# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

July 2019 , Volume 15 , Issue 3

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2019, 15(3): 1001-1015 doi: 10.3934/jimo.2018082 +[Abstract](2867) +[HTML](1666) +[PDF](391.82KB)
Abstract:

In the context of index tracking, the tracking error measures the difference between the return an investor receives and that of the benchmark he was attempting to imitate. In this paper, we use the weighted $\ell_{2}$ and $\ell_{p}$ $(0 < p < 1)$ norm penalties as well as the shortsale constraints ($\ell_2-\ell_p$ model for short) to the tracking portfolio model in order to get a robust and sparse portfolio for index tracking. The $\ell_{2}$ norm penalty imposes smoothness to alleviate the effect of the existence of highly correlated variables and hence has better out-of-sample performance and the $\ell_{p}$ norm penalty achieves sparsity to account for transaction costs. We enroll in the model explicitly the non-negativity constraints, that is, the shortsale constraints appeared in practice. The $\ell_p$ norm penalty is non-Lipschitz, nonconvex which leads to computational difficulty. We adopt the smoothing projected gradient (SPG) method to solve the robust and sparse portfolio model. We show that any accumulation point of the SPG method is a special limiting stationary point. We find our proposed $\ell_2-\ell_p$ model outperforms the $\ell_2 +\ell_0$ model proposed by Takeda et al. [26] for real stock data set S&P500 in terms of in-sample and out-of-sample errors.

2019, 15(3): 1017-1048 doi: 10.3934/jimo.2018084 +[Abstract](4455) +[HTML](1223) +[PDF](1951.05KB)
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2019, 15(3): 1049-1083 doi: 10.3934/jimo.2018085 +[Abstract](3515) +[HTML](1401) +[PDF](769.18KB)
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A stockless production system is considered, in which the products are not produced until the orders are accepted. Due to this character, the duration of the preventive maintenance has an influence on the lead time. In addition, in this stockless production system, the cost of the preventive maintenance depends on its duration; if the lead time exceeds to the quoted lead time, some penalty cost should be considered; and the non-conforming products can still be sold by a discount. A condition-based duration-varying preventive maintenance policy is designed for the stockless production system, by making a tradeoff among the duration of the preventive maintenance, the time for the machine continuously producing, and the lead time of the order. According to the characters of the stockless production system with the designed preventive maintenance policy, it can be modeled by a BMAP/G/1 infinite-buffer queueing model with gated service and queue-length dependent vacation. Based on this queueing model, the stationary probability distributions of four performance measures for the stockless production system are analyzed, including, the number of the products produced in a production cycle, the number of the unfulfilled orders at arbitrary time, the time required to fulfill the tasks present at arbitrary time, and the lead time of the order accepted at arbitrary time. Moreover, based on some information of these performance measures, a profit function, which represents the average profit of the manufacture in a production cycle, is constructed to optimize the designed preventive maintenance policy according to specific conditions. Finally, given an example with the purchasers having different sensitivities to the lead time, some numerical experiments are carried out; and from the numerical experiments, some general results can be inferred for the stockless production system with the designed preventive maintenance policy.

2019, 15(3): 1085-1100 doi: 10.3934/jimo.2018086 +[Abstract](4532) +[HTML](1885) +[PDF](607.09KB)
Abstract:

The aim of this study is to provide a mathematical framework for studying node cooperation, and to define strategies leading to optimal node behaviour in ad hoc networks. In this study we show time performances of three different methods, namely, Dijkstra's algorithm, Dijkstra's algorithm with battery times and cooperative flow game algorithm constructed from a flow network model. There are two main outcomes of this study regarding the shortest path problem which is that of finding a path of minimum length between two distinct vertices in a network. The first one finds out which method gives better results in terms of time while finding the shortest path, the second one considers the battery life of wireless devices on the network to determine the remaining nodes on the network. Further, optimization performances of the methods are examined in finding the shortest path problem. The study shows that the battery times play an important role in network routing and more devices provided to keep the network. To view the time performance analysis of the methods MATLAB is used. Also, considering the cooperation between the nodes, it is envisaged that using cooperative game theory brings a new approach to network traffic engineering and routing methods.

2019, 15(3): 1101-1116 doi: 10.3934/jimo.2018087 +[Abstract](3452) +[HTML](1084) +[PDF](373.97KB)
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This paper is devoted to the study of unified optimality conditions for constrained set-valued optimization problems via image space analysis. Necessary and sufficient optimality conditions are given in terms of tangent cones of extended image set. By exploiting such results, we analyse the optimality conditions employing different generalized derivatives.

