# American Institue of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

2016 , Volume 12 , Issue 2

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Christina Burt , Louis Caccetta , Leon Fouché and  Palitha Welgama
2016, 12(2): 403-430 doi: 10.3934/jimo.2016.12.403 +[Abstract](49) +[PDF](535.7KB)
Abstract:
In the surface mining industry, the Equipment Selection Problem involves choosing an appropriate fleet of trucks and loaders such that the long-term mine plan can be satisfied. An important characteristic for multi-location (multi-location and multi-dumpsite) mines is that the underlying problem is a multi-commodity flow problem. The problem is therefore at least as difficult as the fixed-charge, capacitated multi-commodity flow problem. For long-term schedules it is useful to consider both the purchase and salvage of the equipment, since equipment may be superseded, and there is the possibility of used pre-existing equipment. This may also lead to heterogeneous fleets and arising compatibility considerations. In this paper, we consider two case studies provided by our industry partner. We develop a mixed-integer linear programming model for heterogeneous equipment selection in a surface mine with multiple locations and a multiple period schedule. Encoded in the solution is an allocation scheme in addition to a purchase and salvage policy. We develop a solution approach, including variable preprocessing, to tackle this large-scale problem. We illustrate the computational effectiveness of the resulting model on the two case studies for large sets of equipment and long-term schedule scenarios.
Wan Nor Ashikin Wan Ahmad Fatthi , Adibah Shuib and  Rosma Mohd Dom
2016, 12(2): 431-447 doi: 10.3934/jimo.2016.12.431 +[Abstract](118) +[PDF](1333.7KB)
Abstract:
This paper address the problem at the inbound phase at the cross docking warehouse. The fundamental issues in cross docking facility is to assign the incoming truck to the door and to coordinate the sequences of the trucks in order to minimize the completion time at the inbound phase. Using the theories and methodologies of assignment and scheduling, paper on hand proposed a mixed integer programming model for solving the truck-to-door assignment and scheduling problem with the objective to minimize the total service time of trucks. Meanwhile, reduce the waiting time of trucks before being served at the designated door. A preliminary computation is conducted to verify the logic of the mathematical model proposed.
Dandan Hu and  Zhi-Wei Liu
2016, 12(2): 449-470 doi: 10.3934/jimo.2016.12.449 +[Abstract](41) +[PDF](829.7KB)
Abstract:
This article deals with the problem of making simultaneous decisions on the location, capacity and demand flow assignment for intermediate facilities in a network. Two nonlinear mixed-integer program (NMIP) models for continuous and discrete capacity decisions are proposed, respectively. The objective is to minimize the total costs, including fixed location cost, transportation cost, congestion cost and capacity cost. Congestion at intermediate facilities is modeled as the ratio of total flow to surplus capacity by viewing each facility as an M/M/1 queuing system. To solve NMIP with continuous capacity decision, we apply the Lagrangean algorithm that has been proposed to solve the classic inventory-location model. For the NMIP with discrete capacity decision, we propose another Lagrangean algorithm where the problem is decomposed into $|K|$ subproblems that can be solved to optimality. The measures of allocation heuristic, capacity increase and capacity adjustment are taken to construct feasible solutions. Computational results indicate that the heuristics for the two models are both efficient and effective.
Yi Zhang , Yuyun Zhao , Tao Xu and  Xin Liu
2016, 12(2): 471-486 doi: 10.3934/jimo.2016.12.471 +[Abstract](123) +[PDF](367.9KB)
Abstract:
In this paper we discuss the $p$th moment absolute exponential stability of stochastic control system with Markovian switching. We first give a new concept of $p$th moment absolute exponential stability, then we establish some theorems under different hypotheses to guarantee the system $p$th moment absolutely exponentially stable. These sufficient conditions in our theorems are algebraic criteria in terms of matrix inequalities, and we introduce an $M$-method with MATLAB to compute them. Finally, some examples are given to illustrate our results.
