# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

April 2015 , Volume 11 , Issue 2

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2015, 11(2): 345-364 doi: 10.3934/jimo.2015.11.345 +[Abstract](2382) +[PDF](466.8KB)
Abstract:
In this paper, we present a new global optimization method to solve nonlinear systems of equations. We reformulate given system of nonlinear equations as a global optimization problem and then give a new auxiliary function method to solve the reformulated global optimization problem. The new auxiliary function proposed in this paper can be a filled function, a quasi-filled function or a strict filled function with appropriately chosen parameters. Several numerical examples are presented to illustrate the efficiency of the present approach.
2015, 11(2): 365-380 doi: 10.3934/jimo.2015.11.365 +[Abstract](1874) +[PDF](351.2KB)
Abstract:
In this paper, the Bühlmann and Bühlmann-Straub's credibility models with a type of dependence structures over risks and over time are discussed. The inhomogeneous and homogeneous credibility estimators of risk premium were derived. The inhomogeneous credibility estimators for the existing credibility models with common effects are extended to slightly more general versions. The results obtained shake the classical meaning of the term credibility premiums''.
2015, 11(2): 381-397 doi: 10.3934/jimo.2015.11.381 +[Abstract](2332) +[PDF](1541.4KB)
Abstract:
The problem of low-skilled workers is an obstacle in the development of the Chinese construction industry. Although many efforts have been focused on occupational training, there were several obstacles in implementing training sessions to labours. Other learning pathways were identified and introduced, but not many efforts could be found in the comparison of different learning pathways. This research simulated different skill learning methods in heterogeneous construction crews. With quantitative simulation, it explored general rules of skill learning and learning limits; discovered different learning patterns in heterogeneous construction workers; compared the effects of different learning methods; and identified the most beneficial learning pathways for workers with different learning patterns. A pre-modelling survey was conducted to determine the distributions of parameters. A network model was built to describe group interaction. Nodes in the network represented individual workers learning from repetitive work and influenced by training sessions and interpersonal communication. Results show that (a) besides training sessions, automatic on-the-job training and interactive learning from co-workers are also sources for working knowledge; (b) workers can be categorized into 5 groups according to their knowledge accumulation patterns; (c) formal training sessions and informal interactive social learning have different impact on workers with different accumulation patterns. The main contribution of this research is that it is among the firsts to discuss and simulate the multi-sourced learning process as supplements to skill trainings, identify different learning patterns corresponding to different learning groups, and make comparisons to give guidance on targeted learning strategies.
2015, 11(2): 399-419 doi: 10.3934/jimo.2015.11.399 +[Abstract](2847) +[PDF](858.4KB)
Abstract:
This paper investigates a three-stage supply chain scheduling problem in the application area of aluminium production. Particularly, the first and the third stages involve two factories, i.e., the extrusion factory of the supplier and the aging factory of the manufacturer, where serial batching machine and parallel batching machine respectively process jobs in different ways. In the second stage, a single vehicle transports jobs between the two factories. In our research, both setup time and capacity constraints are explicitly considered. For the problem of minimizing the makespan, we formalize it as a mixed integer programming model and prove it to be strongly NP-hard. Considering the computational complexity, we develop two heuristic algorithms applied in two different cases of this problem. Accordingly, two lower bounds are derived, based on which the worst case performance is analyzed. Finally, different scales of random instances are generated to test the performance of the proposed algorithms. The computational results show the effectiveness of the proposed algorithms, especially for large-scale instances.
2015, 11(2): 421-437 doi: 10.3934/jimo.2015.11.421 +[Abstract](2231) +[PDF](538.9KB)
Abstract:
This paper considers the problem of calibrating the volatility function using regularization technique and the gradient projection method from given option price data. It is an ill-posed problem because of at least one of three well-posed conditions violating. We start with the European option pricing problem. We formulate the problem by obtaining the integral equation from Dupire equation and provide a theory of identifying the local volatility function $\sigma(y,\tau)$ when the parameter $\mu\neq 0$, and then we apply regularization technique for volatility function retrieval problems. A projected gradient method is developed for recovering the volatility function. Numerical simulations are given to illustrate the feasibility of our method.
