American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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Journal of Industrial & Management Optimization

January 2017 , Volume 13 , Issue 1

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2017, 13(1): 1-21 doi: 10.3934/jimo.2016001 +[Abstract](282) +[HTML](67) +[PDF](509.0KB)
Abstract:

This paper investigates an optimal dividend and capital injection problem for a spectrally positive Lévy process, where the dividend rate is restricted. Both the ruin penalty and the costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, the penalized discounted capital injections before ruin, and the expected discounted ruin penalty. By the fluctuation theory of Lévy processes, the optimal dividend and capital injection strategy is obtained. We also find that the optimal return function can be expressed in terms of the scale functions of Lévy processes. Besides, a series of numerical examples are provided to illustrate our consults.

2017, 13(1): 23-46 doi: 10.3934/jimo.2016002 +[Abstract](330) +[HTML](60) +[PDF](538.3KB)
Abstract:

We study a consumption-portfolio optimization problem in a hidden Markov-modulated asset price model with multiple risky assets, where model uncertainty is present. Under this modeling framework, the appreciation rates of risky shares are modulated by a continuous-time, finite-state hidden Markov chain whose states represent different modes of the model. We consider the situation where an economic agent only has access to information about the price processes of risky shares and aims to maximize the expected, discounted utility from intermediate consumption and terminal wealth within a finite horizon. The standard innovations approach in filtering theory is then used to transform the partially observed consumption-portfolio optimization problem to the one with complete observations. Robust filters of the chain and estimates of some other parameters are presented. Using the stochastic maximum principle, we derive a closed-form solution of an optimal consumption-portfolio strategy in the case of a power utility.

2017, 13(1): 47-62 doi: 10.3934/jimo.2016003 +[Abstract](479) +[HTML](54) +[PDF](1115.7KB)
Abstract:

We consider the numerical solution of nonlinear and nonsmooth operator equations in Hilbert spaces. A semismooth Newton method is used for search direction generation. The operator equation is solved by a globalized semismooth Newton method that is equipped with an Armijo linesearch using a semismooth merit function. We prove that an accumulation point of the globalized algorithm is a solution and transition to fast local convergence under a directional Hadamard-like continuity assumption on the Newton matrix. In particular, no auxiliary descent directions or smoothing steps are required. Finally, we apply this method to a control-constrained and also to a regularized state-constrained optimal control problem subject to partial differential equations.

2017, 13(1): 63-79 doi: 10.3934/jimo.2016004 +[Abstract](240) +[HTML](56) +[PDF](415.4KB)
Abstract:

In this paper, we consider a composite DC optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. By using the properties of the epigraph of the conjugate functions, some necessary and sufficient conditions which characterize the strong Fenchel-Lagrange duality and the stable strong Fenchel-Lagrange duality are given. We apply the results obtained to study the minmax optimization problem and $l_1$ penalty problem.

2017, 13(1): 81-92 doi: 10.3934/jimo.2016005 +[Abstract](186) +[HTML](62) +[PDF](374.9KB)
Abstract:

In this paper, we present a combined homotopy interior point method for solving multiobjective programs with equilibrium constraints. Under suitable conditions, we prove the existence and convergence of a smooth homotopy path from almost any interior point to a solution of the K-K-T system. Numerical results are presented to show the effectiveness of this algorithm.

2017, 13(1): 93-112 doi: 10.3934/jimo.2016006 +[Abstract](224) +[HTML](73) +[PDF](634.9KB)
Abstract:

The high-dimensional linear regression model has attracted much attention in areas like information technology, biology, chemometrics, economics, finance and other scientific fields. In this paper, we use smoothing techniques to deal with high-dimensional sparse models via quantile regression with the nonconvex \begin{document}$\ell_p$\end{document} penalty (\begin{document}$0<p<1$\end{document}). We introduce two kinds of smoothing functions and give the estimation of approximation by our different smoothing functions. By smoothing the quantile function, we derive two types of lower bounds for any local solution of the smoothing quantile regression with the nonconvex \begin{document}$\ell_p$\end{document} penalty. Then with the help of \begin{document}$\ell_1$\end{document} regularization, we propose a smoothing iterative method for the smoothing quantile regression with the weighted \begin{document}$\ell_1$\end{document} penalty and establish its global convergence, whose efficient performance is illustrated by the numerical experiments.