Xiangyu Ge , Tifang Ye , Yanli Zhou and  Guoguang Yan
2016, 12(2): 487-504 doi: 10.3934/jimo.2016.12.487 +[Abstract](41) +[PDF](384.2KB)
Abstract:
In this paper, we study the economic growth and social welfare in an endogenous growth model with spillovers of public goods, leviathan taxation and imperfectly flow capital in heterogeneous economies. We show that the effect of spillovers and capital flow on economic growth and welfare is different for well endowed region and poorly endowed region under fiscal centralization and fiscal decentralization. We also show that a decentralized system dominates a centralized system in terms of economic growth no matter whether the region is well or poorly endowed. However, the difference between a decentralized system and a centralized system is ambiguous in social welfare. It is dependent on the degree of spillovers and capital flow no matter whether the region is well or poorly endowed.
Ricai Luo , Honglei Xu , Wu-Sheng Wang , Jie Sun and  Wei Xu
2016, 12(2): 505-514 doi: 10.3934/jimo.2016.12.505 +[Abstract](52) +[PDF](378.5KB)
Abstract:
The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function $V$ and on the strict negativity of the function $dV/dt$, which often come as a result of boundedness or uniformly almost periodicity of the activation functions. In this paper, we investigate the asymptotical stability problem of Hopfield neural networks with time delays under weaker conditions. By constructing a suitable Lyapunov function, sufficient conditions are derived to guarantee global asymptotical stability and exponential stability of the equilibrium of the system. These conditions do not require the strict negativity of $dV/dt$, nor do they require that the activation functions to be bounded or uniformly almost periodic.
Renato Bruni , Gianpiero Bianchi and  Alessandra Reale
2016, 12(2): 515-527 doi: 10.3934/jimo.2016.12.515 +[Abstract](27) +[PDF](358.9KB)
Abstract:
In the case of some large statistical surveys, the set of units that will constitute the scope of the survey must be selected. We focus on the real case of a Census of Agriculture, where the units are farms. Surveying each unit has a cost and brings a different portion of the whole information. In this case, one wants to determine a subset of units producing the minimum total cost for being surveyed and representing at least a certain portion of the total information. Uncertainty aspects also occur, because the portion of information corresponding to each unit is not perfectly known before surveying it. The proposed approach is based on combinatorial optimization, and the arising decision problems are modeled as multidimensional binary knapsack problems. Experimental results show the effectiveness of the proposed approach.
Kun Fan , Yang Shen , Tak Kuen Siu and  Rongming Wang
2016, 12(2): 529-541 doi: 10.3934/jimo.2016.12.529 +[Abstract](144) +[PDF](352.4KB)
Abstract:
In this paper, we discuss a Markov chain approximation method to price European options, American options and barrier options in a Markovian regime-switching environment. The model parameters are modulated by a continuous-time, finite-state, observable Markov chain, whose states represent the states of an economy. After selecting an equivalent martingale measure by the regime-switching Esscher transform, we construct a discrete-time, inhomogeneous Markov chain to approximate the dynamics of the logarithmic stock price process. Numerical examples and empirical analysis are used to illustrate the practical implementation of the method.
Sohana Jahan and  Hou-Duo Qi
2016, 12(2): 543-563 doi: 10.3934/jimo.2016.12.543 +[Abstract](73) +[PDF](1159.3KB)
Abstract:
The classical Multi-Dimensional Scaling (MDS) is an important method for data dimension reduction. Nonlinear variants have been developed to improve its performance. One of them is the MDS with Radial Basis Functions (RBF). A key issue that has not been well addressed in MDS-RBF is the effective selection of its centers. This paper treats this selection problem as a multi-task learning problem, which leads us to employ the $(2,1)$-norm to regularize the original MDS-RBF objective function. We then study its two reformulations: Diagonal and spectral reformulations. Both can be effectively solved through an iterative block-majorization method. Numerical experiments show that the regularized models can improve the original model significantly.
