# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

July 2015 , Volume 11 , Issue 3

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2015, 11(3): 701-714 doi: 10.3934/jimo.2015.11.701 +[Abstract](2182) +[PDF](363.8KB)
Abstract:
In this paper, we introduce two types of Levitin-Polyak well-posedness for a system of generalized vector variational inequality problems. By means of a gap function of the system of generalized vector variational inequality problems, we establish equivalence between the two types of Levitin-Polyak well-posedness of the system of generalized vector variational inequality problems and the corresponding well-posednesses of the minimization problems. We also present some metric characterizations for the two types of Levitin-Polyak well-posedness of the system of generalized vector variational inequality problems. The results in this paper generalize, extend and improve some known results in the literature.
2015, 11(3): 715-731 doi: 10.3934/jimo.2015.11.715 +[Abstract](2679) +[PDF](370.1KB)
Abstract:
In this paper, we consider the balking behavior of customers in an M/G/1 queueing system with a removable server under N-policy, where the server may be turned off when no customers are present, and be turned on when the queue length reaches size $N$. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. For the unobservable and partially observable queues, we first analyze the stationary behavior of the system; then derive the equilibrium mixed strategies and compare them to the socially optimal strategies. We take the number $N$ as a decision variable and discuss the optimal operations policy in equilibrium states. Finally, we present two examples to demonstrate some of the phenomena in the considered models.
2015, 11(3): 733-746 doi: 10.3934/jimo.2015.11.733 +[Abstract](2543) +[PDF](369.9KB)
Abstract:
In this paper, we consider using the inexact nonsmooth Newton method to efficiently solve the symmetric cone constrained variational inequality (VISCC) problem. It red provides a unified framework for dealing with the variational inequality with nonlinear constraints, variational inequality with the second-order cone constraints, and the variational inequality with semidefinite cone constraints. We get convergence of the above method and apply the results to three special types symmetric cones.
2015, 11(3): 747-762 doi: 10.3934/jimo.2015.11.747 +[Abstract](2768) +[PDF](321.5KB)
Abstract:
We develop a ranking process for multi-objective decision making. For optimizing the multi-objective problem having both quantitative and qualitative objectives, weight assessment is important to convert the problem into the corresponding single objective problem. Therefore, a ranking process is proposed to simultaneously obtain the objective weights and the evaluation of alternatives with multiple objectives. Several new concepts are developed to handle the dynamism in distance computation and ranking of decisions in a multi-objective model having qualitative evaluations. The proposed process is illustrated in a numerical example.
2015, 11(3): 763-777 doi: 10.3934/jimo.2015.11.763 +[Abstract](2142) +[PDF](353.9KB)
Abstract:
We consider a single server cyclic polling system with multiple infinite-buffer queues where the server follows an adaptive mechanism: if a queue is empty at its polling moment the server will skip this queue in the next cycle. After being skipped, a queue is always visited in the next cycle. The service discipline in each queue is 1-limited. Using the fluid limit approach, we find the necessary and sufficient condition for the stability of such polling system.
2015, 11(3): 779-806 doi: 10.3934/jimo.2015.11.779 +[Abstract](2327) +[PDF](492.1KB)
Abstract:
This paper considers a discrete-time GI$^X$/Geo/1/N-G queue with randomized working vacations, where upon arrival, a negative customer removes one positive (ordinary) customer in service if any is present and disappears immediately; otherwise, it has no effect on the system if the system is empty. As soon as the system becomes empty, the server immediately takes a working vacation. If there are no customers in the system at the end of the working vacation, the server takes another working vacation with probability $p$ or remains dormant in the system with probability $1-p$. Otherwise, the server starts to serve the customers with the normal service rate immediately if there are some customers at the end of a working vacation. This pattern does not terminate until the server has taken $J$ successive working vacations. Steady-state system length distributions at various epochs such as, pre-arrival, arbitrary and outside observer's observation epochs have been obtained. Based on the various system length distributions, we also give some important performance measures including blocking probabilities, mean queue length, probability mass function of waiting time and other performance measures along with some numerical examples. Then, we use the parabolic method to search the optimum value of the normal service rate under a established cost function.
