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Journal of Industrial & Management Optimization

2015 , Volume 11 , Issue 4

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Production planning in a three-stock reverse-logistics system with deteriorating items under a continuous review policy
Abdelghani Bouras and Lotfi Tadj
2015, 11(4): 1041-1058 doi: 10.3934/jimo.2015.11.1041 +[Abstract](712) +[PDF](530.8KB)
Abstract:
We consider in this paper a reverse supply chain with three stocks. Newly manufactured items are stored in the first stock. The second stock is reserved for remanufactured items, while the third stock contains the items that are returned from the market. One of our main assumptions is that remanufactured items are not as-good-as-new. We also assume that new and remanufactured items are subject to deterioration and to dynamic demands, that customer return rate is also dynamic, and that the firm adopts a continuous-review policy. Using optimal control theory, we obtain the explicit expressions of the optimal manufacturing rate, remanufacturing rate, disposal rate, and inventory levels in all three stocks. Numerical examples and sensitivity analyses illustrate the results obtained.
Determining optimal price, replenishment lot size and number of shipments for an EPQ model with rework and multiple shipments
Ata Allah Taleizadeh, Solaleh Sadat Kalantari and Leopoldo Eduardo Cárdenas-Barrón
2015, 11(4): 1059-1071 doi: 10.3934/jimo.2015.11.1059 +[Abstract](727) +[PDF](333.2KB)
Abstract:
In a regular manufacturing process at the end of each production cycle defective items are identified. Then some defective items are considered scrap and the others, after a reworking process with a defective rate, could convert in a perfect quality items. In this direction, this research work deals with the problem of the joint determination of selling price, replenishment lot size and the number of shipments for an economic production quantity (EPQ) model with rework of defective items when multi-shipment policy is used. After proving concavity of the long-run average benefit function, a practical algorithm is developed to find the optimal price, replenishment lot size and number of shipments in order to maximize the average long-run benefit function. A special case when there is no scrap is identified and explained. Furthermore, in order to show the practical usage of the proposed algorithm a case study from real world is presented and solved.
Comparative analysis of supply chain financing strategies between different financing modes
Nina Yan and Baowen Sun
2015, 11(4): 1073-1087 doi: 10.3934/jimo.2015.11.1073 +[Abstract](647) +[PDF](381.7KB)
Abstract:
In the supply chain finance (SCF) system composed of a capital-constrained retailer, a manufacturer and a commercial bank, we design two different limited financing modes, namely, a financing mode based on order and on the capital-gap. Considering the retailer's capital constraint and bankruptcy risk, we formulate a Stackelberg game in which the manufacturer acts as the leader and analyze the optimal decisions for each participant. Finally, we conduct numerical examples and make comparative analyses between these two different financing modes in terms of optimal ordering and pricing decisions, as well as optimal expected profits. It is concluded that the optimal expected profit of SCF under either financing mode would be higher than that in the case of no capital constraint or capital-constrained without financing. Moreover, the financing mode based on order would encourage the manufacturer to earn more and the financing mode based on capital-gap would be more favorable to the retailer.
An interactive MOLP method for solving output-oriented DEA problems with undesirable factors
Ali Ebrahimnejad, Madjid Tavana and Seyed Mehdi Mansourzadeh
2015, 11(4): 1089-1110 doi: 10.3934/jimo.2015.11.1089 +[Abstract](721) +[PDF](438.3KB)
Abstract:
Data Envelopment Analysis (DEA) and Multiple Objective Linear Programming (MOLP) are widely used for performance assessment in organizations. Although DEA and MOLP are similar in structure, DEA is used to assess and analyze past performance and MOLP is used to predict future performance. Several equivalence models between output-oriented DEA models and MOLP models have been proposed in the literature. However these models are not applicable to performance evaluation problems with undesirable outputs. We propose an interactive method for solving output-oriented DEA models with undesirable outputs. We show that the output-oriented BCC model of Seiford and Zhu [47] can be equivalently stated as the maximization of the minimum of several objectives over the production possibility set, which in turn is a scalarization of a multi-objective linear program. We then employ the well-known Zionts-Wallenius procedure to solve the multi-objective optimization problem. We present an example to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.