2017, 13(1): 113-133 doi: 10.3934/jimo.2016007 +[Abstract](403) +[HTML](55) +[PDF](4811.4KB)
Abstract:

Category captainship, the approach where retailers use manufacturer-retailer collaboration, is a common way to leverage resources and capabilities in order to improve the sales/shelf performance ratio. However, evidence suggests that the depth and effectiveness of category captains and collaboration in retail are not as high as theory or best practice would predict. Suppliers and retailers suspect each other of opportunistic behaviour detrimental to both. In a stylized dyadic supply chain model prior to the effective contracting of the category captain, we show why information asymmetry between both is preferred: the retailer will hint at or develop retaliatory power to keep the supplier in check whereas the supplier will try to extract a rent by taking advantage of available information about relationship specific investment. We model single-period interaction when the retailer has to invest in relationship specific assets and alternative category manager grooming. We provide normative and positive support both to the captain's potential opportunistic behaviour as well as the retailer's investment decision in alternative captains and monitoring ability. In a two-period extension, we show how the retailer can discipline the captain ex ante. The model and its results complement and extend research in pre-contractual category captainship and supplier-retailer collaboration and coordination. They represent a departure from the usual vision in which sharing information and collaborating generate higher supply chain rent.

2017, 13(1): 135-146 doi: 10.3934/jimo.2016008 +[Abstract](250) +[HTML](45) +[PDF](353.9KB)
Abstract:

In the classical stochastic continuous review, \begin{document}$(Q,r)$\end{document} model [18, 19], the inventory cost \begin{document}$c(Q,r)$\end{document} has an averaging term which is given as an integral of the expected costs over the different inventory positions during the lead time on any given cycle. The main objective of the article is to study risk averse optimization in the classical \begin{document}$(Q,r)$\end{document} model using \begin{document}$CVaR_{α}$\end{document} as a coherent risk measure with respect to the probability distribution of the demand \begin{document}$D$\end{document} on inventory position costs (the sum of the inventory holding and backorder penality cost), for any given (generic) confidence level \begin{document}$α∈[0,1)$\end{document}.

We show that the objective function is jointly convex in \begin{document}$(Q,r)$\end{document}. We also compare the risk averse solution and some other solutions in both analytical and computational ways. Additionally, some general and useful results are obtained.

2017, 13(1): 147-153 doi: 10.3934/jimo.2016009 +[Abstract](185) +[HTML](51) +[PDF](405.3KB)
Abstract:

In this paper, we consider the problem of computing the smallest enclosing circle. An efficient cutting plane algorithm is derived. It is based on finding the valid cut and reducing the problem into solving a series of linear programs. The numerical performance of this algorithm outperforms other existing algorithms in our computational experiments.

2017, 13(1): 155-185 doi: 10.3934/jimo.2016010 +[Abstract](558) +[HTML](53) +[PDF](525.3KB)
Abstract:

Consider a non-standard renewal risk model with dependence structures, where claim sizes follow a one-sided linear process with independent and identically distributed step sizes, the step sizes and inter-arrival times respectively form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. An insurance company is allowed to make risk-free and risky investments, where the price process of the investment portfolio follows an exponential Lévy process. When the step-size distribution is dominatedly-varying-tailed, some asymptotic estimates for the finite-and infinite-time ruin probabilities are obtained.

2017, 13(1): 187-206 doi: 10.3934/jimo.2016011 +[Abstract](266) +[HTML](53) +[PDF](2690.5KB)
Abstract:

In literature, many inventory studies have been developed by assuming deterioration of items as either a variable or constant. But in real life situation, deterioration of goods can be reduced by adding some extra effective capital investment in preservation technology. In this paper, a deteriorating inventory model with ramp-type demand under stock-dependent consumption rate by assuming preservation technology cost as a decision variable is formulated. Shortages are allowed and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time. The objective of this study is to obtain the optimal replenishment and preservation technology investment strategies so that the total profit per unit time is maximum. Further, the necessary and sufficient conditions are considered to prove the existence and uniqueness of the optimal solution. Some numerical examples along with graphical representations are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed.

2017, 13(1): 207-222 doi: 10.3934/jimo.2016012 +[Abstract](262) +[HTML](58) +[PDF](406.8KB)
Abstract:

In the paper, we give an asymptotic formula for the finite-time ruin probability in a generalized renewal risk model. We consider the renewal risk model with independent strongly subexponential claim sizes and independent not necessarily identically distributed inter occurrence times having finite variances. We find out that the asymptotic formula for the finite-time ruin probability is insensitive to the homogeneity of inter-occurrence times.

