# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial and Management Optimization

April 2012 , Volume 8 , Issue 2

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2012, 8(2): 271-283 doi: 10.3934/jimo.2012.8.271 +[Abstract](2590) +[PDF](349.1KB)
Abstract:
In this paper, we study two problems of scheduling a set of linear deteriorating non-resumable jobs on a single machine with a mandatory maintenance. The maintenance has to be started prior to a given deadline. Not only the jobs but also the maintenance are required to be scheduled. Two goals are investigated. One is to minimize the makespan and the other is to minimize the total completion time. For both objectives, we show that two problems are weakly NP-hard and propose fully polynomial time approximation schemes respectively.
2012, 8(2): 285-297 doi: 10.3934/jimo.2012.8.285 +[Abstract](3394) +[PDF](692.5KB)
Abstract:
To increase productivity, companies are in search of techniques that enable them to make faster and more effective decisions. Data mining and fuzzy clustering algorithms can serve for this purpose. This paper models the decision making process of a ceramics production company using a fuzzy clustering algorithm and data mining. Factors that affect the quality of slurry are measured over time. Using this data, a fuzzy clustering algorithm assigns the degrees of memberships of the slurry for the different quality clusters. An expert can decide on acceptance or rejection of slurry based on calculated degrees of memberships. In addition, by using data mining techniques we generated some rules that provide the optimum conditions for acceptance of the slurry.
2012, 8(2): 299-323 doi: 10.3934/jimo.2012.8.299 +[Abstract](2887) +[PDF](280.8KB)
Abstract:
We study the optimal demand allocation policies to induce high service capacity and achieve minimum expected sojourn times in equilibrium in a queueing system with multiple strategic servers. We propose the mixed threshold allocation policy as an optimal state-dependent policy that induces optimal service capacity from strategic servers. Compensation to the server can be paid at customer allocation or upon job completion. Our study focuses on the use of a multiple-server mixed threshold allocation policy to replicate the demand of a given state-independent policy to achieve a symmetric equilibrium with lower expected sojourn time. The results indicate that, under both payment schemes, for any given multiple-server state-independent policy, there exists a multiple-server threshold policy that produces identical demand allocation and Nash equilibrium (if any). Moreover, the policy can be designed to minimize the expected sojourn time at a symmetric equilibrium. Furthermore, under the payment-at-allocation scheme, our results, combining with existing results on the optimality of the multiple-server linear allocation policy, show that the mixed threshold policy can achieve the maximum feasible service capacity and thus the minimum feasible equilibrium expected sojourn time. Hence, our results agree with previous two-server results and affirm that a trade-off between incentives and efficiency need not exist in the case of multiple servers.
2012, 8(2): 325-341 doi: 10.3934/jimo.2012.8.325 +[Abstract](3355) +[PDF](494.7KB)
Abstract:
This paper proposes a new defect detection scheme for woven fabrics. The proposed scheme is divided into two parts, namely the training part and the defect detection part. In the training part, a non-defective fabric image is used as a template image, and a finite set of multi-level Gabor wavelets are tuned to match the texture information of the image. In the defect detection part, filtered images from different levels are fused together and the constructed detection scheme is used to detect defects in fabric sample images with the same texture background as that of the template image. A filter selection method is also developed to select optimal filters to facilitate defect detection. The novelty of the method comes from the observation that a Gabor filter with finer resolutions than the fabric defects yarn can contribute very little for defect segmentation but need additional computational time. The proposed scheme is tested by using 78 homogeneous textile fabric images. The results exhibit accurate defect detections with lower false alarms than using the standard Gabor wavelets. Analysis of the computational complexity of the proposed detection scheme is derived, which shows that the scheme can be implemented in real time easily.
2012, 8(2): 343-362 doi: 10.3934/jimo.2012.8.343 +[Abstract](3210) +[PDF](1112.2KB)
Abstract:
In this paper, a portfolio selection model with a combined Worst-Case Conditional Value-at-Risk (WCVaR) and Multi-Factor Model is proposed. It is shown that the probability distributions in the definition of WCVaR can be determined by specifying the mean vectors under the assumption of multivariate normal distribution with a fixed variance-covariance matrix. The WCVaR minimization problem is then reformulated as a linear programming problem. In our numerical experiments, to compare the proposed model with the traditional mean variance model, we solve the two models using the real market data and present the efficient frontiers to illustrate the difference. The comparison reveals that the WCVaR minimization model is more robust than the traditional one in a market recession period and it can be used in a long-term investment.
2012, 8(2): 363-378 doi: 10.3934/jimo.2012.8.363 +[Abstract](2908) +[PDF](367.4KB)
Abstract:
Due to the lower consumption level to the flights in some regions, the flights' vacancy rate is usually very high and the service level is low. To airlines, the common procedure to handle such problems is to employ different price systems. But this in return results in unsatisfying effects. In this paper we discussed the above issue from another standpoint. Firstly, we introduced a parameter, called region factor, and then constructed a stochastic dynamic model of a single-leg flight related to it. Secondly, we derived some monotone properties for the expected revenue functions. These properties ensured that we could choose appropriate region factor to recover the high vacancy rate caused by the lower consumption levels, but also adopt the similar optimal threshold control strategy as the traditional revenue management did. Furthermore, in addition to improving the service levels, the proper region factor can increase the total revenue sometimes. Lastly, Numerical results were used to illustrate properties of the model.
