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Journal of Industrial & Management Optimization

2009 , Volume 5 , Issue 1

A special issue
for the 7th International Conference on Optimization, Techniques and Applications

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Preface
Xiaoling Sun and Song Wang
2009, 5(1): i-ii doi: 10.3934/jimo.2009.5.1i +[Abstract](51) +[PDF](38.6KB)
Abstract:
This special issue is a collection of selected papers presented at the 7th International Conference on Optimization: Techniques and Applications (ICOTA 7), which took place from December 12-15, 2007 in Kobe, Japan. ICOTA is an official conference series of POP (The Pacific Optimization Research Activity Group) and ICOTA 7 was organized by the Institute of Intelligent Information and Communications Technology (IICT) of Konan University. The purpose of this tri-annual conference is to provide a forum for international researchers and practitioners to highlight their major advances in optimization techniques and applications since ICOTA 6 held in December, 2004 in Ballarat, Australia.
Over two hundred papers were presented at ICOTA 7. The thirteen papers published in this special issue cover a wide range of topics in optimization techniques and their applications, as outlined below.

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A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales
Y. Gong and X. Xiang
2009, 5(1): 1-10 doi: 10.3934/jimo.2009.5.1 +[Abstract](84) +[PDF](155.2KB)
Abstract:
This paper is mainly concerned with a class of optimal control problems of systems governed by the first order linear dynamic equations on time scales with quadratic cost functionals. Introducing the weak solutions of the first order linear dynamic equations and presenting the Arzela-Ascoli theorem on time scales, we prove the existence of solution to a class of linear quadratic optimal control problems on time scales.
An efficient search algorithm for obtaining the optimal replenishment strategies in multi-stage just-in-time supply chain systems
Ming-Jong Yao and Tien-Cheng Hsu
2009, 5(1): 11-32 doi: 10.3934/jimo.2009.5.11 +[Abstract](68) +[PDF](314.5KB)
Abstract:
In this study, we focus on the coordination of the replenishment activities among all firms in a multi-stage supply chain system in which Just-In-Time (JIT) philosophy applies. Similar to all JIT systems, kanban is used to control information flows and material flows between two adjacent manufacturing plants, which is called a kanban stage. In this supply chain, suppliers provide raw materials to the manufacturing plant in the first kanban stage and end-products are delivered from the plant in the last kanban stage to the warehouses or directly to the customers. Studies in the literature formulated this problem as a Mixed-Integer Non-Linear Program (MINLP). The objective of this study is to propose an efficient search algorithm that solves an optimal solution for this MINLP model. We conduct theoretical analysis on the optimality structure of the model and assert that the optimal cost curve is piece-wise convex. The characteristics of the optimal cost curve, especially the "junction points'', provide essential foundation to the design of our search algorithm. Also, in order to reinforce the effectiveness of the proposed search algorithm, we utilize a relaxation of the problem to obtain tight bounds on the search range. Using randomly generated instances in our numerical experiments, we demonstrated that the proposed search algorithm outperforms a previously published heuristic.
An empirical study on discrete optimization models for portfolio selection
Xueting Cui, Xiaoling Sun and Dan Sha
2009, 5(1): 33-46 doi: 10.3934/jimo.2009.5.33 +[Abstract](74) +[PDF](188.1KB)
Abstract:
In this paper, we investigate four discrete optimization models arising from single period portfolio selection: Mean-variance model, mean-absolute-deviation model, minimax model and conditional Value-at-Risk model. These four models are established by considering the minimal transaction unit and the cardinality constraint in real-world investment practice. Extensive computational results are reported to compare the features of the models. We evaluate the performance of the models by analyzing the in-sample and out-of-sample numerical results with real data from Shanghai Stock Exchange.
A Lagrangian dual and surrogate method for multi-dimensional quadratic knapsack problems
Xiaoling Sun, Xiaojin Zheng and Juan Sun
2009, 5(1): 47-60 doi: 10.3934/jimo.2009.5.47 +[Abstract](62) +[PDF](191.8KB)
Abstract:
Quadratic 0-1 knapsack problems have a variety of applications in various areas such as flexible manufacturing systems, location of transportation facilities and telecommunications. In this paper we present a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems. Outer approximation and bundle method are used to compute the Lagrangian bound where the Lagrangian relaxation is solved by the maximum flow algorithm. We also present a surrogate constraint heuristic for finding feasible solutions. Preliminary computational results for small to medium size test problems are reported.