2017, 13(1): 223-235 doi: 10.3934/jimo.2016013 +[Abstract](184) +[HTML](63) +[PDF](740.4KB)
Abstract:

This paper investigates the talent scheduling problem in film production, which is known as rehearsal scheduling in music and dance performances. The first lower bound on the minimization of talent hold cost is based upon the outside-in branching strategy. We introduce two approaches to add extra terms for tightening the lower bound. The first approach is to formulate a maximum weighted matching problem. The second approach is to retrieve structural information and solve a maximum weighted 3-grouping problem. We make two contributions: First, our results can fathom the matrix of a given partial schedule. Second, our second approach is free from the requirement to schedule some shooting days in advance for providing anchoring information as in the other approaches, i.e., a lower bound can be computed once the input instance is given. The lower bound can fit different branching strategies. Moreover, the second contribution provides a state-of-the-art research result for this problem. Computational experiments confirm that the new bounds are much tighter than the original one.

2017, 13(1): 237-249 doi: 10.3934/jimo.2016014 +[Abstract](328) +[HTML](48) +[PDF](348.1KB)
Abstract:

This work considers providing a common base for measuring the relative efficiency for all the decision-making units (DMUs) with multiple fuzzy inputs and outputs under the fuzzy data envelopment analysis (DEA) framework. It is shown that the fuzzy DEA model with common weights can be reduced into an auxiliary bi-objective fuzzy optimization problem by considering the most and the least favorable conditions simultaneously. An algorithm with the implementation issue for finding the compromise solution of the fuzzy DEA program is developed. A numerical example is included for illustration and comparison purpose. Our results show that the proposed approach is able to provide decision makers the flexibility in measuring the relative efficiency for DMUs with fuzzy inputs and outputs, which not only differentiates efficient units on a common base but also detects some abnormal efficiency scores calculated from other existing methods.

2017, 13(1): 251-265 doi: 10.3934/jimo.2016015 +[Abstract](211) +[HTML](47) +[PDF](682.8KB)
Abstract:

Carbon emission allowance(CEA) has been becoming an important factor for firms to make production policies. Cap-and-trade system is fulfilling in many countries and regions as a market scheme promoted by many politicians and economists for its efficiency in resources assignment and promotion to abatement of carbon emission. More and more firms take CEA into their production plan which makes them confronted with influences from two markets, product market and CEA trade market in the meanwhile. Based on the Newsboy model for simplicity, and with assumption that demand of product is a stochastic variable, this paper establishes optimization models to get the optimal production policy under administrative scheme (command-and-control) and market scheme (cap-and-trade) respectively. By comparing the firms' production policy and expected net income(ENI) with or without the existence of CEA trade market, it is found that CEA trade market can reduce the optimal amount of production and carbon emission on the one hand, and it does not decrease firms' ENI on the another hand because the CEA trade market provides more options for firms to make production policy. Hence, in the proposed complete and perfect market, we concluded cautiously that market-based carbon emission abatement scheme is effective to reduce carbon emission and to accomplish regulatory carbon emission abatement goal.

2017, 13(1): 267-282 doi: 10.3934/jimo.2016016 +[Abstract](216) +[HTML](56) +[PDF](439.5KB)
Abstract:

This paper studies a linear-quadratic control problem for discrete-time switched systems with subsystems perturbed by uncertainty. Analytical expressions are derived for both the optimal objective function and the optimal switching strategy. A two-step pruning scheme is developed to efficiently solve such problem. The performance of this method is shown by two examples.

2017, 13(1): 283-295 doi: 10.3934/jimo.2016017 +[Abstract](249) +[HTML](58) +[PDF](345.0KB)
Abstract:

In this paper, we consider a multivariate spectral DY-type projection method for solving nonlinear monotone equations with convex constraints. The search direction of the proposed method combines those of the multivariate spectral gradient method and DY conjugate gradient method. With no need for the derivative information, the proposed method is very suitable to solve large-scale nonsmooth monotone equations. Under appropriate conditions, we prove the global convergence and R-linear convergence rate of the proposed method. The preliminary numerical results also indicate that the proposed method is robust and effective.

2017, 13(1): 297-312 doi: 10.3934/jimo.2016018 +[Abstract](332) +[HTML](65) +[PDF](385.9KB)
Abstract:

Product pricing strategy has a significant impact on a service company's competitive edge. Considering the heterogeneous and time-sensitive customer choice behavior, monopoly service companies price their service products depending on cost parameters as well as time-sensitive customer choice behavior. According to the different time sensitivity, customers are classed into two groups (i.e., two market segments). By considering the impact of customer choice behavior, this paper investigates how a monopoly service firm decides its service product's response time and price under two product design strategies, i.e., offering two service products respectively to two market segments, or offering one standard service product to two market segments. Results indicate that, under the two strategies, the service firm adopts a segmented pricing strategy based on the customer perceived values and time-sensitive degrees. Besides, the service firm's profit under the strategy of offering two products is always higher than that under the other strategy. This indicates that, along with the individuation of customer demand, firms should firstly segment the market, and then, design targeted products for different customers. As a result, the degree of customer satisfaction can be increased, and firms can obtain higher profits.

