ISSN:

1547-5816

eISSN:

1553-166X

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## Journal of Industrial & Management Optimization

July 2016 , Volume 12 , Issue 3

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2016, 12(3): 811-817
doi: 10.3934/jimo.2016.12.811

*+*[Abstract](1107)*+*[PDF](294.8KB)**Abstract:**

In this paper, we re-visit the problem of scheduling a set of proportional deteriorating non-resumable jobs on a single machine subject to maintenance. The maintenance has to be started prior to a given deadline. The jobs as well as the maintenance are to be scheduled so that to minimize the total completion time. For this problem we propose a new dynamic programming algorithm and a faster fully polynomial time approximation scheme improving a recent result by Luo and Chen [JIMO (2012), 8:2, 271-283].

2016, 12(3): 819-831
doi: 10.3934/jimo.2016.12.819

*+*[Abstract](1120)*+*[PDF](508.0KB)**Abstract:**

This paper investigates the optimal design of variable fractional delay (VFD) filter with discrete coefficients as a means of achieving low complexity and efficient hardware implementation. The filter coefficients are expressed as the sum of signed power-of-two (SPT) terms with a restriction on the total number of power-of-two terms. An optimization problem with least squares criterion is formulated as a mixed-integer programming problem. An optimal scaling factor quantization scheme is applied to the problem resulting in an optimal scaling factor quantized solution. This solution is then improved further by applying a discrete filled function, that has been extended for a mixed integer optimization problem. To apply the discrete filled function method, it requires multiple calculations of the objective function around the neighborhood of a searched point. Thus, an updating scheme is developed to efficiently calculate the objective function in a neighborhood of a point. Design examples demonstrate the effectiveness of the proposed optimization approach.

2016, 12(3): 833-850
doi: 10.3934/jimo.2016.12.833

*+*[Abstract](1136)*+*[PDF](626.0KB)**Abstract:**

Auctions, e.g. market clearing price (MCP) auctions, have been widely adopted in electricity markets, and progressive second price (PSP) auctions are stated possessing promising properties of incentive compatibility and efficiency. In this work, we study the coordination of large-scale elastic loads in deregulated electricity markets under MCP and PSP auctions. To explore the performances of these auctions in the underlying problems, we focus on the key issues of the payment comparison, incentive compatibility and efficiency of Nash equilibrium (NE), and develop the following results: (i) The individual payment under MCP is always higher than that under PSP, and their difference vanishes asymptotically as the system scale increases; (ii) The incentive compatibility holds under PSP, and holds under MCP only with respect to others' efficient bid profile; (iii) The efficient bid profile under PSP is an NE, while that under MCP is an $\varepsilon$-NE which degenerates to an NE asymptotically as the system scale increases. With these analyses, we claim that it is pretty promising to apply both MCP and PSP auctions to the large-scale load coordination problems in deregulated electricity markets.

2016, 12(3): 851-878
doi: 10.3934/jimo.2016.12.851

*+*[Abstract](1136)*+*[PDF](604.3KB)**Abstract:**

We consider a single server renewal input queueing system under multiple vacation policy. When the system becomes empty, the server commences a vacation of random length, and either begins an ordinary vacation with probability $q\, (0\le q\le 1)$ or takes a working vacation with probability $1-q$. During a working vacation period, customers can be served at a rate lower than the service rate during a normal busy period. If there are customers in the system at a service completion instant, the working vacation can be interrupted and the server will come back to a normal busy period with probability $p\, (0\le p\le 1)$ or continue the working vacation with probability $1-p$. The server leaves for repeated vacations as soon as the system becomes empty. Upon arrival, customers decide for themselves whether to join or to balk, based on the observation of the system-length and/or state of the server. The equilibrium threshold balking strategies of customers under four cases: fully observable, almost observable, almost unobservable and fully unobservable have been studied using embedded Markov chain approach and linear reward-cost structure. The probability distribution of the system-length at pre-arrival epoch is derived using the roots method and then the system-length at an arbitrary epoch is derived with the help of the Markov renewal theory and semi-Markov processes. Various performance measures such as mean system-length, sojourn times, net benefit are derived. Finally, we present several numerical results to demonstrate the effect of the system parameters on the performance measures.