2015, 11(2): 439-459 doi: 10.3934/jimo.2015.11.439 +[Abstract](2718) +[PDF](1782.7KB)
Abstract:
This paper develops a game model of a vendor-managed inventory supply chain consisting of one manufacturer and one retailer to study the manufacturer's consumer returns policy and the retailer's store assistance service decision, and explore the effects of both supply chain decentralization and the service subsidy rate on the consumer returns policy. We find that when the consumer return is not allowed, the retailer would like to sell the products to only the consumers with low mismatching loss if the market scale is sufficiently low. Allowing consumer return decreases the retail price if the basic returns rate is sufficiently high and decreases the unit wholesale price if the subsidy rate of service investment is sufficiently high. Moreover, allowing consumer return decreases the service level but increases the subsidy rate. The expected loss of mismatching can reverse the effects of both the subsidy rate and the service cost factor on the returns policy; the manufacturer allows consumer return if the basic mismatching rate is not too high. In addition, we find that the store's returns handling cost increases the effect of supply chain decentralization on returns policy while the loss of mismatching for the high-type consumer decreases it.
2015, 11(2): 461-478 doi: 10.3934/jimo.2015.11.461 +[Abstract](2550) +[PDF](421.9KB)
Abstract:
We assume that the asset value process of some company is directly related to its stock price dynamics, which can be modeled by geometric Brownian motion. The company can control its asset by paying dividends and injecting capitals, of course both procedures imply proportional and fixed costs for the company. To maximize the expected present value of the dividend payments minus the capital injections until the time of bankruptcy, which is defined as the first time when the asset value falls below the regulation requirement $m$, we seek to find the joint optimal dividend payment and capital injection strategy. By solving the Quasi-variational inequalities, the optimal control problem is addressed, which depends on the parameters of the model and the costs. The sensitivities of transaction costs (such as tax, consulting fees) to the optimal strategy, the expected growth rate and volatility of the firm asset value are also examined, some interesting economic insights are included.
2015, 11(2): 479-492 doi: 10.3934/jimo.2015.11.479 +[Abstract](2139) +[PDF](433.8KB)
Abstract:
There are two kinds of two levels of trade credit policies addressed by Huang [15] and Teng [29], respectively. Liao [24] presents the EPQ model with deteriorating items under two-level trade credit policy from the viewpoint of Huang [15], while Chang, Teng and Chern [2] discuss the model from the viewpoint of Teng [29]. However, errors are found in the process of the modeling in Chang et al. [2]. The main purpose of this study is to improve the model of Chang et al. [2] and develop a more general EPQ inventory model. A theorem is also provided for practitioners to make right decisions.
2015, 11(2): 493-514 doi: 10.3934/jimo.2015.11.493 +[Abstract](1993) +[PDF](455.0KB)
Abstract:
In this paper, we consider pricing and hedging of catastrophe equity put options under a Markov-modulated jump diffusion process with a Markov switching compensator. We assume that the risk free interest rate, the appreciation rate and the volatility of the risky asset depend on a finite-state Markov chain. We investigate the pricing of catastrophe equity put options and obtain the explicit pricing formulas. A numerical analysis is provided to illustrate the effect of regime switching on the price of catastrophe equity put options. In the end, since the market which we consider is not complete, we also provide an optimal hedging strategy by using the local risk minimization method.
2015, 11(2): 515-528 doi: 10.3934/jimo.2015.11.515 +[Abstract](2343) +[PDF](347.9KB)
Abstract:
In this paper, we investigate the selection of cleaner products with the consideration of the tradeoff between risk and the return of players in two different of supply chain structures: a vertically integrated structure and a decentralized setting. In an integrated supply chain, the price of cleaner products is decided according to the maximum utility for the whole supply chain, while the retailer offers their price with respect to their own maximum utility in a decentralized setting. A numerical example of a green supply chain of household electrical appliances in China is presented to illustrate related issues. Finally, conclusions are drawn and some topics for future work are suggested.
