# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

July 2020 , Volume 16 , Issue 4

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2020, 16(4): 1555-1569 doi: 10.3934/jimo.2019017 +[Abstract](2233) +[HTML](803) +[PDF](676.97KB)
Abstract:

Split feasibility problem (SFP) is to find a point which belongs to one convex set in one space, such that its image under a linear transformation belongs to another convex set in the image space. This paper deals with a unified regularized SFP for the convex case. We first construct a self-adaptive regularization iterative algorithm by using Armijo-like search for the SFP and show it converges at a subliner rate of \begin{document}$O(1/k)$\end{document}, where \begin{document}$k$\end{document} represents the number of iterations. More interestingly, inspired by the acceleration technique introduced by Nesterov[12], we present a fast Armijo-like regularization iterative algorithm and show it converges at rate of \begin{document}$O(1/k^{2})$\end{document}. The efficiency of the algorithms is demonstrated by some random data and image debluring problems.

2020, 16(4): 1571-1584 doi: 10.3934/jimo.2019018 +[Abstract](2360) +[HTML](763) +[PDF](388.38KB)
Abstract:

The conventional CES production function model fails to consider the influences of policy factors on economic growth in different stages. This paper proposes a modified model of the CES production function. Regarding model parameter estimation, the paper proposes a modern intelligent algorithm, the firefly algorithm (FA). The paper improves conventional FA to enhance the convergence rate and precision. To overcome the shortcomings of the conventional method in model application, the paper presents a new method of calculating the contribution rates of factors influencing economic growth and provides examples.

2020, 16(4): 1585-1612 doi: 10.3934/jimo.2019019 +[Abstract](2931) +[HTML](863) +[PDF](748.13KB)
Abstract:

In this paper, we formulate and solve an Economic Production Quantity inventory model with deteriorating items. To reduce the rate of deterioration, we apply a preservation technology and calculate the amount for preservation technology investment. The demand function is dependent on stock-level and price. We assume that the production rate is linearly dependent on time, based on customer demand. Shortages are allowed in our consideration, and the shortages amount is partially backlogged for the interested customers for the next slot. The effect of inflation is incorporated, which indicates a critical factor in modern days. Our main objective is to find the optimal cycle length and the optimal amount of preservation technology investment by adjusting the inflation rate with maximizing the profit. A numerical example is provided to illustrate the features and advances of the model. A sensitivity analysis with respect to major parameters is performed in order to assess the stability of our model. The paper ends with a conclusion and an outlook at possible future directions.

2020, 16(4): 1613-1633 doi: 10.3934/jimo.2019020 +[Abstract](2647) +[HTML](1125) +[PDF](414.99KB)
Abstract:

This paper presents an inventory model for a three-echelon supply chain with multiple products and multiple members considering the demand as an increasing function of the marketing effort. In the proposed inventory model, a collaborative approach is studied and an analytical method is applied to obtain the optimal production lot size and the optimal marketing effort in order to achieve the maximum profits. Some numerical examples are illustrated to justify the model. Moreover, a sensitivity analysis is well done in order to analysis the effect of the changes of key parameters of inventory model on the the maximum benefits of all members of the chain.

2020, 16(4): 1635-1654 doi: 10.3934/jimo.2019021 +[Abstract](2928) +[HTML](1171) +[PDF](568.19KB)
Abstract:

This paper aims to investigate the efficiency of the value-at-risk (VaR) backtests in the model selection from different types of generalised autoregressive conditional heteroskedasticity (GARCH) models with skewed and non-skewed innovation distributions. Extensive simulation is carried out to compare the model selection based on VaR backtests and Akaike Information Criteria (AIC). When the model is given but the innovation distribution is one of the six selected distributions which may be skewed or non-skewed, the simulation results show that both AIC and the VaR backtests succeed in selecting the correct innovation distribution from the set of six distributions under consideration. This indicates that both AIC and the VaR backtests are able to distinguish between skewed and non-skewed distributions when the innovation distribution is misspecified. Using an empirical data from NASDAQ index, we observe that the selected combination of model and innovation distribution based on the smallest AIC does not agree with that selected by using the in-sample VaR backtests. Examination of confidence limits for VaR and the expected shortfall forecasts under various loss functions provides evidence that the selected combination of model and innovation distribution using the VaR backtests tends to possess smaller mean absolute percentage error and logarithmic loss.