2017, 13(1): 313-327 doi: 10.3934/jimo.2016019 +[Abstract](229) +[HTML](59) +[PDF](116.0KB)
Abstract:

The behavior of the perturbation map is analyzed quantitatively by using the concept of higher-order contingent derivative for the set-valued maps under Henig efficiency. By using the higher-order contingent derivatives and applying a separation theorem for convex sets, some results concerning higher-order sensitivity analysis are established.

2017, 13(1): 329-347 doi: 10.3934/jimo.2016020 +[Abstract](239) +[HTML](79) +[PDF](423.4KB)
Abstract:

Non-instantaneously deteriorating products retain their quality for a certain period before beginning to deteriorate. Retailers commonly adjust their retail prices when products shift from a non-deteriorating state to a deteriorating state in order to stimulate demand. It is essential to consider this price adjustment for inventory models of non-instantaneously deteriorating products under trade credit, due to the fact that the calculation of earned interest is based on the retail price. This paper considers the problem of ordering non-instantaneously deteriorating products under price adjustment and trade credit. Our objective was to determine the optimal replenishment cycle time while minimizing total costs. The problem is formulated as three piecewise nonlinear functions, which are solved through optimization. Numerical simulation is used to illustrate the solution procedures and discuss how system parameters influence inventory decisions and total cost. We also show that a policy of price adjustment is superior to that of fixed pricing with regard to profit maximization.

2017, 13(1): 349-373 doi: 10.3934/jimo.2016021 +[Abstract](230) +[HTML](53) +[PDF](453.3KB)
Abstract:

This paper considers a supply chain with an unregulated upstream monopolist (she) supplying a kind of products to a regulated downstream monopolist (he). The upstream monopolist's production efficiency, which represents her type, is only privately known to herself. When the downstream monopolist trades with the upstream monopolist, his pricing discretion is constrained by price cap regulation (PCR). We model this problem as a game of adverse selection with the price cap constraint. In this model, the downstream monopolist offers a menu of contracts, each of which consists of two parameters: the transfer payment and the retail price. We show that private information can weaken PCR's impact on the optimal contract, and PCR can dampen the effects of private information. We also shed light on the influences of private information and PCR on the optimal contract, the downstream monopolist's profit, the upstream monopolist's profit, the consumers' surplus and the social total welfare, respectively. Finally, a numerical example is given to illustrate the proposed results.

2017, 13(1): 375-397 doi: 10.3934/jimo.2016022 +[Abstract](478) +[HTML](65) +[PDF](747.8KB)
Abstract:

This paper deals with the optimal investment-reinsurance strategy for an insurer under the criterion of mean-variance. The risk process is the diffusion approximation of a compound Poisson process and the insurer can invest its wealth into a financial market consisting of one risk-free asset and one risky asset, while short-selling of the risky asset is prohibited. On the side of reinsurance, we require that the proportion of insurer's retained risk belong to $[0, 1]$, is adopted. According to the dynamic programming in stochastic optimal control, the resulting Hamilton-Jacobi-Bellman (HJB) equation may not admit a classical solution. In this paper, we construct a viscosity solution for the HJB equation, and based on this solution we find closed form expressions of efficient strategy and efficient frontier when the expected terminal wealth is greater than a certain level. For other possible expected returns, we apply numerical methods to analyse the efficient frontier. Several numerical examples and comparisons between models with constrained and unconstrained proportional reinsurance are provided to illustrate our results.

2017, 13(1): 399-411 doi: 10.3934/jimo.2016023 +[Abstract](217) +[HTML](59) +[PDF](380.9KB)
Abstract:

This paper provides a general ground for the problems of optimal stopping times over the families of partially available (or restricted) stopping times. It subsumes the classical framework in continuous-time, discrete-time, as well as semi-Markov settings as special cases. We model the problem by a restricted pool of stopping times meeting certain natural conditions and present its solution by means of Snell's envelope technique that extends the classical results. We further extend this type of problems to the stochastic processes indexed by partially ordered set.