2012, 8(2): 379-389 doi: 10.3934/jimo.2012.8.379 +[Abstract](4035) +[PDF](170.5KB)
Abstract:
This paper introduces a novel approach to discuss an optimal inventory level of a retail product using a real option framework. We consider stochastic models for the evolution of the demand and unit price of the product over time. The profit structure of the retailer is represented by the payoff of the real option. An actuarial approach is then used to price the option. The retailer determines an optimal inventory level of the product with a view to maximizing the net expected profit. Numerical examples will be given to illustrate the practical implementation of the proposed approach and to investigate the impacts of changes in parameters on the optimal inventory level of the product.
2012, 8(2): 391-410 doi: 10.3934/jimo.2012.8.391 +[Abstract](2789) +[PDF](426.3KB)
Abstract:
In this paper, we model the value of a firm and a default threshold using two dependent jump-diffusion processes. We give the explicit solutions for the Laplace transform of the first passage time and the expected discounted ratio of the firm value to the default threshold at default, and show the impact of dependent jumps of the firm value and the default threshold on the default probabilities and the spreads of corporate defaultable bonds.
2012, 8(2): 411-427 doi: 10.3934/jimo.2012.8.411 +[Abstract](3441) +[PDF](362.8KB)
Abstract:
In this paper, a generalized $\epsilon-$subdifferential, which was defined by a norm, is first introduced for a vector valued mapping. Some existence theorems and the properties of the generalized $\epsilon-$subdifferential are discussed. A relationship between the generalized $\epsilon-$subdifferential and a directional derivative is investigated for a vector valued mapping. Then, the calculus rules of the generalized $\epsilon-$subdifferential for the sum and the difference of two vector valued mappings were given. The positive homogeneity of the generalized $\epsilon-$subdifferential is also provided. Finally, as applications, necessary and sufficient optimality conditions are established for vector optimization problems.
2012, 8(2): 429-455 doi: 10.3934/jimo.2012.8.429 +[Abstract](2679) +[PDF](1155.9KB)
Abstract:
Convexification transformation is vital for solving Generalized Geometric Problems (GGP) in global optimization. Björk et al. [3] posited that transforming non-convex signomial terms in a GGP into 1-convex functions is currently the most efficient convexification technique. However, to the best of our knowledge, an efficient convexification method based on the concept of 1-convex functions has not been proposed. To address this research gap, we present a Beta method to maximally improve the efficiency of convexification based on the concept of 1-convex functions, and thereby enhance the accuracy of linearization without increasing the number of break points and binary variables in the piecewise linear function. The Beta method yields an excellent solution quality and computational efficiency. We compare its performance, with that of three existing approaches using four numerical examples. The computational results demonstrate that, in terms of solution quality and computation time, the proposed method outperforms the compared approaches.
2012, 8(2): 457-468 doi: 10.3934/jimo.2012.8.457 +[Abstract](3384) +[PDF](333.1KB)
Abstract:
This paper presents a new heuristic algorithm for solving a class of dynamic laser antimissile problems. The main virtue of this algorithm is that it can find a satisfactory local optimal solution within allowable short time duration which is the rigid requirement in this application. Two examples are considered and solved to illustrate the effectiveness of algorithm proposed.
2012, 8(2): 469-484 doi: 10.3934/jimo.2012.8.469 +[Abstract](3870) +[PDF](527.3KB)
Abstract:
A mixed integer programming mathematical formulation of vehicle routing problem with simultaneous pickups and deliveries, and time window constraints (VRP-SPDTW) is presented in this paper. The proposed model aims at minimizing the vehicle number and the overall travel cost. A novel two-stage hybrid metaheuristic method for VRP-SDPTW is also proposed. The first stage adopts improved ant colony optimization (IACO) to determine the minimum number of used vehicles. The second stage employs improved Tabu search to optimize the total travel cost, in which the initial solutions are obtained by IACO in the first stage. Experimental results demonstrate the effectiveness of the proposed metaheuristic method.
2012, 8(2): 485-491 doi: 10.3934/jimo.2012.8.485 +[Abstract](3380) +[PDF](292.7KB)
Abstract:
This note is to provide a refinement of the convergence analysis of the new exact penalty function method proposed recently.
2012, 8(2): 493-505 doi: 10.3934/jimo.2012.8.493 +[Abstract](2609) +[PDF](384.7KB)
Abstract:
In this paper, a polymorphic uncertain nonlinear programming (PUNP) model is constructed to formulate the problem of maximizing the V-belt's fatigue life according to the practical engineering design conditions. The model is converted into an equivalent interval programming only involved with interval parameters for any given degree of membership and confidence level. Then, a deterministic equivalent formulation (DEF) for the original model is obtained based on the concept of possibility degree for the order of two interval numbers. An algorithm, called sampling based algorithm, is developed to find a robust optimal design scheme for maximizing the fatigue life of the V-belt. Case study is employed to demonstrate the validity and the practicability of the constructed model and the algorithm.
2012, 8(2): 507-520 doi: 10.3934/jimo.2012.8.507 +[Abstract](3722) +[PDF](398.9KB)
Abstract:
For the urban public transport management problem, based on analysis of the competition and cooperation relationship among operators on a common network, we establish a generalized Nash equilibrium game first; and then by analyzing the dynamic interaction between manager and operators, we propose a non-cooperative Stackelberg game model in which the manager is the leader and the operators are the followers. To solve the model, we transform it into a variational inequality problem, and the gap function method and the augmented Lagrange algorithm are applied. The given numerical experiments show the efficiency of the proposed model and algorithms.

2020 Impact Factor: 1.801
5 Year Impact Factor: 1.688
2020 CiteScore: 1.8