2020, 16(4): 1655-1662 doi: 10.3934/jimo.2019022 +[Abstract](2441) +[HTML](1034) +[PDF](327.42KB)
Abstract:

The progressive hedging algorithm of Rockafellar and Wets for multistage stochastic programming problems could be viewed as a two-block alternating direction method of multipliers. This correspondence brings in some useful results. In particular, it provides a new proof for the convergence of the progressive hedging algorithm with a flexibility in the selection of primal and dual step lengths and it helps to develop a new progressive hedging algorithm for solving risk averse stochastic optimization problems with cross constraints.

2020, 16(4): 1663-1683 doi: 10.3934/jimo.2019023 +[Abstract](1924) +[HTML](747) +[PDF](428.63KB)
Abstract:

In this paper, we consider an optimal control problem in which the control is almost smooth and the state and control are subject to terminal state constraints and continuous state and control inequality constraints. By introducing an extra set of differential equations for this almost smooth control, we transform this constrained optimal control problem into an equivalent problem involving both control function and system parameter vector as decision variables. Then, by the control parametrization technique and a time scaling transformation, the equivalent problem is approximated by a sequence of constrained optimal parameter selection problems, each of which is a finite dimensional optimization problem. For each of these constrained optimal parameter selection problems, a novel exact penalty function method is constructed by appending penalized constraint violations to the cost function. This gives rise to a sequence of unconstrained optimal parameter selection problems; and each of which can be solved by existing optimization algorithms or software packages. Finally, a practical container crane operation problem is solved, showing the effectiveness and applicability of the proposed approach.

2020, 16(4): 1685-1698 doi: 10.3934/jimo.2019024 +[Abstract](1714) +[HTML](591) +[PDF](3023.75KB)
Abstract:

Dynamic background extraction has been a fundamental research topic in video analysis. In this paper, a novel robust principal component analysis (RPCA) approach for foreground extraction is proposed by decomposing video frames into three parts: rank-one static background, dynamic background and sparse foreground. First, the static background is represented by a rank-one matrix, which can avoid the computation of singular value decomposition because usually the dimensionality of a surveillance video is very large. Secondly, the dynamic background is characterized by \begin{document}$\ell_{2,1}$\end{document}-norm, which can exploit the shared information. Thirdly, the sparse foreground is enhanced by total variation, which can preserve sharp edges that are usually the most important for clear object extraction. An efficient symmetric Gauss-Seidel based alternating direction method of multipliers (sGS-ADMM) is established with convergence analysis. Extensive experiments on real-world datasets show that our proposed approach outperforms the existing state-of-the-art approaches. In fact, to the best of our knowledge, this is the first time to integrate the joint sparsity and total variation into a RPCA framework, which has demonstrated the superiority of performance.

2020, 16(4): 1699-1729 doi: 10.3934/jimo.2019025 +[Abstract](1722) +[HTML](710) +[PDF](797.01KB)
Abstract:

This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of [26], especially on the moment generating function, and second the approximation of density distributions based on Edgeworth or Gram-Charlier expansions. By exploring the analytical tractability of moments up to fourth order, we are able to perform an adjustment of the reference Bachelier model with normal volatilities for skewness and kurtosis, and as a by-product to derive a smile formula relating the volatility to the moneyness with interpretable parameters. As a main conclusion, our numerical results show a 98% reduction in computational time for the DD-SV-LMM calibration process compared to the classical numerical integration method developed by [17].

