where both firms are better-off at the expense of modular design. Our research reveals that Stackelberg game improves the modularity levels in most of the cases, though both firms perform better in Bertrand competition in these cases when jointly deciding the prices and modularity levels in the two firms.

2020, 16(1): 309-324 doi: 10.3934/jimo.2018153 +[Abstract](3370) +[HTML](1068) +[PDF](205.89KB)
Abstract:

In this article, the M-eigenvalue of fourth-order partially symmetric tensors is estimated by choosing different components of M-eigenvector. As an application, some upper bounds for the M-spectral radius of nonnegative fourth-order partially symmetric tensors are discussed, which are sharper than existing upper bounds. Finally, numerical examples are reported to verify the obtained results.

2020, 16(1): 325-356 doi: 10.3934/jimo.2018154 +[Abstract](3156) +[HTML](1245) +[PDF](598.86KB)
Abstract:

This study examines the optimal investment and dividend problem for an insurer with CRRA preference. The insurer's goal is to maximize the expected discounted accumulated utility from dividend before ruin and the insurer subjects to high gain tax payment. Both the surplus process and the financial market are modulated by an external Markov chain. Using the weak dynamic programming principle (WDPP), we prove that the value function of our control problem is the unique viscosity solution to coupled Hamilton-Jacobi-Bellman (HJB) equations with first derivative constraints. Solving an auxiliary problem without regime switching, we prove that, it is optimal for the insurer in a multiple-regime market to adopt the policies in the same way as in a single-regime market. The regularity of the viscosity solution on its domain is proved and thus the HJB equations admits classical solution. A numerical scheme for the value function is provided by the Markov chain approximation method, two numerical examples are given to illustrate the impact of the high gain tax and regime switching on the optimal policies.

2020, 16(1): 357-369 doi: 10.3934/jimo.2018155 +[Abstract](2904) +[HTML](1189) +[PDF](461.02KB)
Abstract:

The nonlocal modified Poisson-Boltzmann equation (NMPBE) is one important variant of a commonly-used dielectric continuum model, Poisson-Boltzmann equation (PBE). In this paper, we use a nonlinear block relaxation method to develop a new nonlinear solver for the nonlinear equation of \begin{document} $\Phi$ \end{document} and thus a new NMPBE solver, which is then programmed as a software package in \begin{document} $\texttt{C}\backslash\texttt{C++}$ \end{document}, \begin{document} $\texttt{Fortran}$ \end{document} and \begin{document} $\texttt{Python}$ \end{document} for computing the electrostatics of a protein in a symmetric 1:1 ionic solvent. Numerical tests validate the new package and show that the new solver can improve the efficiency by at least \begin{document}$40\%$ \end{document} than the finite element NMPBE solver without compromising solution accuracy.

2020, 16(1): 371-386 doi: 10.3934/jimo.2018157 +[Abstract](3733) +[HTML](1308) +[PDF](523.7KB)
Abstract:

This paper analyzes the optimal and equilibrium strategies in fuzzy Markovian queues where the system parameters are all fuzzy numbers. In this work, tools from both fuzzy logic and queuing theory have been used to investigate the membership functions of the optimal and equilibrium strategies in both observable and unobservable cases. By Zadeh's extension principle and $α$-cut approach, we formulate a pair of parametric nonlinear programs to describe the family of crisp strategy. Then the membership functions of the strategies in single and multi-server models are derived. Furthermore, the grated mean integration method is applied to find estimate of the equilibrium strategy in the fuzzy sense. Finally, numerical examples are solved successfully to illustrate the validity of the proposed approach and a sensitivity analysis is performed, which show the relationship of these strategies and social benefits. Our finding reveals that the value of equilibrium and optimal strategies have no deterministic relationship, which are different from the results in the corresponding crisp queues. Since the performance measures of such queues are expressed by fuzzy numbers rather than by crisp values, the system managers could get more precise information.

Cuilian You and
2020, 16(1): 387-396 doi: 10.3934/jimo.2018158 +[Abstract](3262) +[HTML](915) +[PDF](292.75KB)
Abstract:

Fuzzy stock model has been studied by many scholars in recent years, in which option pricing problem is the most important part. In this paper, we studied option pricing for a new generalized fuzzy stock model. Based on credibility theory, pricing formulas of European option and American option were obtained.