2019, 15(3): 1117-1131 doi: 10.3934/jimo.2018088 +[Abstract](3735) +[HTML](1339) +[PDF](408.82KB)
Abstract:

This paper deals with a single machine bi-criterion scheduling problem with exponentially time-dependent learning effects and non-zero job release times. The goal is to minimize the weighted sum of the makespan and the total completion time. First, a branch-and-bound algorithm incorporating with some dominance properties and three lower bounds is developed for the optimal solutions. Then heuristic and particle swarm optimization algorithms are presented for near-optimal solutions. Finally, computational experiments are conducted to evaluate the performances of the proposed algorithms. Computational results indicate that the algorithms perform well in either solving the problem or efficiently generating near-optimal solutions.

2019, 15(3): 1133-1151 doi: 10.3934/jimo.2018089 +[Abstract](3518) +[HTML](1118) +[PDF](429.69KB)
Abstract:

In this paper, we consider minimax nondifferentiable fractional programming problems with data uncertainty in both the objective and constraints. Via robust optimization, we establish the necessary and sufficient optimality conditions for an uncertain minimax convex-concave fractional programming problem under the robust subdifferentiable constraint qualification. Making use of these optimality conditions, we further obtain strong duality results between the robust counterpart of this programming problem and the optimistic counterpart of its conventional Wolf type and Mond-Weir type dual problems. We also show that the optimistic counterpart of the Wolf type dual of an uncertain minimax linear fractional programming problem with scenario uncertainty (or interval uncertainty) in objective function and constraints is a simple linear programming, and show that the robust strong duality results in sense of Wolf type always hold for this linear minimax fractional programming problem.

2019, 15(3): 1153-1184 doi: 10.3934/jimo.2018090 +[Abstract](3543) +[HTML](1226) +[PDF](535.5KB)
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Temperature sensitive products such as down jackets are commonly used in customers' daily life. The market demand for these products is directly related to the average temperature during the selling period. This study focuses on joint pricing and ordering decisions for temperature sensitive products. First, the four types of temperature sensitive products are considered: HTSPs, MTSPs, LTSPs and HLTSPs. By analyzing the demand characteristics of these types of products, four corresponding demand functions are constructed. Then, the four joint pricing and ordering decision models are constructed considering the temperature sensitive products. By solving the four constructed models, the retailer's optimal policy regarding price and order quantity for HTSPs, MTSPs, LTSPs and HLTSPs can be determined. Furthermore, the impacts of the average temperature and temperature sensitive parameter on retailer's optimal policy are analyzed for HTSPs, MTSPs, LTSPs and HLTSPs. The results show that both average temperature during the selling period and temperature sensitive parameter can affect retailer's optimal policy, but the trend and extent of the impacts differ for the four types of products.

2019, 15(3): 1185-1211 doi: 10.3934/jimo.2018091 +[Abstract](4787) +[HTML](1785) +[PDF](987.89KB)
Abstract:

This paper considers a maritime inventory routing problem with multiple time windows. The typical time windows considered that certain ports permit ships entering and leaving during the daytime only due to various operational limitations. We have developed an exact algorithm to represent this problem. However, due to the excessive computational time required for solving the model, we have proposed a multi-heuristics based genetic algorithm. The multi-heuristics are composed of a set of strategies that correspond to four decision points: ship selection, ship routing, the product type and the quantity of loading and unloading products. The experimental results show that the multi-heuristics can obtain acceptable solutions within a reasonable computational time. Moreover, the flexibility to add or remove the strategies means that the proposed method would not be difficult to implement for other variants of the maritime inventory routing problem.

2019, 15(3): 1213-1223 doi: 10.3934/jimo.2018092 +[Abstract](4584) +[HTML](1236) +[PDF](369.49KB)
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In this paper, we are interested by the linear bilevel multiobjective programming problem, where both the upper level and the lower level have multiple objectives. We approach this problem via an exact penalty method. Then, we propose an exact penalty function algorithm. Numerical results showing viability of the algorithm proposed are presented.