2020, 16(4): 1731-1752 doi: 10.3934/jimo.2019026 +[Abstract](1953) +[HTML](573) +[PDF](704.3KB)
Abstract:

In practice, suppliers and third-party logistics providers sometimes both offer credit in supply chain financing. To examine the supplier's financing decision, we firstly design a multiple-participant supply chain finance system comprising a supplier, a capital-constrained retailer, and a 3PL firm. Secondly, we compare combined credit financing (CCF), which includes both the supplier's partial trade credit and the 3PL firm's credit with trade credit financing (TCF), to analyze the supplier's optimal decision given the retailer's initial capital level and immediate payment coefficient. Thirdly, we consider the operational and financial parameters to obtain the optimal decisions of supply chain participants under both TCF and CCF. Finally, we perform a numerical analysis of the retailer's initial capital level and immediate payment coefficient. The results show that: when the retailer's initial capital level is low or the retailer's capital constraint is insignificant, the supplier will choose TCF; otherwise, the supplier would better choose CCF. It is more profitable for the supplier to cooperate with a retailer with limited assets under both TCF and CCF. Moreover, we obtained the threshold level of the retailer's initial capital to ensure the retailer's participation and the immediate payment coefficient that ensures the 3PL firm's participation under CCF.

2020, 16(4): 1753-1767 doi: 10.3934/jimo.2019027 +[Abstract](1801) +[HTML](742) +[PDF](648.55KB)
Abstract:

In a two-echelon single-supplier and single-retailer supply chain with permissible delay in payment, we investigate the two-level trade credit policy in which the supplier offers the retailer with limited capital a credit period and in turn the retailer also provides a credit period to customers. The demand rate is sensitive to both retail price and the customerso credit period. By using the backward induction method, we analytically derive the unique equilibrium of both credit periods in the Stackelberg game to determine the retaileros pricing strategy. We find that the optimal retail price is not always decreasing in the credit period offered by the supplier to the retailer. In addition, we characterize the conditions under which the retailer is willing to voluntarily provide customers a credit period. Numerical examples and sensitivity analysis of key parameters are presented to illustrate the theoretical results and managerial insights.

2020, 16(4): 1769-1781 doi: 10.3934/jimo.2019028 +[Abstract](1927) +[HTML](882) +[PDF](415.36KB)
Abstract:

Coming up with effective inventory-ordering strategies for fast-moving consumer goods (FMCGs) through online channels has a major characteristic that the goods are promoted frequently. In this paper, a multi-period inventory model is employed wherein each period represents the promotion period, and the inventory level can be adjusted by replenishing or salvaging the inventory at the beginning of each promotion period. A two-threshold ordering policy is proven to be optimal for each promotion period. The benefits of salvaging can be significantly high for decision makers. This study contributes to the literature of inventory management that products are frequently promoted under an e-commerce environment.

2020, 16(4): 1783-1799 doi: 10.3934/jimo.2019029 +[Abstract](1955) +[HTML](625) +[PDF](770.4KB)
Abstract:

Supervised Distance Preserving Projection (SDPP) is a dimension reduction method in supervised setting proposed recently by Zhu et. al in [43]. The method learns a linear mapping from the input space to the reduced feature space. While the method showed very promising result in regression task, for classification problems the performance is not satisfactory. The preservation of distance relation with neighborhood points forces data to project very close to one another in the projected space irrespective of their classes which ends up with low classification rate. To avoid the crowdedness of SDPP approach we have proposed a modification of SDPP which deals both regression and classification problems and significantly improves the performance of SDPP. We have incorporated the total variance of the projected co-variates to the SDPP problem which is maximized to preserve the global structure. This approach not only facilitates efficient regression like SDPP but also successfully classifies data into different classes. We have formulated the proposed optimization problem as a Semidefinite Least Square (SLS) SDPP problem. A two block Alternating Direction Method of Multipliers have been developed to learn the transformation matrix solving the SLS-SDPP which can easily handle out of sample data.