2016, 12(3): 879-890
doi: 10.3934/jimo.2016.12.879

*+*[Abstract](940)*+*[PDF](374.9KB)**Abstract:**

In this paper, we exploit a new parallel splitting method for the typical structured variational inequality problems which can be interpreted as a game with a leader and two followers. In the framework of this method, two followers decide their strategies simultaneously based on the instruction of the leader. Then, the leader improves his instruction by revising his own variable value according to the feedback information from the followers. The convergence of the method is established under some suitable conditions. Finally, we apply the proposed method to solve some application problems. Computational studies show that the method is reliable and efficient.

2016, 12(3): 891-905
doi: 10.3934/jimo.2016.12.891

*+*[Abstract](884)*+*[PDF](596.8KB)**Abstract:**

Consumers may overestimate the precisions of their valuation predictions. In this paper, we propose a decision model of this overconfidence in valuation and analyze a retailer's advance selling strategy in a two-period setting. The presence of overconfident consumers yields new insights in the retailer's selling strategy. We find that advance selling strategy is not always beneficial to the retailer. The retailer should practice advance selling when the difference of the regular consumers' expected valuation and expected surplus when not buying in advance is no less than a certain threshold. This threshold is weakly decreasing in overconfidence level given the same risk aversion degree, strictly decreasing in consumers' risk aversion degree if overconfidence level is high, and strictly increasing otherwise. When consumers become either more overconfident or risk averse with a high overconfidence level, the retailer becomes more likely to sell in both periods. We also show that, the retailer will set a higher price in the advance selling period in the market with overconfident consumers than that without overconfident consumers when selling in both periods.

2016, 12(3): 907-930
doi: 10.3934/jimo.2016.12.907

*+*[Abstract](1508)*+*[PDF](678.3KB)**Abstract:**

This paper presents a new mathematical model for integrating the virtual dynamic cellular manufacturing system into supply chain management with an extensive coverage of important manufacturing features. The considered model regards multi-plants and facility locations, multi-market allocation, multi-period planning horizons with demand and part-mix variation, machine and labor time-capacity, labor assignment, training and purchasing or selling of new machines for an increased level of plant capacity. The main constraints are market demand satisfaction in each period, machine and labor availability, production volume for each plant and the amounts allocated to each market. To validate and verify the proposed model is explained in terms of an industrial case from a typical equipment manufacturer. Some of the hard constraints of the proposed model are relaxed in order to obtain a lower bound on the objective function value. In fact, the number of machines and workers allocated to each cell are restricted to yield feasible solutions and tight upper bounds on the objective values for medium size instances in a shorter time. The relaxed model yields tight lower bounds for medium instances in a reasonable computational time. Furthermore, a Benders decomposition is developed for solving the upper bounding model.

2016, 12(3): 931-947
doi: 10.3934/jimo.2016.12.931

*+*[Abstract](1092)*+*[PDF](406.8KB)**Abstract:**

This paper studies the effect of risk-aversion in the competitive newsvendor game. Multiple newsvendors with risk-averse preferences face a random demand and the demand is allocated proportionally to their inventory levels. Each newsvendor aims to maximize his expected utility instead of his expected profit. Assuming a general form of risk-averse utility function, we prove that there exists a pure Nash equilibrium in this game, and it is also unique under certain conditions. We find that the order quantity of each newsvendor is decreasing in the degree of risk-aversion and increasing in the initial wealth. Newsvendors with moderate preferences of risk-aversion make more profits compared with the risk-neutral situation. We also discuss the joint effect of risk-aversion and competition. If the effect of risk-aversion is strong enough to dominate the effect of competition, the total inventory level under competition will be lower than that under centralized decision-making.

An interior-point $l_{\frac{1}{2}}$-penalty method for inequality constrained nonlinear optimization

2016, 12(3): 949-973
doi: 10.3934/jimo.2016.12.949

*+*[Abstract](1210)*+*[PDF](642.4KB)**Abstract:**

In this paper, we study inequality constrained nonlinear programming problems by virtue of an $\ell{\frac12}$-penalty function and a quadratic relaxation. Combining with an interior-point method, we propose an interior-point $\ell_{\frac12}$-penalty method. We introduce different kinds of constraint qualifications to establish the first-order necessary conditions for the quadratically relaxed problem. We apply the modified Newton method to a sequence of logarithmic barrier problems, and design some reliable algorithms. Moreover, we establish the global convergence results of the proposed method. We carry out numerical experiments on 266 inequality constrained optimization problems. Our numerical results show that the proposed method is competitive with some existing interior-point $\ell_1$-penalty methods in term of iteration numbers and better when comparing the values of the penalty parameter.