Second order sufficient conditions for a class of bilevel programs with lower level second-order cone programming problem
Xiaoni Chi, Zhongping Wan and Zijun Hao
2015, 11(4): 1111-1125 doi: 10.3934/jimo.2015.11.1111 +[Abstract](523) +[PDF](407.0KB)
Abstract:
When there is uncertainty in the lower level optimization problem of a bilevel programming, it can be formulated by a robust optimization method as a bilevel program with lower level second-order cone programming problem (SOCBLP). In this paper, we show that the Lagrange multiplier set mapping of the lower level problem of a class of the SOCBLPs is upper semicontinuous under suitable assumptions. Based on this fact, we detect the similarities and relationships between the SOCBLP and its KKT reformulation. Then we derive the specific expression of the critical cone at a feasible point, and show that the second order sufficient conditions are sufficient for the second order growth at an M-stationary point of the SOCBLP under suitable conditions.
Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit
Songtao Sun, Qiuhua Zhang, Ryan Loxton and Bin Li
2015, 11(4): 1127-1147 doi: 10.3934/jimo.2015.11.1127 +[Abstract](555) +[PDF](1181.4KB)
Abstract:
This paper considers a spacecraft pursuit-evasion problem taking place in low earth orbit. The problem is formulated as a zero-sum differential game in which there are two players, a pursuing spacecraft that attempts to minimize a payoff, and an evading spacecraft that attempts to maximize the same payoff. We introduce two associated optimal control problems and show that a saddle point for the differential game exists if and only if the two optimal control problems have the same optimal value. Then, on the basis of this result, we propose two computational methods for determining a saddle point solution: a semi-direct control parameterization method (SDCP method), which is based on a piecewise-constant control approximation scheme, and a hybrid method, which combines the new SDCP method with the multiple shooting method. Simulation results show that the proposed SDCP and hybrid methods are superior to the semi-direct collocation nonlinear programming method (SDCNLP method), which is widely used to solve pursuit-evasion problems in the aerospace field.
Modelling and optimal control of blood glucose levels in the human body
Zahra Al Helal, Volker Rehbock and Ryan Loxton
2015, 11(4): 1149-1164 doi: 10.3934/jimo.2015.11.1149 +[Abstract](486) +[PDF](390.6KB)
Abstract:
Regulating the blood glucose level is a challenging control problem for the human body. Abnormal blood glucose levels can cause serious health problems over time, including diabetes. Although several mathematical models have been proposed to describe the dynamics of glucose-insulin interaction, none of them have been universally adopted by the research community. In this paper, we consider a dynamic model of the blood glucose regulatory system originally proposed by Liu and Tang in 2008. This model consists of eight state variables naturally divided into three subsystems: the glucagon and insulin transition subsystem, the receptor binding subsystem and the glucose subsystem. The model contains 36 model parameters, many of which are unknown and difficult to determine accurately. We formulate an optimal parameter selection problem in which optimal values for the model parameters must be selected so that the resulting model best fits given experimental data. We demonstrate that this optimal parameter selection problem can be solved readily using the optimal control software MISER 3.3. Using this approach, significant improvements can be made in matching the model to the experimental data. We also investigate the sensitivity of the resulting optimized model with respect to the insulin release rate. Finally, we use MISER 3.3 to determine optimal open loop controls for the optimized model.
Bounds on price of anarchy on linear cost functions
Fan Sha, Deren Han and Weijun Zhong
2015, 11(4): 1165-1173 doi: 10.3934/jimo.2015.11.1165 +[Abstract](479) +[PDF](322.7KB)
Abstract:
The price of anarchy (POA) is a quite powerful tool to characterize the efficiency loss of competition on networks. In this paper, we derive a bound for POA for the case that the cost function is linear but asymmetric. The result is a generalization of that of Han et. al. in the sense that the involved matrix is only assumed to be positive semidefinite, but not positive definite. Consequently, the range of application of the result is widened. We give two simple examples to illustrate our result.