2015, 11(3): 807-828 doi: 10.3934/jimo.2015.11.807 +[Abstract](2305) +[PDF](455.4KB)
Abstract:
In this paper, we consider a multi-channel cognitive radio network with multiple secondary users (SUs) and analyze the performance of users in the network. We assume primary users (PUs) adopt the automatic repeat request (ARQ) protocol at the medium access control layer. We have two main goals. Our first goal is to develop a cross-layer performance model of the cognitive radio network by considering the retransmission characteristics of the ARQ protocol and the interference between PUs and SUs due to imperfect channel sensing. Using the cross-layer performance model we analyze the throughput performance of SUs and the delay performance of PUs.
Our second goal is to propose an optimal channel sensing method that maximizes the throughput performance of SUs while a given delay requirement of PUs is guaranteed. To this end, using our cross-layer performance model, we formulate an optimization problem and solve it to get an optimal channel sensing method that satisfies the design objectives. Numerical and simulation results are provided to validate our analysis and to investigate the performance of the optimal channel sensing method.
2015, 11(3): 829-848 doi: 10.3934/jimo.2015.11.829 +[Abstract](1958) +[PDF](457.7KB)
Abstract:
In this paper, we study a discrete-time buffer system with a time-correlated packet arrival process and one unreliable output line. In particular, packets arrive to the buffer in the form of variable-length packet trains at a fixed rate of exactly one packet per slot. The packet trains are assumed to have a geometric length, such that each packet has a fixed probability of being the last of its corresponding train. The output line is governed by a Markovian process, such that the probability that the line is available during a slot depends on the state of the underlying $J$-state Markov process during that slot.
First, we provide a general analysis of the state of the buffer system based on a matrix generating functions approach. This also leads to an expression for the mean buffer content. Additionally, we take a closer look at the distributions of the packet delay and the train delay. In order to make matters more concrete, we next present a detailed and explicit analysis of the buffer system in case the output line is governed by a $2$-state Markov process. Some numerical examples help to visualise the influence of the various model parameters.
2015, 11(3): 849-866 doi: 10.3934/jimo.2015.11.849 +[Abstract](2430) +[PDF](274.9KB)
Abstract:
With the development of communication technology, the functions of the mobile terminals are becoming ever more enhanced, and the energy requirements for the terminals become harder than before. In this paper we propose a novel Active Discontinuous Reception (DRX) mechanism with a sleep-delay strategy in the Long Term Evolution (LTE) technology in order to reduce the average latency while saving more energy in 4G networks. The key idea is to influence the control of the downlink transmission on that way that the system would go to sleep only when there is no data frame arrival within the sleep-delay timer. Considering several logical channels for one connection, we model the network using the novel Active DRX mechanism with a sleep-delay strategy as a multiple synchronous vacation queueing system with a wake-up period and a sleep-delay. We derive several performance measures, such as the energy saving ratio, the system blocking ratio and the average latency. We also provide numerical results by means of analysis and simulation to show the validity of the novel Active DRX mechanism. Finally by constructing a profit function, we optimize several system parameters in terms of the number of the logical channels for one connection, the time lengths of the sleep-delay timer and the sleep period.
2015, 11(3): 867-886 doi: 10.3934/jimo.2015.11.867 +[Abstract](2475) +[PDF](459.9KB)
Abstract:
2015, 11(3): 887-920 doi: 10.3934/jimo.2015.11.887 +[Abstract](1820) +[PDF](1573.8KB)
Abstract:
One of the key issues in recent mobile telecommunication is to increase the scalability of current packet data networks. This comes along with the requirement of reducing the load of signaling related to establishment and handover procedures. This paper establishes an analytical model to analyze the signaling overhead of two different secure mobile architectures. Both are based on the Host Identity Protocol for secure signaling and use IPsec for secure data transport. The paper presents the cumulative distribution function and moments of security association periods and calculates the rate of different signaling procedures in a synthetic network model assuming M/G/$\infty$ process for session establishments between end-nodes. Using the model, it is shown that the Ultra Flat Architecture has significant performance gains over the traditional End-to-End HIP protocol in large-scale mobile environment in the access networks and toward the rendezvous service, but performs worse in the core transport network between the GWs.
2015, 11(3): 921-932 doi: 10.3934/jimo.2015.11.921 +[Abstract](2689) +[PDF](2692.1KB)
Abstract:
In this study, a new algorithm based on polyhedral conic functions (PCFs) is developed to solve multi-class supervised data classification problems. The $k$ PCFs are constructed for each class in order to separate it from the rest of the data set. The $k$-means algorithm is applied to find vertices of PCFs and then a linear programming model is solved to calculate the parameters of each PCF. The separating functions for each class are obtained as a pointwise minimum of the PCFs. A class label is assigned to the test point according to its minimum value over all separating functions. In order to demonstrate the performance of the proposed algorithm, it is applied to solve classification problems in publicly available data sets. The comparative results with some mainstream classifiers are presented.