2016, 12(3): 975-990
doi: 10.3934/jimo.2016.12.975

*+*[Abstract](1200)*+*[PDF](388.6KB)**Abstract:**

Lower bounds and upper bounds for the spectral radius of a nonnegative tensor are provided. And it is proved that these bounds are better than the corresponding bounds in [Y. Yang, Q. Yang, Further results for Perron-Frobenius Theorem for nonnegative tensors, SIAM. J. Matrix Anal. Appl. 31 (2010), 2517-2530].

2016, 12(3): 991-1007
doi: 10.3934/jimo.2016.12.991

*+*[Abstract](1320)*+*[PDF](878.8KB)**Abstract:**

In this paper, we develop two game theoretic models of a one-manufacturer and one-retailer supply chain to study the store assistance service decision and channel coordination mechanism, where the retailer allows consumers to return mismatching product and invests on store assistance service to reduce mismatching rate. Under manufacturer Stackelberg model, we find that the players' profits increase with mismatching rate and mismatching cost if market scale is sufficiently large. We design a quantity discount-subsidy contract to coordinate the pricing and service investment behavior of the retailer and find that the coordinated unit wholesale price increases with mismatching cost and mismatching rate if both subsidy fee and service cost are sufficiently high. By comparing with the retailer Stackelberg model, we find that (i) there exists a first-mover advantage; (ii) the unit wholesale price under retailer Stackelberg is lower than that under manufacturer Stackelberg while the retail price and service level under retailer Stackelberg is higher; and (iii) the retailer's channel leadership raises product quantity if the probability of high mismatching loss is sufficiently low. We design a two-part margin-subsidy rate mechanism to coordinate the retailer Stackelberg supply chain.

2016, 12(3): 1009-1029
doi: 10.3934/jimo.2016.12.1009

*+*[Abstract](2175)*+*[PDF](519.5KB)**Abstract:**

This paper presents a literature review on risk and disruption management in production-inventory and supply chain systems. The review is conducted on the basis of comparing various works published in this research domain, specifically the papers, which considered real-life risk factors, such as imperfect production processes, risk and disruption in production, supply, demand, and transportation, while developing models for production-inventory and supply chain systems. Emphasis is given on the assumptions and the types of problems considered in the published research. We also focus on reviewing the mathematical models and the solution approaches used in solving the models using both hypothetical and real-world problem scenarios. Finally, the literature review is summarized and future research directions are discussed.

2016, 12(3): 1031-1039
doi: 10.3934/jimo.2016.12.1031

*+*[Abstract](1141)*+*[PDF](333.9KB)**Abstract:**

In this paper, $E$-super efficiency of set-valued optimization problems is investigated. Firstly, based on the improvement set, a new notion of $E$-super efficient point is introduced in real locally convex spaces. Secondly, under the assumption of near $E$-subconvexlikeness of set-valued maps, scalarization theorems of set-valued optimization problems are established in the sense of $E$-super efficiency. Finally, Lagrange multiplier theorems of set-valued optimization problems are obtained in the sense of $E$-super efficiency.

2016, 12(3): 1041-1056
doi: 10.3934/jimo.2016.12.1041

*+*[Abstract](1733)*+*[PDF](420.8KB)**Abstract:**

In this paper, we propose a completely positive programming reformulation of the cardinality constrained portfolio selection problem. By constructing a sequence of computable cones of nonnegative quadratic forms over a union of second-order cones, an $\epsilon$-optimal solution of the original problem can be found in finite iterations using semidefinite programming techniques. In order to obtain a good lower bound efficiently, an adaptive scheme is adopted in our approximation algorithm. The numerical results show that the proposed algorithm can find better approximate and feasible solutions than other known methods in the literature.