2017, 13(1): 413-428 doi: 10.3934/jimo.2016024 +[Abstract](368) +[HTML](65) +[PDF](695.0KB)
Abstract:

This paper studies a real-world problem of simultaneous lot-sizing and scheduling in a capacitated flow shop. The problem combines two significant characteristics in production which are multiple-stage production with heterogeneous multiple machines and sequence-dependent setup time. Setup time does not hold the triangle inequality, thus there may be a setup for a product without actual production. Consequently, a novel mixed integer programming (MIP) formulation is proposed and tested on real data sets of wheel production. Exact approaches cannot find a feasible solution for the model in a reasonable time, so MIP-based heuristics are developed to solve the model more quickly. Test results show that the formulation is able to contain the problem requirements and the heuristics are computationally effective. Moreover, the obtained solution can improve on a real practice at the plant.

2017, 13(1): 429-447 doi: 10.3934/jimo.2016025 +[Abstract](228) +[HTML](61) +[PDF](474.9KB)
Abstract:

In this paper, we present a dynamic pricing model for two firms selling products displaying network effects for which consumers are with bounded rationality. We formulate this model in the form of differential games and derive the open-loop equilibrium prices for the firms. Then, we show the existence and uniqueness of such open-loop equilibrium prices. The model is further extended to the case with heterogeneous network effects. Their steady-state prices obtained are compared. A numerical example is solved and the results obtained are used to analyze how the steady-state prices and market shares of both firms are influenced by the cost, price sensitivity and the network effects of the products.

2017, 13(1): 449-475 doi: 10.3934/jimo.2016026 +[Abstract](237) +[HTML](58) +[PDF](308.4KB)
Abstract:

This paper studies the impacts of some reorder options on the performance as well as the coordination issues in a supply chain. A large category of products requires a long procurement lead time yet only has a relatively short selling season. Hence the purchase decisions usually have to be made well in advance of the opening of the sales. However, when uncertainty exists, the actual market demand may turn out to severely deviate from the initial order amount. To make up for the deficiency arising from this situation, a reorder option is introduced which renders a second manufacturing chance available shortly before he selling season. This reorder option facilitates an adjustment of the inventory level according to the realization of market demand. Since the market under investigation is facing a downward sloping demand curve, the effect of implementing this option is multi-fold. Moreover, the launch of the reorder option may also affect the decision makings at other levels of operations, such as altering the size of the initial order. Therefore, the overall impact of such option is not immediately clear. In this paper, it is shown that a properly designed reorder option is able to bring in profit growth and stabilize the fluctuations in the market retail price. Besides, quantity discount contracts are constructed to coordinate decisions on the initial inventory amount within the supply chain, so as to achieve higher economic efficiency. Finally, numerical examples are given to demonstrate the conclusions obtained in this paper.

2017, 13(1): 477-488 doi: 10.3934/jimo.2016027 +[Abstract](279) +[HTML](53) +[PDF](395.8KB)
Abstract:

In this paper, new continuity (both lower and upper semicontinuities) results of solution mappings to parametric generalized (strong) vector equilibrium problems are established by scalarization approaches, under $f$-strict pseudomonotonicity assumptions. Especially, based on this new kind of monotonicity, the compactness of the mapping $F$ is not required, which is different from the related literature. Some examples are also provided to illustrate main conclusions.

2017, 13(1): 489-503 doi: 10.3934/jimo.2016028 +[Abstract](252) +[HTML](64) +[PDF](436.4KB)
Abstract:

The very challenging emergency issues because of large scale natural or man-created disasters promote the research on evacuation planning. The earliest arrival contraflow is an important model for evacuation planning that rescue as many evacuees as possible at any point in time by reversing the direction of arcs towards the safe destinations with increased outbound arc capacity. We present efficient algorithms to solve the earliest arrival contraflow problem on multiple sources and on multiple sinks networks separately. We also introduce an approximate-earliest arrival contraflow solution on multi-terminal networks.

2017, 13(1): 505-529 doi: 10.3934/jimo.2016029 +[Abstract](277) +[HTML](58) +[PDF](559.1KB)
Abstract:

This paper studies a model of on-the-job search and savings under reference-dependent preferences that implies loss aversion in a worker's consumption behaviors. The model analyzes how loss aversion affects the worker's consumption decisions in job search. The results demonstrate that the presence of loss aversion will lead to a set of high steady-state consumption levels and the range of steady-state consumption levels is wider if the worker is more loss averse. Nevertheless, we show that there is a unique steady-state consumption level, which is a lower bound of the set, in the absence of loss aversion. In addition, we also find that great loss aversion may reduce consumption level, while small loss aversion not only causes consumption to remain at a high level, but also induces that the worker's future consumption level goes down when the employment status changes.

2016  Impact Factor: 0.994