2020, 16(4): 1801-1834 doi: 10.3934/jimo.2019030 +[Abstract](3240) +[HTML](693) +[PDF](2912.61KB)
Abstract:

The aim of this research is to study the dynamic facility layout and job-shop scheduling problems, simultaneously. In fact, this paper intends to measure the synergy between these two problems. In this paper, a multi-objective mixed integer nonlinear programming model has been proposed where areas of departments are unequal. Using a new approach, this paper calculates the farness rating scores of departments beside their closeness rating scores. Another feature of this paper is the consideration of input and output points for each department, which is crucial for the establishment of practical facility layouts in the real world. In the scheduling problem, transportation delay between departments and machines' setup time are considered that affect the dynamic facility layout problem. This integrated problem is solved using a hybrid two-phase algorithm. In the first phase, this hybrid algorithm incorporates the non-dominated sorting genetic algorithm. The second phase also applies two local search algorithms. To increase the efficacy of the first phase, we have tuned the parameters of this phase using the Taguchi experimental design method. Then, we have randomly generated 20 instances of different sizes. The numerical results show that the second phase of the hybrid algorithm improves its first phase significantly. The results also demonstrate that the simultaneous optimization of those two problems decreases the mean flow time of jobs by about 10% as compared to their separate optimization.

2020, 16(4): 1835-1859 doi: 10.3934/jimo.2019031 +[Abstract](2779) +[HTML](674) +[PDF](707.2KB)
Abstract:

This paper addresses the determination of personnel promotion policies in public Higher Education Institutions (HEI) considering aspects such as worker's promotion rules, hiring and laying off, workforce diversity and budget constraints. The problem is formulated as a Mixed Integer Linear Program. The objective of the proposed optimization model is not only expressed in economic terms but also addressing the achievement of a preferable staff composition and service level. The model is formulated generally, hence it can be useful for different types of universities taken into account their specificities and characteristics. Specifically, this paper addresses the problem of finding the relationship between economic resources for workers'promotion and the pursued preferable staff composition. The model is applied to a real case, in which several analyses are performed under different scenarios characterized by possible trends in the available budget and the demand. The analyses are for different workforce structures, which reflect different academic and personnel policies. The results address the performance of the proposed model in achieving the preferable structure and also on how promotions --and associated expenditures--, are for young researchers and experienced personnel according to each considered scenario.

2020, 16(4): 1861-1871 doi: 10.3934/jimo.2019032 +[Abstract](2132) +[HTML](848) +[PDF](380.48KB)
Abstract:

This study relaxes the distributional assumption of the return of the risky asset, to arrive at the optimal portfolio. Studies of portfolio selection models have typically assumed that stock returns conform to the normal distribution. The application of robust optimization techniques means that only the historical mean and variance of asset returns are required instead of distributional information. We show that the method results in an optimal portfolio that has comparable return and yet equivalent risk, to one that assumes normality of asset returns.

2020, 16(4): 1873-1884 doi: 10.3934/jimo.2019033 +[Abstract](1810) +[HTML](582) +[PDF](329.23KB)
Abstract:

In this work, a pair of higher-order symmetric dual multiobjective optimization problems is formulated. Weak, strong and converse duality theorems are established under suitable assumptions. Some examples are also given to illustrate our main results. Furthermore, certain deficiencies in the formulations and the proof of the work of Kassem [Applied Mathematics and Computation, 209 (2009), 405-409] are pointed out.

2020, 16(4): 1885-1905 doi: 10.3934/jimo.2019034 +[Abstract](2182) +[HTML](598) +[PDF](524.68KB)
Abstract:

In this paper, we mainly consider optimization problems involving the sum of largest eigenvalues of nonlinear symmetric matrices. One of the difficulties with numerical analysis of such problems is that the eigenvalues, regarded as functions of a symmetric matrix, are not differentiable at those points where they coalesce. The \begin{document}$\mathcal {U}$\end{document}-Lagrangian theory is applied to the function of the sum of the largest eigenvalues, with convex matrix-valued mappings, which doesn't need to be affine. Some of the results generalize the corresponding conclusions for linear mapping. In the approach, we reformulate the first- and second-order derivatives of \begin{document}${\mathcal U}$\end{document}-Lagrangian in the space of decision variables \begin{document}$R^m$\end{document} under some mild conditions in terms of \begin{document}$\mathcal{VU}$\end{document}-space decomposition. We characterize smooth trajectory, along which the function has a second-order expansion. Moreover, an algorithm framework with superlinear convergence is presented. Finally, an application of \begin{document}$\mathcal{VU}$\end{document}-decomposition derivatives shows that \begin{document}$\mathcal{U}$\end{document}-Lagrangian possesses proper execution in matrix variable.

2020, 16(4): 1907-1925 doi: 10.3934/jimo.2019035 +[Abstract](1573) +[HTML](719) +[PDF](517.58KB)
Abstract:

In this paper, we propose two classes of the approximations to the cardinality function via the Moreau envelope of the \begin{document}$\ell_{1}$\end{document} norm. We show that these two approximations are good choices of the merit function for sparsity and are essentially the truncated \begin{document}$\ell_{1}$\end{document} norm and the truncated \begin{document}$\ell_{2}$\end{document} norm. Moreover, we apply the approximations to solve sparse signal recovery problems and then provide new weights for reweighted \begin{document}$\ell_{1}$\end{document} minimization and reweighted least squares to find sparse solutions of underdetermined linear systems of equations. Finally, we present some numerical experiments to illustrate our results.

2020, 16(4): 1927-1941 doi: 10.3934/jimo.2019036 +[Abstract](2229) +[HTML](632) +[PDF](723.32KB)
Abstract:

In this paper, we mathematically associate Crypto Cloud Computing, that has become an emerging research area, with Cooperative Game Theory in the presence of uncertainty. In the sequel, we retrieve data from the database of Amazon Web Service. The joint view upon Crypto Cloud Computing, Cooperative Game Theory and Uncertainty management is a novel approach. For this purpose, we construct a cooperative interval game model and apply this model to Social Networks. Then, we suggest some interval solutions related with the model by proposing a novel elliptic curve public key encryption scheme over finite fields having the property of semantic security. The paper ends with concluding words and an outlook to future studies.

2020, 16(4): 1943-1965 doi: 10.3934/jimo.2019037 +[Abstract](2116) +[HTML](906) +[PDF](502.48KB)
Abstract:

This study examines a two-echelon supply chain consisting of two competing manufacturers and one retailer that has the channel power, in which one manufacturer is engaged in sustainable technology to curb carbon emissions under the cap-and-trade regulation while the other one operates its business as usual in a traditional manner. Two different supply chain configurations concerning risk attributes of the agents are considered, that is, (ⅰ) two risk-neutral manufacturers with one risk-averse retailer; and (ⅱ) two risk-averse manufacturers with one risk-neutral retailer. Under the mean-variance framework, we use a retailer-leader game optimization approach to study operational decisions of these two systems. Specifically, optimal operational decisions of the agents are established in closed-form expressions and the corresponding profits and carbon emissions are assessed. Numerical experiments are conducted to analyze the impact of risk aversion of the underlying supply chains. The results show that each risk-averse agent would benefit from a low scale risk aversion. Further, low carbon emissions could be attainable if risk aversion scale of the underlying manufacturer is small or moderate. In addition, the carbon emissions might increase when risk aversion of the traditional manufacturer or the retailer is of small or moderate scale.

2020, 16(4): 1967-1986 doi: 10.3934/jimo.2019038 +[Abstract](1837) +[HTML](682) +[PDF](611.04KB)
Abstract:

In this paper, we model the insurance company's surplus flow by a perturbed compound Poisson model. Suppose that at a sequence of random time points, the insurance company observes the surplus to decide dividend payments. If the observed surplus level is larger than the maximum of a threshold \begin{document}$b>0$\end{document} and the last observed level (after dividends payment if possible), then a fraction \begin{document}$0<\theta<1$\end{document} of the excess amount is paid out as a lump sum dividend. We assume that the solvency is also discretely monitored at these observation times, so that the surplus process stops when the observed value becomes negative. Integro-differential equations for the expected discounted dividend payments before ruin and the Gerber-Shiu expected discounted penalty function are derived, and solutions are also analyzed by Laplace transform method. Numerical examples are given to illustrate the applicability of our results.