2015, 11(2): 529-547 doi: 10.3934/jimo.2015.11.529 +[Abstract](2430) +[PDF](505.2KB)
Abstract:
We first propose an exact penalty method to solve strong-weak linear bilevel programming problem (for short, SWLBP) for every fixed cooperation degree from the follower. Then, we prove that the solution of penalized problem is also that of the original problem under some conditions. Furthermore, we give some properties of the optimal value function (as a function of the follower's cooperation degree) of SWLBP. Finally, we develop a method to acquire the critical points of the optimal value function without enumerating all values of the cooperation degree from the follower, and thus this function is also achieved. Numerical results show that the proposed methods are feasible.
2015, 11(2): 549-562 doi: 10.3934/jimo.2015.11.549 +[Abstract](2244) +[PDF](413.8KB)
Abstract:
In this paper, by using a scalarization method, we establish sufficient conditions for Hölder continuity of approximate solution mapping to a class of parametric weak generalized Ky Fan Inequality with set-valued mappings. These results extend and improve some known results in the literature. Furthermore, some examples are given to illustrate the obtained results.
2015, 11(2): 563-574 doi: 10.3934/jimo.2015.11.563 +[Abstract](2096) +[PDF](339.3KB)
Abstract:
The purpose of this paper is to present necessary and sufficient optimality conditions for a feasible solution to be weakly efficient or Henig weakly efficient solution of a nonconvex vector equilibrium problem with cone constraints. These theorems are based on the quasi-relative interior notion and a very recent separation theorem which involves this notion. Our results deal with some conditions where no previous results are applicable.
2015, 11(2): 575-594 doi: 10.3934/jimo.2015.11.575 +[Abstract](2824) +[PDF](453.4KB)
Abstract:
This paper investigates the role of dual information on the performances of heuristics designed for solving the set covering problem. After solving the linear programming relaxation of the problem, the dual information is used to obtain the two main approaches proposed here: (i) The size of the original problem is reduced and then the resulting model is solved with exact methods. We demonstrate the effectiveness of this approach on a rich set of benchmark instances compiled from the literature. We conclude that set covering problems of various characteristics and sizes may reliably be solved to near optimality without resorting to custom solution methods. (ii) The dual information is embedded into an existing heuristic. This approach is demonstrated on a well-known local search based heuristic that was reported to obtain successful results on the set covering problem. Our results demonstrate that the use of dual information significantly improves the efficacy of the heuristic in terms of both solution time and accuracy.
2015, 11(2): 595-617 doi: 10.3934/jimo.2015.11.595 +[Abstract](2680) +[PDF](2896.3KB)
Abstract:
The lack of early security arrangements during the construction period can increase the vulnerability of construction project. To support current construction security standards, this paper proposes a bilevel multi-objective model for construction site security problem (CSSP). In contrast to prior studies of CSSP, the bilevel relationship and twofold random phenomenon are considered. Specifically, the upper level programming denotes that project security officer must first decide which facilities to be secured under limited funds whilst maximizing the efficiency of the construction facilities system and minimizing the countermeasure cost and economic loss. The lower level programming denotes that the attacker will destroy a subset of the facilities to inflict maximum loss of efficiency in the construction facilities system. To deal with the uncertainties, expected value method and chance constraint method are introduced to transform the uncertain model into a calculable one. Thereafter, a stochastic simulation based constraint checking procedure is designed. Plant Growth Simulation Algorithm (PGSA) is applied to solve this model. Finally, the approach is carried out in the Longtan hydropower construction project to illustrate the efficiency of the proposed model and algorithm.