2019, 15(3): 1225-1239 doi: 10.3934/jimo.2018093 +[Abstract](3605) +[HTML](1749) +[PDF](968.75KB)
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Depletion of energy and environment pollution problems are the unprecedented challenges faced by the conventional chemical industry in China. The ever-growing awareness of energy and environment protection makes sustainable development increasingly play the crucial role in China's chemical industry. Most existing methods about chemical industry evaluation are economic-oriented, which neglect the environmental and social issues, especially conflicts among them. This paper develops a novel hybrid multiple criteria decision making framework under bipolar linguistic fuzzy environment based on VIKOR and fuzzy cognitive map to evaluate sustainable chemical industry. The new method captures the characteristics of uncertainty, inconsistency and complexity in the evaluation process of sustainable chemical industry. Meanwhile, combination of fuzzy cognitive map technique makes the new method consider not only the importance but also the interrelations about criteria and obtain better insight into sustainable chemical industry evaluation. A case study and comparison analysis with existing methods reflect the new proposed framework is more suitable to the needs of environment and energy protection in the sustainable chemical industry.

2019, 15(3): 1241-1261 doi: 10.3934/jimo.2018094 +[Abstract](4537) +[HTML](1320) +[PDF](450.63KB)
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In this paper, we consider a class of nonsmooth and nonconvex optimization problem with an abstract constraint. We propose an augmented Lagrangian method for solving the problem and construct global convergence under a weakly nonsmooth Mangasarian-Fromovitz constraint qualification. We show that any accumulation point of the iteration sequence generated by the algorithm is a feasible point which satisfies the first order necessary optimality condition provided that the penalty parameters are bounded and the upper bound of the augmented Lagrangian functions along the approximated solution sequence exists. Numerical experiments show that the algorithm is efficient for obtaining stationary points of general nonsmooth and nonconvex optimization problems, including the bilevel program which will never satisfy the nonsmooth Mangasarian-Fromovitz constraint qualification.

2019, 15(3): 1263-1288 doi: 10.3934/jimo.2018095 +[Abstract](5044) +[HTML](2056) +[PDF](3084.71KB)
Abstract:

Motivated by observing the importance of logistics cost in the cost structure of some products, this paper aims at multi-objective optimization of integrating supply chain network design with the selection of transportation modes (TMs) for a single-product four-echelon supply chain composed of suppliers, production plants, distribution centers (DCs) and customer zones. The key design decisions are the number, capacity and location of plants and DCs, the flow of products through the network, and the selection of TMs for each flow path. A bi-objective mixed integer linear programming model is first formulated. The two incompatible objectives are minimizing the total cost and maximizing the demand fill rate. The model is validated by applying to the case of the design of fresh apple supply chain. Then, a new metaheuristic, called multi-objective modified particle swarm optimization (MMPSO), is presented to find non-dominated solutions. A new modified binary PSO for updating binary variables along with the adaptive mutation is incorporated into the MMPSO. The MMPSO is compared with a multi-objective basic PSO (MBPSO) and the NSGA-Ⅱ against three small cases and six randomly generated medium and large size problems. The comparative results indicate that the MMPSO is better than the NSGA-Ⅱ and the MBPSO with respect to solution quality and computation efficiency for the problem.

2019, 15(3): 1289-1315 doi: 10.3934/jimo.2018096 +[Abstract](5384) +[HTML](1751) +[PDF](602.63KB)
Abstract:

In the recently published paper [Gour Chandra Mahata and Sujit Kumar De, Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit-risk customers, International Journal of Management Science and Engineering Management, 2017, DOI:10.1080/17509653.2015.1109482], a supplier-retailer supply chain model of a deteriorating item with maximum lifetime and partial trade credit to credit risk customers is studied. In their study, unfortunately the amount of the payable bank interest due to the deteriorated units is omitted in the retailer's profit function for making the marketing decision. Some other unrealistic studies are also found in the numerical section of the paper. In this study those non-trivial flaws are identified and technically corrected. After correction, the theoretical existence of the optimal solutions of different scenarios are established and the solutions are derived using a soft computing technique.