Zhe Zhang and  Jiuping Xu
2016, 12(2): 565-593 doi: 10.3934/jimo.2016.12.565 +[Abstract](83) +[PDF](1187.5KB)
Abstract:
This study focuses on the multi-mode resource-constrained projects scheduling problem (MRCPSP), which considers the complex hierarchical organization structure and hybrid uncertainty environment in the decision making process. A bi-level multi-objective MRCPSP model with fuzzy random coefficients and bi-random coefficients is developed for the MRCPSP. In the model, construction contractor, the upper level decision maker (ULDM), aims to minimize the consumption of resources and maximize the quality level of project. Meanwhile, outsourcing partner, the lower level decision maker (LLDM), tries to schedule the activities under resource allocation with the objective of minimizing the total tardiness penalty cost. To deal with the uncertainty variables, the fuzzy random parameters are transformed into the trapezoidal fuzzy variables, which are de-fuzzified by the expected value subsequently. For the bi-random parameters, the expected value operator is employed. After obtaining the equivalent crisp model, the passive congregation-based bi-level multiple objective particle swarm optimization algorithm (PC-based BL-MOPSO) is designed to obtain the Pareto solutions. Finally, a practical application is presented to verify the practicability of the proposed bi-level multi-objective MRCPSP model and the efficiency of algorithm.
Bin Li , Hai Huyen Dam and  Antonio Cantoni
2016, 12(2): 595-607 doi: 10.3934/jimo.2016.12.595 +[Abstract](26) +[PDF](377.2KB)
Abstract:
In this paper, we investigate a zero-forcing beamformer design with signed power-of-two coefficients for rural applications. In this design, the minimum user information rate is taken as the performance measure, while a practical system design constraint, the per-antenna power constraint, is imposed. The problem is formulated as a constrained zero-one integer programming problem. Based on a transform between two different integer spaces, the problem is transformed into an equivalent constrained integer programming problem. A global optimal two-stage design is proposed for solving the problem. In the first stage, a polynomial time quantization method is applied to obtain an initial design. In the second stage, an auxiliary function method is used to find the global optimal design. For illustration, numerical examples under several different scenarios are studied and the results are compared with those obtained by an existing method. Furthermore, the impact of the mutual interference terms in the performance measure is also studied.
Sung-Seok Ko , Jangha Kang and  E-Yeon Kwon
2016, 12(2): 609-624 doi: 10.3934/jimo.2016.12.609 +[Abstract](63) +[PDF](604.7KB)
Abstract:
Inventory models are widely used in a variety of real-world applications. In particular, inventory systems with perishable items have received a significant amount of attention. We consider an $(s,S)$ continuous inventory model with perishable items, impatient customers, and random lead times. Two characteristic behaviors of impatient customers are balking and reneging. Balking is when a customer departs the system if the item they desire is unavailable. Reneging occurs when a waiting customer leaves the system if their demand is not met within a set period of time. The proposed system is modeled as a two-dimensional Markov process with level-dependent $G/M/1$-type structure. We also consider independent and identically distributed replenishment lead times that follow a phase-type distribution. We find an efficient approximation method for the joint stationary distribution of the number of items in the system, and provide formulas for several performance measures. Moreover, to minimize system costs, we find the optimal values of $s$ and $S$ numerically and perform a sensitivity analysis on key parameters.
Fengjun Wang , Qingling Zhang , Bin Li and  Wanquan Liu
2016, 12(2): 625-636 doi: 10.3934/jimo.2016.12.625 +[Abstract](108) +[PDF](347.8KB)
Abstract:
In this paper, we will investigate a duopoly competition issue in a commencing period of horizontal expansion. This is an important problem in marketing investment for new products in free market. First, we propose a new market model characterized by nonlinear differential-algebraic equations with continuous inequality constraints, which aims to maximize an enterprise's product market share rather than its profit in the commencing period in an environment of the duopoly market. In order to solve the investment problem numerically based on proposed model, the control parameterization technique together with the constraint transcription method is used by transforming the proposed problem into a sequence of optimal parameter selection problems. Finally, a practical example on beer sales is used to show the effectiveness of proposed model and we present the optimal advertising strategies corresponding to different competition situations.
Byeongchan Lee , Jonghun Yoon , Yang Woo Shin and  Ganguk Hwang
2016, 12(2): 637-652 doi: 10.3934/jimo.2016.12.637 +[Abstract](32) +[PDF](412.5KB)
Abstract:
The appearance of heavy-tailedness in users' traffic significantly degrades the performance of communication systems, and a distributed server system is considered as a good solution to this problem because of its distributed service characteristic by multiple servers. So we tackle the question in this paper that a distributed server system can alleviate heavy-tailedness, so that users experience good QoS as if there were no heavy-tailedness. To this end, we first mathematically model a distributed server system and obtain a heavy-tailed random sum with the help of the theory of perturbed random walk. We then analyze the tail asymptotic of the heavy-tailed random sum to find a condition with which the distributed server system can alleviate heavy-tailedness.