2020, 16(4): 1987-1998 doi: 10.3934/jimo.2019039 +[Abstract](1485) +[HTML](581) +[PDF](374.12KB)
Abstract:

To locate all \begin{document}$Z$\end{document}-eigenvalues of a tensor more precisely, we establish three \begin{document}$Z$\end{document}-eigenvalue exclusion sets such that all \begin{document}$Z$\end{document}-eigenvalues do not belong to them and get three tighter \begin{document}$Z$\end{document}-eigenvalue inclusion sets of tensor by using these \begin{document}$Z$\end{document}-eigenvalue exclusion sets. Furthermore, we show that the new inclusion sets are tighter than the existing results via two running examples.

2020, 16(4): 1999-2027 doi: 10.3934/jimo.2019040 +[Abstract](2019) +[HTML](852) +[PDF](1078.89KB)
Abstract:

We investigate the cost-sharing strategies of a retailer and a manufacturer in a Nash game considering government subsidy, consumers' green preference and retailer's sales effort. We provide a function to describe the demand for green products considering the effect of green preference of consumers and the sales effort of the retailer. Next, we construct profit functions of the manufacturer and the retailer considering government subsidy for four scenarios: no sharing of cost (NSC), sharing of carbon emission reduction cost (SCERC), sharing of sales effort cost (SSEC), and sharing both carbon emission reduction cost and sales effort cost (SBC). Furthermore, we determine the optimal policies of price, sales effort level, wholesale price and carbon emission reduction effort level for the four scenarios by maximizing the profits of the manufacturer and the retailer in the Nash game. We find that the sales effort cost-sharing ratio and the carbon emission reduction cost-sharing ratio can affect the optimal policies of the manufacturer and the retailer, and the trends and extent of effects may be different. Our results show that it is advantageous for the manufacturer and the retailer to consider the cost-sharing effects of sales effort and carbon emission reduction effort, and the optimal policies of the retailer and the manufacturer are different for different scenarios.

2020, 16(4): 2029-2044 doi: 10.3934/jimo.2019041 +[Abstract](2588) +[HTML](581) +[PDF](424.88KB)
Abstract:

Sensitivity analysis is applied to the robust linear programming problem in this paper. The coefficients of the linear program are assumed to be perturbed in three perturbation manners within ellipsoidal sets. Our robust sensitivity analysis is to calculate the maximal radii of the perturbation sets to keep some properties of the robust feasible set. Mathematical models are formulated for the robust sensitivity analysis problems and all models are either reformulated into linear programs or convex quadratic programs except for the bi-convex programs where more than one row of the constraint matrix is perturbed. For the bi-convex programs, we develop a binary search algorithm.

2020, 16(4): 2045-2063 doi: 10.3934/jimo.2019042 +[Abstract](1979) +[HTML](570) +[PDF](601.63KB)
Abstract:

Several existing \begin{document}$Z$\end{document}-eigenvalue localization sets for tensors are first generalized to \begin{document}$E$\end{document}-eigenvalue localization sets. And then two tighter \begin{document}$E$\end{document}-eigenvalue localization sets for tensors are presented. As applications, a sufficient condition for the positive definiteness of fourth-order real symmetric tensors, a sufficient condition for the positive semi-definiteness of fourth-order real symmetric tensors, and a new upper bound for the \begin{document}$Z$\end{document}-spectral radius of weakly symmetric nonnegative tensors are obtained. Finally, numerical examples are given to verify the theoretical results.

2019  Impact Factor: 1.366