2019, 15(3): 1317-1344 doi: 10.3934/jimo.2018097 +[Abstract](4570) +[HTML](1619) +[PDF](2954.61KB)
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In this paper investigate a production system with the defective quality process and preventive maintenance to establish the inspection policy and optimum inventory level for production items with considering uncertainty environment. The shortage occurs because of preventive maintenance and is considered as partial backlogging. Through the production process, at a random moment, the production of items from the state in-control turns into an out-of-control mode, so that parts of the defective product are manufactured an in-control state and outside of the control process mode. The online item inspection process begins after a time variable through the production period. The human inspection process has also been considered for the classify of defective goods. Uninspected products are accepted to the customer/buyer with minimal repair warranty and the defective items classify by the inspector at fixed cost before being shipped subject to salvaged items. Also, the inspection process of manufactured goods includes a human inspection error. Therefore, two types of classification errors (Type Ⅰ & Ⅱ) are considered to be more realistic than the proposed model. The input parameters of the model are considered as a triangular fuzzy environment, and the output parameters of the model are solved by the Zadeh's extension principle and nonlinear parametric programming. As a final point, a numerical example by graphical representations is obtainable to illustrate the proposed model.

2019, 15(3): 1345-1373 doi: 10.3934/jimo.2018098 +[Abstract](4857) +[HTML](1292) +[PDF](627.76KB)
Abstract:

This article is concerned with a multi-item inventory model for deteriorating items. The model is formed on the basis of a two-level supply chain policy, i.e., based on manufacturer's and retailer's perspective. The deterioration rate is considered as constant. The demand factor of any items suffer from a large amount of stock level; so, we consider stock-dependent demand function. The demand of any item is also dependent on its selling price; thus, a price-dependent demand function is introduced here. The retailer adopts the trade-credit policy for his customers in order to promote market competitiveness. He can earn revenue and interest after the customer pays the amount of purchasing cost to the retailer until the end of the trade-credit period, offered by the supplier. Shortages are allowed in the retailer's model as it is a very realistic item, too. A price discount on backordered commodities is offered for those customers who are willing to backorder their demand. Thereafter, we present an easy analytical solution procedure to find the total profit for both manufacturer and retailer. We also use the classical game theory and Nash equilibrium approach to find an optimal solution of the joint profit. The results are discussed with several numerical examples to illustrate our model and to provide some managerial insights related to the model. Furthermore, a parametric sensitivity analysis of the optimal solutions is provided and a concavity figure of our profit function is supplied to stabilize our model. The paper ends with a conclusion and an outlook to future research projects.

2019, 15(3): 1375-1385 doi: 10.3934/jimo.2018099 +[Abstract](3528) +[HTML](1031) +[PDF](168.59KB)
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Fuzzy differential equation driven by Liu process is an important tool to deal with dynamic system in fuzzy environment. Stability for a fuzzy differential equation plays a key role in differential equation, which means influence of the state of a system to small changes in the initial state. In order to discuss the influence of different initial value on the solution, this paper proposes a concept of stability in mean for fuzzy differential equation driven by Liu process. Some stability theorems for fuzzy differential equation being stable in mean are given. In addition, the concept of stability in mean for fuzzy differential equation driven by Liu process is extended to the case of multi-dimensional. A sufficient condition for multi-dimensional fuzzy differential equation being stable in mean is also provided in this paper.

2019, 15(3): 1387-1397 doi: 10.3934/jimo.2018100 +[Abstract](3871) +[HTML](1219) +[PDF](339.44KB)
Abstract:

We consider the stability of a class of parameterized conic programming problems which are more general than $C^2$-smooth parameterization. We show that when the Karush-Kuhn-Tucker (KKT) condition, the constraint nondegeneracy condition, the strict complementary condition and the second order sufficient condition (named as Jacobian uniqueness conditions here) are satisfied at a feasible point of the original problem, the Jacobian uniqueness conditions of the perturbed problem also hold at some feasible point.

2019, 15(3): 1399-1419 doi: 10.3934/jimo.2018101 +[Abstract](3674) +[HTML](929) +[PDF](462.88KB)
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This paper focuses on the development of necessary optimality conditions for nonautonomous optimal control problems with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality conditions for nonautonomous optimal control problems with mixed state and control constraints are derived under the Mangasarian-Fromovitz condition or even stronger. In this paper we derive the necessary optimality conditions for nonautonomous optimal control problems under constraint qualifications which are weaker than Mangasarian-Fromovitz condition. Moreover necessary optimality conditions with an Euler inclusion taking a bounded explicit multiplier form are derived for certain cases. Specifying these results to bilevel optimal control problems with finite-dimensional lower level we obtain necessary optimality conditions under weaker qualification conditions.