2015, 11(3): 933-949 doi: 10.3934/jimo.2015.11.933 +[Abstract](3206) +[PDF](442.8KB)
Abstract:
This paper develops an Economic Order Quantity (EOQ) model for non-instantaneous deteriorating items with selling price- and inflation-induced demand under the effect of inflation and customer returns. The customer returns are assumed as a function of demand and price. Shortages are allowed and partially backlogged. The effects of time value of money are studied using the Discounted Cash Flow approach. The main objective is to determine the optimal selling price, the optimal length of time in which there is no inventory shortage, and the optimal replenishment cycle simultaneously such that the present value of total profit is maximized. An efficient algorithm is presented to find the optimal solution of the developed model. Finally, a numerical example is extracted to solve the presented inventory model using the proposed algorithm and the effects of the customer returns, inflation, and non-instantaneous deterioration are also discussed. The paper ends with a conclusion and outlook to future studies.
2015, 11(3): 951-968 doi: 10.3934/jimo.2015.11.951 +[Abstract](2264) +[PDF](421.4KB)
Abstract:
This paper considers a mathematical program with second-order cone complementarity constrains (MPSOCC). We present two approximation methods for solving the MPSOCC. One employs some smoothing functions to approximate the MPSOCC and the other makes use of some techniques to relax the complementarity constrains in the MPSOCC. We investigate the limiting behavior of both methods. In particular, we show that, under mild conditions, any accumulation point of stationary points of the approximation problems must be a Clarke-type stationary point of the MPSOCC.
2015, 11(3): 969-983 doi: 10.3934/jimo.2015.11.969 +[Abstract](2992) +[PDF](346.6KB)
Abstract:
On the basis of capital structure theory and the option pricing model, the revenues and costs of debts are quantified. Combining with the financing characteristics of real estate enterprises, a mathematical model in consideration of the effect of interest-free debt was established in this paper to determine the optimal capital structure of real estate enterprises, and then a simulation analysis was conducted. The results indicated that the interest-bearing debt interest rate, the tax rate, the risk-free interest rate and the proportion of interest-bearing debt are all positively correlated with the optimal debt ratio of real estate enterprises, the annual average growth rate of housing price and the annual volatility of enterprise assets are negatively correlated with that, and as the debt maturity increases, the optimal debt ratio of real estate enterprises will decrease.
2015, 11(3): 985-998 doi: 10.3934/jimo.2015.11.985 +[Abstract](2857) +[PDF](325.0KB)
Abstract:
In a restructured electricity sector, day-ahead markets can be modeled as a game where some players - the producers - submit their proposals. To analyze the companies' behavior we have used the concept of Nash equilibrium as a solution in these multi-agent interaction problems. In this paper, we present new and crucial adaptations of two well-known mechanisms, the adjustment process and the relaxation algorithm, in order to achieve the goal of computing Nash equilibria. The advantages of these approaches are highlighted and compared with those available in the literature.
2015, 11(3): 999-1019 doi: 10.3934/jimo.2015.11.999 +[Abstract](2377) +[PDF](923.5KB)
Abstract:
We consider numerical methods for the extreme eigenvalue problem of large scale symmetric positive definite matrices. By the variational principle, the extreme eigenvalue can be obtained by minimizing some unconstrained optimization problem. Firstly, we propose two adaptive nonmonotone Barzilai-Borwein-like methods for the unconstrained optimization problem. Secondly, we prove the global convergence of the two algorithms under some conditions. Thirdly, we compare our methods with eigs and the power method for the standard test problems from the UF Sparse Matrix Collection. The primary numerical experiments indicate that the two algorithms are promising.
2015, 11(3): 1021-1040 doi: 10.3934/jimo.2015.11.1021 +[Abstract](2021) +[PDF](557.0KB)
Abstract:
This study focuses on the inventory problems for serial-type and assembly-type supply chains. Since the mainline and each branch line of the assembly-type supply chain can be treated as a serial-type supply chain, a model of a serial-type supply chain is first constructed and then an integrated model is developed for the whole assembly-type supply chain. Both problems are solved optimally by the proposed polynomial-time algorithm, which determines the economic lot size, the optimal batch sizes, and the number of batches for each stage. Numerical examples are included to illustrate the algorithmic procedures.

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