Dequan Yue , Wuyi Yue and  Guoxi Zhao
2016, 12(2): 653-666 doi: 10.3934/jimo.2016.12.653 +[Abstract](36) +[PDF](381.0KB)
Abstract:
We consider an M/M/1 queueing system with vacations and impatient customers. Whenever a customer arrives at the system, it activates an random impatience timer". If the customer's service has not been completed before the customer's impatience timer expires, the customer abandons the queue, and never returns. It is assumed that the impatience timer depends on the server's states. We analyze both multiple and single vacation scenarios and derive the probability generating functions of the number of customers in the system when the server is in vacation period and busy period. Then, we obtain explicit expressions for various performance measures such as the mean system sizes when the server is either on vacation or busy, the proportion of customers served, and the average rate of abandonments due to impatience. We present some numerical results for multiple vacation scenario to show the effects of the parameters of impatience timers on some performance measures. Finally, we show some inequalities on some performances under the single vacation policy and under multiple vacation policy.
Masataka Kato , Hiroyuki Masuyama , Shoji Kasahara and  Yutaka Takahashi
2016, 12(2): 667-685 doi: 10.3934/jimo.2016.12.667 +[Abstract](139) +[PDF](473.9KB)
Abstract:
Large-scale data centers for cloud computing services consist of a number of commodity servers, resulting in a huge amount of power consumption. In order to save power consumption, BEEMR (Berkeley Energy Efficient MapReduce), a MapReduce workload manager, is proposed. In a BEEMR-based data center, servers are allocated to either of the interactive and batch zones. Arriving jobs of a small size begin to be processed immediately in the interactive zone, while large-sized jobs are queued and served simultaneously at every fixed service period in the batch zone. In this paper, we analyze the performance of BEEMR-type job scheduling. We consider two queueing models for the interactive and batch zones. The interactive zone is modeled as a single-server queueing system with processor-sharing (PS) service. In terms of the batch zone, we consider a queueing system with gated service in which arriving jobs are queued and begin to be served when a fixed service period starts. For these models, the time-average power consumption and the mean response time are derived. Numerical examples show that the power consumption is significantly affected by the allocation of servers to both zones, while the power consumption is insensitive to the length of the batch-service period.
Shunfu Jin , Wuyi Yue and  Zsolt Saffer
2016, 12(2): 687-702 doi: 10.3934/jimo.2016.12.687 +[Abstract](30) +[PDF](463.8KB)
Abstract:
In Cognitive Radio Networks the licensed users and the cognitive users are called Primary Users and Secondary Users, respectively. The Primary Users enjoy preemptive priority during the spectrum usage, while the Secondary Users are allowed to access the unused parts of the spectrum opportunistically. In this paper we focus on the problem of improving the fairness of spectrum usage for real-time applications. We propose a novel centralized spectrum allocation mechanism with a gated polling strategy, which we model by a gated polling system with a non-zero switchover times. The approximate analysis of this polling model is performed. We derive formulas for estimating the system measures in terms of throughput of the system, average latency and delay jitter of the Secondary Users packets as well as the spectrum switching ratio and the spectrum utility. Numerical results based on the analysis and the simulation are provided to validate the analytical results and to investigate the impact of different parameters on the system performance. Finally we discuss the optimal system design by the help of building an appropriate cost function.
Y. K. Lin and  C. S. Chong
2016, 12(2): 703-717 doi: 10.3934/jimo.2016.12.703 +[Abstract](104) +[PDF](467.2KB)
Abstract:
This research presents a tabu search algorithm with a restart (TSA-R) approach to minimize total weighted tardiness (TWT) for the job shop scheduling problem. Jobs have non-identical due dates. The problem belongs to the class of NP-hard problems. The TSA-R approach uses dispatching rules to obtain an initial solution and searches for new solutions in a neighborhood based on the critical paths of jobs and blocks of operations. The TSA-R applies a new diversification scheme to exploit the initial solutions and its neighborhood structures so as to overcome entrapment issues and to enhance solutions. A computational result based on standard benchmark instances from the literature is presented to show the effectiveness of the proposed tabu search algorithm.