2020, 16(1): 397-407 doi: 10.3934/jimo.2018159 +[Abstract](2658) +[HTML](934) +[PDF](356.54KB)
Abstract:

Low-rank matrix recovery has become a popular research topic with various applications in recent years. One of the most popular methods to dual with this problem for overcoming its NP-hardness is to relax it into some tractable optimization problems. In this paper, we consider a nonconvex relaxation, the Schatten-\begin{document}$p$\end{document} quasi-norm minimization (\begin{document}$0<p<1$\end{document}), and discuss conditions for the equivalence between the original problem and this nonconvex relaxation. Specifically, based on null space analysis, we propose a \begin{document}$p$\end{document}-spherical section property for the exact and approximate recovery via the Schatten-\begin{document}$p$\end{document} quasi-norm minimization (\begin{document}$0<p<1$\end{document}).

2020, 16(1): 409-429 doi: 10.3934/jimo.2018160 +[Abstract](3476) +[HTML](1941) +[PDF](696.74KB)
Abstract:

The packing problem study how to pack multiple objects without overlap. Various exact and approximate algorithms have been developed for two-dimensional regular and irregular packing as well as three-dimensional bin packing. However, few results are reported for three-dimensional irregular packing problems. This paper will develop a method for solving three-dimensional irregular packing problems. A three-grid approximation technique is first introduced to approximate irregular objects. Then, a hybrid heuristic method is developed to place and compact each individual objects where chaos search is embedded into firefly algorithm in order to enhance the algorithm's diversity for optimizing packing sequence and orientations. Results from several computational experiments demonstrate the effectiveness of the hybrid algorithm.

2020, 16(1): 431-443 doi: 10.3934/jimo.2018161 +[Abstract](3293) +[HTML](1128) +[PDF](419.47KB)
Abstract:

State estimation in power grids is a crucial step for monitoring and control tasks. It was shown that the state estimation problem can be solved using a convex relaxation based on semi-definite programming. In the present paper, we propose a fast algorithm for solving this relaxation. Our approach uses the Bürer Monteiro factorisation is a special way that solves the problem on the sphere and and estimates the scale in a Gauss-Seidel fashion. Simulations results confirm the promising behavior of the method.

2020, 16(1): 445-467 doi: 10.3934/jimo.2018162 +[Abstract](4415) +[HTML](1651) +[PDF](474.72KB)
Abstract:

In the present article, we extended the idea of the linguistic intuitionistic fuzzy set to linguistic interval-valued intuitionistic fuzzy (LIVIF) set to represent the data by the interval-valued linguistic terms of membership and non-membership degrees. Some of the desirable properties of the proposed set are studied. Also, we propose a new ranking method named as possibility degree measures to compare the two or more different LIVIF numbers. During the aggregation process, some LIVIF weighted and ordered weighted aggregation operators are proposed to aggregate the collections of the LIVIF numbers. Finally, based on these proposed operators and possibility degree measure, a new group decision making approach is presented to rank the different alternatives. A real-life case has been studied to manifest the practicability and feasibility of the proposed group decision making method.

2020, 16(1): 469-493 doi: 10.3934/jimo.2018163 +[Abstract](3720) +[HTML](1058) +[PDF](501.98KB)
Abstract:

In this paper, we consider an uncertain convex optimization problem with a robust convex feasible set described by locally Lipschitz constraints. Using robust optimization approach, we give some new characterizations of robust solution sets of the problem. Such characterizations are expressed in terms of convex subdifferentails, Clarke subdifferentials, and Lagrange multipliers. In order to characterize the solution set, we first introduce the so-called pseudo Lagrangian function and establish constant pseudo Lagrangian-type property for the robust solution set. We then used to derive Lagrange multiplier-based characterizations of robust solution set. By means of linear scalarization, the results are applied to derive characterizations of weakly and properly robust efficient solution sets of convex multi-objective optimization problems with data uncertainty. Some examples are given to illustrate the significance of the results.

2020, 16(1): 495-510 doi: 10.3934/jimo.2018164 +[Abstract](3550) +[HTML](1465) +[PDF](764.38KB)
Abstract:

This paper presents a heuristic algorithm for solving a specific NP-hard 2D rectangular packing problem in which a rectangle called central rectangle is required to be placed in the center of the final layout, and the aspect ratio of the container is also required to be in a given range. The key component of the proposed algorithm is a greedy constructive procedure, according to which, the rectangles are packed into the container one by one and each rectangle is packed into the container by an angle-occupying placement with maximum fit degree. The proposed algorithm is evaluated on two groups of 35 well-known benchmark instances. Computational results disclose that the proposed algorithm outperforms the previous algorithm for the packing problem. For the first group of test instances, solutions with average filling rate 99.31% can be obtained; for the real-world layout problem in the second group, the filling rate of the solution is 94.75%.

2020 Impact Factor: 1.801
5 Year Impact Factor: 1.688
2020 CiteScore: 1.8