The inventory model under supplier's partial trade credit policy in a supply chain system
Kun-Jen Chung and Pin-Shou Ting
2015, 11(4): 1175-1183 doi: 10.3934/jimo.2015.11.1175 +[Abstract](804) +[PDF](302.0KB)
Abstract:
A lot of researchers explore the inventory EOQ model under the assumption that the supplier would offer the retailer full trade credit but not partial trade credit. In practice, the supplier's partial trade credit policy is frequently adopted in business transactions. This paper incorporates a real payment mode in which the retailers could still gradually settle the partial payment in the inventory EOQ model under the supplier's partial trade credit. Some theorems for the optimal cycle time are also proposed.
A closed-form solution for outperformance options with stochastic correlation and stochastic volatility
Jacinto Marabel Romo
2015, 11(4): 1185-1209 doi: 10.3934/jimo.2015.11.1185 +[Abstract](461) +[PDF](551.0KB)
Abstract:
Outperformance options allow investors to benefit from a view on the relative performance of two underlying assets without taking any directional exposure to the evolution of the market. These structures exhibit high sensitivity to the correlation between the underlying assets and are usually priced assuming constant instantaneous correlations.
    This article considers a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlations between the assets returns, as well as between their volatilities. Under the assumptions of the model this article provides semi-closed form solutions for the price of outperformance options. The article shows that the price of these options depends crucially on the term structure of the correlation corresponding to the assets returns. Furthermore, the comparison of the prices obtained under this model and under other models with constant correlations commonly used by financial institutions reveals the existence of a stochastic correlation premium.
On EOQ cost models with arbitrary purchase and transportation costs
Ş. İlker Birbil, Kerem Bülbül, J. B. G. Frenk and H. M. Mulder
2015, 11(4): 1211-1245 doi: 10.3934/jimo.2015.11.1211 +[Abstract](561) +[PDF](495.8KB)
Abstract:
We analyze an economic order quantity cost model with unit out-of-pocket holding costs, unit opportunity costs of holding, fixed ordering costs, and general purchase-transportation costs. We identify the set of purchase-transportation cost functions for which this model is easy to solve and related to solving a one-dimensional convex minimization problem. For the remaining purchase-transportation cost functions, when this problem becomes a global optimization problem, we propose a Lipschitz optimization procedure. In particular, we give an easy procedure which determines an upper bound on the optimal cycle length. Then, using this bound, we apply a well-known technique from global optimization. Also for the class of transportation functions related to full truckload (FTL) and less-than-truckload (LTL) shipments and the well-known carload discount schedule, we specialize these results and give fast and easy algorithms to calculate the optimal lot size and the corresponding optimal order-up-to-level.
Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs
Chuancun Yin and Kam Chuen Yuen
2015, 11(4): 1247-1262 doi: 10.3934/jimo.2015.11.1247 +[Abstract](478) +[PDF](403.3KB)
Abstract:
In this paper, we study the optimal control problem for a company whose surplus process evolves as an upward jump diffusion with random return on investment. Three types of practical optimization problems faced by a company that can control its liquid reserves by paying dividends and injecting capital. In the first problem, we consider the classical dividend problem without capital injections. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of capital injections over strategies with positive surplus at all times. The third problem has the same objective as the second one, but without the constraints on capital injections. Under the assumption of proportional transaction costs, we identify the value function and the optimal strategies for any distribution of gains.
Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors
Haibin Chen and Liqun Qi
2015, 11(4): 1263-1274 doi: 10.3934/jimo.2015.11.1263 +[Abstract](448) +[PDF](341.3KB)
Abstract:
Motivated by symmetric Cauchy matrices, we define symmetric Cauchy tensors and their generating vectors in this paper. Hilbert tensors are symmetric Cauchy tensors. An even order symmetric Cauchy tensor is positive semi-definite if and only if its generating vector is positive. An even order symmetric Cauchy tensor is positive definite if and only if its generating vector has positive and mutually distinct entries. This extends Fiedler's result for symmetric Cauchy matrices to symmetric Cauchy tensors. Then, it is proven that the positive semi-definiteness character of an even order symmetric Cauchy tensor can be equivalently checked by the monotone increasing property of a homogeneous polynomial related to the Cauchy tensor. The homogeneous polynomial is strictly monotone increasing in the nonnegative orthant of the Euclidean space when the even order symmetric Cauchy tensor is positive definite. At last, bounds of the largest H-eigenvalue of a positive semi-definite symmetric Cauchy tensor are given and several spectral properties on Z-eigenvalues of odd order symmetric Cauchy tensors are shown. Further questions on Cauchy tensors are raised.
Portfolio optimization using a new probabilistic risk measure
Yufei Sun, Grace Aw, Kok Lay Teo and Guanglu Zhou
2015, 11(4): 1275-1283 doi: 10.3934/jimo.2015.11.1275 +[Abstract](646) +[PDF](314.7KB)
Abstract:
In this paper, we introduce a new portfolio selection method. Our method is innovative and flexible. An explicit solution is obtained, and the selection method allows for investors with different degree of risk aversion. The portfolio selection problem is formulated as a bi-criteria optimization problem which maximizes the expected portfolio return and minimizes the maximum individual risk of the assets in the portfolio. The efficient frontier using our method is compared with various efficient frontiers in the literature and found to be superior to others in the mean-variance space.
A multidimensional information model for managing construction information
Rui Wang, Denghua Zhong, Yuankun Zhang, Jia Yu and Mingchao Li
2015, 11(4): 1285-1300 doi: 10.3934/jimo.2015.11.1285 +[Abstract](615) +[PDF](2254.4KB)
Abstract:
With the increasing scale of construction projects, coupled with their complexity, information management in the construction process becomes more complex and trivial. Moreover, the communication among project participants is hindered by the large amount and scattered structure of the information involved in the construction process. Most present studies on the information management of construction focus on the special needs of construction sectors rather than a total information integration of general aspects. This paper presents a multidimensional information model that combines Workflow, Work Breakdown Structures (WBS) and Time factor to manage information based on process control. Unlike previous researches, the present work puts emphasis on process control to enhance the communication process. The proposed information model uses the WBS and Time factor to manage information in the spatial and time dimension and control the process information of each work package during project execution through the workflow technology. In order to test the proposed information model, a web-based project management system (WPMS) was developed using the three layer architecture. The system structure realizes the invisible logic of the information model through the business logic layer and the data access layer. The system has been applied to a construction project of an underground cavern group in a hydropower project in the southwest of China. The application has shown that it achieves managing information based on process control and provides structured information.
The interaction between BIM's promotion and interest game under information asymmetry
Jide Sun and Lili Wang
2015, 11(4): 1301-1319 doi: 10.3934/jimo.2015.11.1301 +[Abstract](545) +[PDF](905.2KB)
Abstract:
The application of Building Information Modeling can break the barrier between project owner and contractor. However, its application may cause an interest conflict between them. The conflict is focusing on the scramble for potential benefits brought by information asymmetry, and it may hinder the application of BIM in reverse. Focusing on information asymmetry, this research analyzed the interaction between BIM's promotion and project owner, contractor's interest game by combining Asymmetric Information theory and game theory. Based on the description of the interest conflict process, this research built a modified Principal-Agent model. By numerical analysis, it is proved that through BIM's effect of reducing information asymmetry in project, BIM's negative impact on contractor’s profit may let contractor refuse BIM's contract which will finally lead to the failure of BIM's promotion. Then, this research simulated the interest conflict by using the modified PA model. Through comparative analysis on the results, this research suggested: 1) project owners should choose BIM at proper stage but not the most advanced one, 2) contractor's effort cannot be ignored when promoting BIM, 3) variety of policies should be made in order to deal with specific problems when promoting BIM at different stages.