2019, 15(3): 1421-1446 doi: 10.3934/jimo.2018102 +[Abstract](3552) +[HTML](1133) +[PDF](713.5KB)
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This paper is concerned with a discrete-time \begin{document}$Geo/G/1$\end{document} retrial queueing system with non-preemptive priority, working vacations and vacation interruption where the service times and retrial times are arbitrarily distributed. If an arriving customer finds the server free, his service commences immediately. Otherwise, he either joins the priority queue with probability \begin{document}$α$\end{document}, or leaves the service area and enters the retrial group (orbit) with probability \begin{document}$\mathit{\bar{\alpha }}\left( = 1-\alpha \right)$\end{document}. Customers in the priority queue have non-preemptive priority over those in the orbit. Whenever the system becomes empty, the server takes working vacation during which the server can serve customers at a lower service rate. If there are customers in the system at the epoch of a service completion, the server resumes the normal working level whether the working vacation ends or not (i.e., working vacation interruption occurs). Otherwise, the server proceeds with the vacation. Employing supplementary variable method and generating function technique, we analyze the underlying Markov chain of the considered queueing model, and obtain the stationary distribution of the Markov chain, the generating functions for the number of customers in the priority queue, in the orbit and in the system, as well as some crucial performance measures in steady state. Furthermore, the relation between our discrete-time queue and its continuous-time counterpart is investigated. Finally, some numerical examples are provided to explore the effect of various system parameters on the queueing characteristics.

2019, 15(3): 1447-1453 doi: 10.3934/jimo.2018103 +[Abstract](3688) +[HTML](1154) +[PDF](418.6KB)
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This paper addresses the new problem of probabilistic robust stabilization for uncertain stochastic systems by using scenario optimization approach, where the uncertainties are not assumed to be norm-bounded. State feedback controllers are designed to guarantee that the closed-loop system is robust probabilistic stable. The problem of designing the controller gains is formulated and solved as linear matrix inequality (LMI) constraints. Simulation results are presented to illustrate the correctness and usefulness of the controllers designed.

2019, 15(3): 1455-1472 doi: 10.3934/jimo.2018104 +[Abstract](4654) +[HTML](1867) +[PDF](792.23KB)
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This study considered the problem of pricing and inventory decision-making where an online retailer and an offline retailer cooperate in a setting where buy-online, pick-up-in-store (BOPS) is implemented. Given the extra revenue generated from additional sales by BOPS customers who purchase additional products at the offline outlet, we considered revenue sharing, service subsidy, and inventory subsidy contracts among the coordinating supply chain partners. Optimization models under centralized and decentralized decision-making structures were established, and the solution was found for the equilibrium states of these optimization models. The results from numerical experiments were examined. We found that (1) the optimal stocking factor had different variation trends with the increase in additional sales under a centralized structure and under the three contracts in decentralized scenarios; (2) the revenue sharing contract was the most effective among the three contracts for coordinating online and offline retailers, and it was optimal for both retailers if the additional sales parameter was relatively low and offline cost share was small; and (3) an inventory subsidy contract had strong operability and steadiness under different product characteristics.

2019, 15(3): 1473-1492 doi: 10.3934/jimo.2018105 +[Abstract](3796) +[HTML](1566) +[PDF](1003.41KB)
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In financial optimization, it is important to quantify the risk of structured financial products. This paper quantifies the risk of structured financial products by perceived risk measures based on a standard measure of risk, and then we construct the risk perception and decision-making models of individual investors considering structured products. Moreover, based on bullish and bearish binary structured products, we introduce the psychological bias of overconfidence to explore how this bias affects investors' perceived risk. This study finds that overconfident investors believe in private signals and underestimate the variance of noise in private signals, which affects their expectation of the underlying asset price of structured financial products. Furthermore, overconfidence bias leads investors to overestimate the probability of obtaining a better return. With the increase in overconfidence, the overestimation of the probability is intensified, which eventually leads to lower perceived risk.

2019, 15(3): 1493-1515 doi: 10.3934/jimo.2018106 +[Abstract](3947) +[HTML](1326) +[PDF](527.62KB)
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This paper investigates the multiperiod asset-liability management problem with quadratic transaction costs. Under the mean-variance criteria, we construct tractability models with/without the riskless asset and obtain the pre-commitment and time-consistent investment strategies through the application of embedding scheme and backward induction approach, respectively. In addition, some conclusions in the existing literatures can be regarded as the degenerated cases under our setting. Finally, the numerical simulations are given to show the difference of frontiers derived by different strategies. Also, some interesting findings on the impact of quadratic transaction cost parameters on efficient frontiers are discussed.

2019  Impact Factor: 1.366