Jian Xiong , Yingwu Chen and  Zhongbao Zhou
2016, 12(2): 719-737 doi: 10.3934/jimo.2016.12.719 +[Abstract](60) +[PDF](494.5KB)
Abstract:
In the real world, project construction usually suffers various uncertain factors. Traditionally, uncertainty is modelled as either random variables or dynamic events. This paper addresses the case that the information about uncertainty is partially known when developing project schedules. The concept of resilience is introduced into project scheduling problems with resource constraint to measure a schedule's ability to absorb possible perturbation. The definition of resilience is given based on project equilibriums. Since the calculation of resilience is time intensive, a new surrogate measure is proposed to indicate schedule resilience. Correlation analysis between resilience and proposed surrogate measure is carried out. The experimental results suggest that the proposed surrogate measure is more appropriate to indicate resilience than makespan or total free slack.
Yanqin Bai , Pengfei Ma and  Jing Zhang
2016, 12(2): 739-756 doi: 10.3934/jimo.2016.12.739 +[Abstract](123) +[PDF](571.5KB)
Abstract:
We present an interior-point method based on kernel functions for circular cone optimization problems, which has been found useful for describing optimal design problems of optimal grasping manipulation for multi-fingered robots. Since the well-known second order cone is a particular circular cone, we first establish an invertible linear mapping between a circular cone and its corresponding second order cone. Then we develop a kernel function based interior-point method to solve circular cone optimization in terms of the corresponding second order cone optimization problem. We derive the complexity bound of the interior-point method and conclude that circular cone optimization is polynomial-time solvable. Finally we illustrate the performance of interior-point method by a real-world quadruped robot example of optimal contact forces taken from the literature [10].
Ganggang Li , Xiwen Lu and  Peihai Liu
2016, 12(2): 757-770 doi: 10.3934/jimo.2016.12.757 +[Abstract](105) +[PDF](345.6KB)
Abstract:
Single-machine scheduling problems with production and delivery are studied in this paper. There is only one delivery vehicle with capacity $z$. Jobs are not allowed to resume. The $P \rightarrow D$ system and $D \rightarrow P$ system are considered, respectively. For the machine with an availability constraint, we present two $4/3$-approximation algorithms and show that the bounds are tight. For the machine with periodic availability constraints, we provide two polynomial time approximation algorithms which are the best possible.
Xianzhao Zhang , Dachuan Xu , Donglei Du and  Cuixia Miao
2016, 12(2): 771-779 doi: 10.3934/jimo.2016.12.771 +[Abstract](31) +[PDF](305.6KB)
Abstract:
We study two unrelated machine scheduling problems with machine dependent release dates to minimize the makespan. For the case with fixed processing time where processing job $j$ on machine $i$ requires time $p_{ij}$ and incurs a cost of $c_{ij}$, we derive a $2$-approximation algorithm. For the problem with variable processing times where the cost increases linearly as the processing time decreases, we propose a $(2+\epsilon)$-approximation algorithm.
Feng Yang , Kok Lay Teo , Ryan Loxton , Volker Rehbock , Bin Li , Changjun Yu and  Leslie Jennings
2016, 12(2): 781-810 doi: 10.3934/jimo.2016.12.781 +[Abstract](235) +[PDF](2465.9KB)
Abstract:
The FORTRAN MISER software package has been used with great success over the past two decades to solve many practically important real world optimal control problems. However, MISER is written in FORTRAN and hence not user-friendly, requiring FORTRAN programming knowledge. To facilitate the practical application of powerful optimal control theory and techniques, this paper describes a Visual version of the MISER software, called Visual MISER. Visual MISER provides an easy-to-use interface, while retaining the computational efficiency of the original FORTRAN MISER software. The basic concepts underlying the MISER software, which include the control parameterization technique, a time scaling transform, a constraint transcription technique, and the co-state approach for gradient calculation, are described in this paper. The software structure is explained and instructions for its use are given. Finally, an example is solved using the new Visual MISER software to demonstrate its applicability.

2016  Impact Factor: 0.994