Deterministic modeling of whole-body sheep metabolism
Emma Smith, Volker Rehbock and Norm Adams
2009, 5(1): 61-80 doi: 10.3934/jimo.2009.5.61 +[Abstract](56) +[PDF](226.3KB)
Abstract:
Although not a traditional approach in investigating the effects of external influences on the biological composition of sheep, it is proposed that mathematical modeling and optimisation will prove to be a useful and powerful tool in this area. Research studies investigating the effects of different factors on the biological state of sheep are limited in their ability to monitor results in a whole-body manner. This research aims to provide a working model revolving around protein synthesis of sheep from the age of 12 weeks to approximately two years for simulation and optimisation purposes. Presented in this review is an analysis of previous work in this area, a description of methods undertaken to refine and improve the model, current problems being faced and the anticipated future directions of the study.
Analysis of bullwhip effect in supply chains with heterogeneous decision models
K. F. C. Yiu, L. L. Xie and K. L. Mak
2009, 5(1): 81-94 doi: 10.3934/jimo.2009.5.81 +[Abstract](59) +[PDF](3459.9KB)
Abstract:
In modeling a supply chain, it is often assumed that agents of different echelons adopt similar inventory policies. As a result, bullwhip effect exists across different echelons up the supply chain when the product demand at the retailer level increases and decreases. However, a retailer and a manufacturer are two very different entities in a supply chain, which should employ different decision processes in managing their operations. In view of this, we study the application of heterogeneous decision models for retailers and manufacturers to analyze the bullwhip effect in a supply chain. In particular, we formulate a simple supply chain consisting of many retailers, a manufacturer and a warehouse. The inventory policy of the retailers is simply to use the inventory position to absorb variations in the demand. For the manufacturer, the demand can be met by keeping a higher inventory level or by varying the production rate more frequently. A multi-criteria objective function is formulated and analytic solutions are derived. We illustrate how the bullwhip effect varies for different selections of scaling parameters. By using optimal control theory, we show that the bullwhip effect can be suppressed if a smooth production requirement is enforced.
Online scheduling of two uniform machines to minimize total completion times
P. Liu and Xiwen Lu
2009, 5(1): 95-102 doi: 10.3934/jimo.2009.5.95 +[Abstract](66) +[PDF](123.6KB)
Abstract:
In this paper, we study the online scheduling problem on two uniform machines with speeds 1 and $s \geq 1$, in which jobs are arriving over time. We consider both the preemptive and the non-preemptive machine environments. We first present a 2.618-competitive algorithm for the non-preemptive setting with the objective to minimize the total completion times. In the preemptive setting with the objective to minimize the total weighted completion times, we give an online algorithm which has a competitive ratio of 2.
A tandem queueing system with applications to pricing strategy
Wai-Ki Ching, Tang Li, Sin-Man Choi and Issic K. C. Leung
2009, 5(1): 103-114 doi: 10.3934/jimo.2009.5.103 +[Abstract](95) +[PDF](152.2KB)
Abstract:
In this paper, we analyze a Markovian queueing system with multiple types of customers and two queues in tandem. All customers have to go through two stages of services. In Stage 1, the queueing system has multiple identical servers while in Stage 2, there is one single-server queue for each type of customers. The queueing discipline in the whole system is Blocked Customer Delayed (BCD). We first obtain the steady-state probability distribution of the queueing system and the expected waiting time for customers. We then apply the queueing model to solve an optimal pricing policy problem in assuming that the demand rate is dependent on the price. The objective is to minimize the number of servers in the first stage and also maximize the expected earnings by taking into account the demand and the prices. We also obtained some analytic results for the optimal pricing strategy.
A gradient method for regularizing retrieval of aerosol particle size distribution function
Yanfei Wang and Qinghua Ma
2009, 5(1): 115-126 doi: 10.3934/jimo.2009.5.115 +[Abstract](81) +[PDF](235.0KB)
Abstract:
The determination of the aerosol particle size distribution function using the particle spectrum extinction equation is an ill-posed integral equation of the first kind ([15, 19]). Even for finite moment case, the problem is still discrete ill-posed, since as is known, in remote sensing the observations are often limited /insufficient or contaminated. To overcome the ill-posedness, various standard or non-standard regularization techniques were developed (see [18] and references therein). However, most of the literature focuses on the application of the Phillips-Twomey's regularization or its variants which is unstable in several cases. Recently in [17], the authors considered Tikhonov's smooth regularization method in $W^{1,2}$ space for ill-posed inversion. But the method still relies on the choice of the regularization parameter and the a priori estimation of the noise level. In addition, these methods do not consider the nonnegative constraints of the model problem. As is known, the particle size distribution is always nonnegative and we are often faced with incomplete data. Therefore, creation of data to establish well-posedness and development of suitable method are urgently needed. We first present a regularization model which incorporates smoothness constraint to the solution, and then propose an efficient gradient method for solving the regularizing problem. Numerical tests are performed to show the efficiency and feasibility of the proposed algorithms.
An optimization approach to the estimation of effective drug diffusivity: From a planar disc into a finite external volume
Song Wang and Xia Lou
2009, 5(1): 127-140 doi: 10.3934/jimo.2009.5.127 +[Abstract](65) +[PDF](198.7KB)
Abstract:
In this paper we propose a new mathematical model based on optimal fitting for estimating effective diffusion coefficients of a drug from a delivery device of 2D disc geometry to an external finite volume. In this model, we assume that the diffusion process occurs within the boundary layer of the external fluid, while outside the layer the drug concentration is uniform because of the convection-domination. An analytical solution to the corresponding diffusion equation with appropriate initial and boundary conditions is derived using the technique of separation of variables. A formula for the ratio of the mass released in the time interval $[0,t]$ for any $t>0$ and the total mass released in infinite time is also obtained. Furthermore, we extend this model to one for problems with two different effective diffusion coefficients, in order to handle the phenomenon of 'initial burst'. The latter model contains more than one unknown parameter and thus an optimization process is proposed for determining the effective diffusion coefficient, critical time and width of the effective boundary layer. These models were tested using experimental data of the diffusion of prednisolone 2-hemisuccinate sodium salt from porous poly(2-hydroxyethylmethacrylate) hydrogel based discs. The numerical results show that the usefulness and accuracy of these models.
A smoothing approach for semi-infinite programming with projected Newton-type algorithm
Zhi Guo Feng, Kok Lay Teo and Volker Rehbock
2009, 5(1): 141-151 doi: 10.3934/jimo.2009.5.141 +[Abstract](70) +[PDF](170.0KB)
Abstract:
In this paper we apply the projected Newton-type algorithm to solve semi-infinite programming problems. The infinite constraints are replaced by an equivalent nonsmooth function which is then approximated by a smoothing function. The KKT system is formulated as a nonsmooth equation. We then apply the projected Newton-type algorithm to solve this equation and show that the accumulation point satisfies the KKT system. Some numerical results are presented for illustration.
$H_\infty$ optimal stabilization of a class of uncertain impulsive systems: An LMI approach
Honglei Xu and Kok Lay Teo
2009, 5(1): 153-159 doi: 10.3934/jimo.2009.5.153 +[Abstract](73) +[PDF](126.9KB)
Abstract:
This paper studies $H_\infty$ optimal control problems for a class of impulsive dynamical systems with norm-bounded time-varying uncertainty. By using a linear matrix inequality approach, some sufficient conditions are established to ensure both internally asymptotical stability and $H_\infty$ optimal performance of the impulsive closed-loop system. Moreover, based on the stability criteria, a linear time-invariant stabilizing control law is designed. Finally, a numerical example is presented to illustrate the effectiveness of our results.
Simultaneous system of vector equilibrium problems
Kenji Kimura, Yeong-Cheng Liou, David S. Shyu and Jen-Chih Yao
2009, 5(1): 161-174 doi: 10.3934/jimo.2009.5.161 +[Abstract](83) +[PDF](208.2KB)
Abstract:
In this paper, we study two kinds of simultaneous systems of vector equilibrium problem (SSVEP in short). We investigate the existence of SSVEP and sensitivity of solution mappings of the corresponding parametric/perturbed SSVEP. Specially, some results concerning the lower semicontinuity of the solution mapping of SSVEP are established.

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