2015, 11(2): 619-630 doi: 10.3934/jimo.2015.11.619 +[Abstract](2088) +[PDF](331.6KB)
Abstract:
In this paper we introduce a class of numerical methods for solving an equilibrium problem. This class depends on a parameter and contains the classical extragradient method and a generalization of the two-step extragradient method proposed recently by Zykina and Melen'chuk for solving variational inequality problems. Convergence of each algorithm of this class to a solution of the equilibrium problem is obtained under the condition that the equilibrium function associated with the problem is pseudomonotone and Lipschitz continuous. Some preliminary numerical results are given to compare the numerical behavior of the two-step extragradient method with respect to the other methods of the class and in particular to the extragradient method.
2015, 11(2): 631-644 doi: 10.3934/jimo.2015.11.631 +[Abstract](2119) +[PDF](517.7KB)
Abstract:
This paper is devoted to develop a robust penalty-based method of reconstructing smooth local volatility surface from the observed American option prices. This reconstruction problem is posed as an inverse problem: given a finite set of observed American option prices, find a local volatility function such that the theoretical option prices matches the observed ones optimally with respect to a prescribed performance criterion. The theoretical American option prices are governed by a set of partial differential complementarity problems (PDCP). We propose a penalty-based numerical method for the solution of the PDCP. Typically, the reconstruction problem is ill-posed and a bicubic spline regularization technique is thus proposed to overcome this difficulty. We apply a gradient-based optimization algorithm to solve this nonlinear optimization problem, where the Jacobian of the cost function is computed via finite difference approximation. Two numerical experiments: a synthetic American put option example and a real market American put option example, are performed to show the robustness and effectiveness of the proposed method to reconstructing the unknown volatility surface.
2015, 11(2): 645-660 doi: 10.3934/jimo.2015.11.645 +[Abstract](2685) +[PDF](391.9KB)
Abstract:
This paper is concerned with solving a stochastic variational inequality problem (for short, SVIP) from a viewpoint of minimization of mixed conditional value-at-risk (CVaR). The regularized gap function for SVIP is used to define a loss function for the SVIP and mixed CVaR to measure the loss. In this setting, SVIP can be reformulated as a deterministic minimization problem. We show that the reformulation is a convex program for a huge class of SVIP under suitable conditions. Since mixed CVaR involves the plus function and mathematical expectation, the neural network smoothing function and Monte Carlo method are employed to get an approximation problem of the minimization reformulation. Finally, we consider the convergence of optimal solutions and stationary points of the approximation.
2015, 11(2): 661-671 doi: 10.3934/jimo.2015.11.661 +[Abstract](2084) +[PDF](330.6KB)
Abstract:
This paper is concerned with the stability for a parametric symmetric vector equilibrium problem. A parametric gap function for the parametric symmetric vector equilibrium problem is introduced and investigated. By virtue of this function, we establish the sufficient and necessary conditions for the Hausdorff lower semicontinuity of solution mapping to a parametric symmetric vector equilibrium problem. The results presented in this paper generalize and improve the corresponding results in the recent literature.
2015, 11(2): 673-683 doi: 10.3934/jimo.2015.11.673 +[Abstract](2517) +[PDF](337.2KB)
Abstract:
In this paper, we characterize approximate solutions of vector optimization problems with set-valued maps. We gives several characterizations of generalized subconvexlike set-valued functions(see [10]), which is a generalization of nearly subconvexlike functions introduced in [34]. We present alternative theorem and derived scalarization theorems for approximate solutions with generalized subconvexlike set-valued maps. And then, Lagrange multiplier theorems under generalized Slater constraint qualification are established.
2015, 11(2): 685-700 doi: 10.3934/jimo.2015.11.685 +[Abstract](2007) +[PDF](382.2KB)
Abstract:
A two-machine scheduling problem where one machine has periodic availability constraints has been studied. The objective is to minimize makepan. For the nonresumable version, we give a better approximation algorithm with performance ratio of $4/3$. For the resumable version, we provide an offline $4/3$-approximation algorithm and an optimal online algorithm, respectively.

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