Construction schedule optimization for high arch dams based on real-time interactive simulation
Tao Guan, Denghua Zhong, Bingyu Ren and Pu Cheng
2015, 11(4): 1321-1342 doi: 10.3934/jimo.2015.11.1321 +[Abstract](494) +[PDF](1555.1KB)
Abstract:
The construction process of high arch dams is extremely complicated. Therefore, optimization of the construction schedule is essential for construction management to save a large amount of time and investment costs. Construction simulation is an important tool for the construction schedule optimization of high arch dams. Most current studies involving construction schedule simulations do not concurrently consider real-time construction situations and site managers' requirements. In this paper, the real-time interactive simulation is proposed that could solve this problem. The real-time construction process is the initial condition of the simulation, and the actual construction parameters are the basis of the simulation parameters. Additionally, site managers can change the simulation strategy dynamically or enter requirements based on real-time construction situations. For a simulation result, different schemes are optimized with the entropy weight method. With this method, the construction simulation can track the rapid changes in construction situations and provide a reasonable construction schedule, which increases the flexibility of the construction simulation. The optimized construction scheme could be an effective guide for site construction. With a 4D (three dimensional model and time) CAD model, the simulation process can be well expressed. A case study shows that the construction schedule can be established in real time, and it's a useful tool for decision-making.
Optimal tracking control for networked control systems with random time delays and packet dropouts
Ying Wu, Zhaohui Yuan and Yanpeng Wu
2015, 11(4): 1343-1354 doi: 10.3934/jimo.2015.11.1343 +[Abstract](555) +[PDF](400.8KB)
Abstract:
This paper studies the problem of optimal output tracking control for networked control system with uncertain time delays and packet dropouts. Active time-varying sampling period strategy is proposed to ensure the random variable time delays always shorter than one sampling period. Hybrid driven modes are adopted by sensor to solve the issues of long time delay and packet dropout. By using augmentation approach, the tracking problem of this formulated within-one-step delayed discrete-time system is transformed into a general problem of non-delayed state linear quadratic regulator. A “gridding” approach is introduced to guarantee the realization of optimal output feedback control law by the solution of a series of Riccati matrix equations from an offline database that is constructed by different combination of time delays and packet dropouts. Simulation results demonstrate the effectiveness of the optimal tracking control law.
Optimal acquisition, inventory and production decisions for a closed-loop manufacturing system with legislation constraint
Xiaochen Sun, Fei Hu, Yancong Zhou and Cheng-Chew Lim
2015, 11(4): 1355-1373 doi: 10.3934/jimo.2015.11.1355 +[Abstract](474) +[PDF](467.3KB)
Abstract:
In order to improve the utilization efficiency of resources, more and more countries have required manufacturing firms to remanufacture or reuse used products through legislation. For many firms, the profit from reusing used products may be less than the profit from producing new products, so how to make decisions under such legislation constraint is a major concern by these firms. In this paper, we study the optimal acquisition, inventory and production decision problem for such firms under a two-period setting, where firms have two different production ways: (i) production with new raw materials, and (ii) production with used products. The return quantity of used products at the second period depends on the demand of the first period and the acquisition effort. The problem is formulated as a stochastic dynamic programming model. We give the optimal production rule and the optimal inventory decision at the second period, and prove the existence of an optimal policy with a simple structure at the first period. Moreover, based on our theoretical analysis, we calculate the optimal decisions under different parameter settings, and discuss how the firm does react when facing with specific market and production conditions.
Optimal double-resource assignment for a distributed multistate network
Shin-Guang Chen
2015, 11(4): 1375-1391 doi: 10.3934/jimo.2015.11.1375 +[Abstract](519) +[PDF](393.3KB)
Abstract:
A distributed multistate network is a multistate network with the flows entering from multiple source nodes and exiting by multiple sink nodes. A multistate network is a network with its nodes and edges having multiple states (capacities) or failures. Such networks are different from the ones solved by the traditional methods in two aspects: the number of source/sink nodes is more than one, and the source nodes are also sink nodes. The optimal double-resource assignment problem for a distributed multistate network (ODRADMN) is to solve the optimal capacity assignment for nodes and edges in the network such that the total capacity requirement of the network is minimized while keeping the network still alive. Traditionally, multi-objective optimization methods are employed to solve such kind of problems. This paper proposes an elegant single-objective optimization method to solve the double-resource optimization problem in terms of network reliability. Several numerical examples are demonstrated to explain the proposed method.
Adjustable admission control with threshold in centralized CR networks: Analysis and optimization
Yuan Zhao, Shunfu Jin and Wuyi Yue
2015, 11(4): 1393-1408 doi: 10.3934/jimo.2015.11.1393 +[Abstract](431) +[PDF](361.6KB)
Abstract:
In order to enhance the Quality of Service (QoS) for the secondary users (SUs) in Cognitive Radio (CR) networks reasonably, in this paper, we propose an adjustable admission control scheme considering an access threshold under a centralized architecture. We assume that a buffer is set for all the SUs. On the arrival instant of an SU packet, if the number of SU packets already in the buffer is equal to or greater than the access threshold that is set in advance, this SU packet will be admitted to join the system with an adjustable access probability, which is inversely proportional to the total number of packets in the system. Based on the adjustable admission control scheme proposed in this paper, considering the priority of the primary users (PUs) in CR networks, we build a preemptive priority queueing model. Aiming to comply with the digital nature of modern networks, we establish a two-dimensional discrete-time Markov chain (DTMC) and construct the transition probability matrix of the Markov chain. Accordingly, we provide the formulas for several performance measures, such as the blocking rate, the throughput and the average latency of the SU packets. With numerical results, we show the influence of the access threshold on different performance measures for the SU packets. Finally, taking into account the trade-off between different performance measures, we build a net benefit function to find the optimal access threshold with an optimization algorithm.
Existence and stability analysis for nonlinear optimal control problems with $1$-mean equicontinuous controls
Hongyong Deng and Wei Wei
2015, 11(4): 1409-1422 doi: 10.3934/jimo.2015.11.1409 +[Abstract](623) +[PDF](359.2KB)
Abstract:
In this paper, the existence and stability of solutions of nonlinear optimal control problems with $1$-mean equicontinuous controls are discussed. In particular, a new existence theorem is obtained without convexity assumption. We investigate the stability of the optimal control problem with respect to the right-hand side functions, which is important in computational methods for optimal control problems when the function is approximated by a new function. Due to lack of uniqueness of solutions for an optimal control problem, the stability results for a class of optimal control problems with the measurable admissible control set is given based on the theory of set-valued mappings and the definition of essential solutions for optimal control problems. We show that the optimal control problems, whose solutions are all essential, form a dense residual set, and so every optimal control problem can be closely approximated arbitrarily by an essential optimal control problem.
A trade-off between time and cost in scheduling repetitive construction projects
Lihui Zhang, Xin Zou and Jianxun Qi
2015, 11(4): 1423-1434 doi: 10.3934/jimo.2015.11.1423 +[Abstract](947) +[PDF](368.6KB)
Abstract:
The discrete time/cost trade-off problem (DTCTP) is commonly encountered in repetitive project scheduling. The current models for this problem assume that logical sequences of activities cannot be changed in different units. However, logical sequences are often changed to shorten the project time and minimize project total cost in many practical situations. This characteristic of repetitive activities is referred to as the soft logic. This paper presents a mixed integer nonlinear programming model that combines the general DTCTP and the concept of soft logic. The execution modes of an activity in different units are also considered. The DTCTP is known to be strongly NP-hard, and the introduction of soft logic makes it even more complex. A genetic algorithm (GA) is proposed to resolve the problem. The effectiveness of the proposed GA is verified using the example of a bridge construction project presented in the previous literature. The model proposed in this paper provides more flexibility to reduce the total cost and time of a repetitive project for the planners.

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