2016, 12(3): 1057-1073
doi: 10.3934/jimo.2016.12.1057

*+*[Abstract](859)*+*[PDF](407.3KB)**Abstract:**

A union $\mathcal{I}=\mathcal{I}_{1}\cup \mathcal{I}_{2}\cup \cdots \cup \mathcal{I}_{m}$ of $m$ sets of items is given, where for each $i=1,2,\ldots,m$, $\mathcal{I}_{i}=\{I_{ik} \mid k=1,2,\ldots,n\}$ denotes a set of $n$ items of the $i$-th type and $I_{ik}$ denotes the $k$-th item of the $i$-th type. Each item $I_{ik}$ has an integral weight $w_{ik}$ and an integral priority $p_{ik}$. The food mixture packing problem to be discussed in this paper asks to find a union $\mathcal{I}'=\mathcal{I}'_{1}\cup \mathcal{I}'_{2}\cup \cdots \cup \mathcal{I}'_{m}$ of $m$ subsets of items so that for each $i=1,2,\ldots,m$, the sum weight of chosen items of the $i$-th type for $\mathcal{I}'_{i} \subseteq \mathcal{I}_{i}$ is no less than an integral indispensable bound $b_{i}$, and the total weight of chosen items for $\mathcal{I}'$ is no less than an integral target weight $t$. The total weight of chosen items for $\mathcal{I'}$ is minimized as the primary objective, and further the total priority of chosen items for $\mathcal{I'}$ is maximized as the second objective. In this paper, the known time complexity $O(mnt+mt^{m})$ is improved to $O(mnt+mt^{2})$ for an arbitrary $m\geq 3$ by a two-stage constitution algorithm with dynamic programming procedures. The improved time complexity figures out the weak NP-hardness of the food mixture packing problem.

2016, 12(3): 1075-1089
doi: 10.3934/jimo.2016.12.1075

*+*[Abstract](1241)*+*[PDF](435.9KB)**Abstract:**

In this paper, we study a reverse supply chain with three stocks for a firm implementing the periodic-review as policy. The first stock consists of newly manufactured items, while the second one is devoted to remanufactured items. The third stock contains all the items returned from the market. We made the following assumptions: items are not as-good-as-new, deterioration and dynamic demands affect new and remanufactured items, and dynamic customer return rate. Using optimal control theory, explicit expressions of the optimal rates in all three stocks have been provided: those for manufacturing, remanufacturing, disposal, and inventory levels. In the case where items deterioration rates are assumed to be unknown, self-tuning optimal control has also been implemented using the recursive least-squares method. Numerical examples and sensitivity analyses illustrate the results.

2016, 12(3): 1091-1119
doi: 10.3934/jimo.2016.12.1091

*+*[Abstract](1744)*+*[PDF](583.1KB)**Abstract:**

The paper deals with an inventory control problem for perishable items where two level credit periods depend on the order quantity over the finite time horizon. We assume that the supplier offers delay in payment on outstanding cost of purchasing goods to the retailer when purchasing amount is more than a fixed large amount. Moreover, the retailer offers a delay period to the customers for payment of their purchasing goods. In the inventory system, shortage is permitted and it is completely backordered.The net present value of the retailer's cost function, including costs of ordering, inventory holding, shortage, purchasing and other opportunities, is optimized. Then, an algorithm is proposed to determine the optimal values of order quantity, shortage quantity, number of cycles and the total cost of the system. Finally, a numerical example with sensitivity analysis of the key parameters is illustrated to show the applicability of the proposed model.

2016, 12(3): 1121-1133
doi: 10.3934/jimo.2016.12.1121

*+*[Abstract](1003)*+*[PDF](466.6KB)**Abstract:**

We consider a discrete-time single server queue with finite buffer. The customers arrive according to a discrete-time batch Markovian arrival process with geometrically distributed batch sizes and the service time is one time slot. For this queueing system, we obtain an exact closed-form expression for the stationary queue length distribution. The expression is in a form of mixed matrix-geometric solution.

2016, 12(3): 1135-1151
doi: 10.3934/jimo.2016.12.1135

*+*[Abstract](1083)*+*[PDF](423.6KB)**Abstract:**

In this paper, a scalarization result and a density theorem concerned with the sets of weakly efficient and efficient approximate solutions to a generalized vector equilibrium problem are given, respectively. By using the scalarization result and the density theorem, the connectedness of the sets of weakly efficient and efficient approximate solutions to the generalized vector equilibrium problem are established without the assumptions of monotonicity and compactness. The lower semicontinuity of weakly efficient and efficient approximate solution mappings to the parametric generalized vector equilibrium problem with perturbing both the objective mapping and the feasible region are obtained without the assumptions of monotonicity and compactness. Furthermore, the upper semicontinuity of weakly efficient approximate solution mapping and the Hausdorff upper semicontinuity of efficient approximate solution mapping to the parametric generalized vector equilibrium problem with perturbing both the objective mapping and the feasible region are also given under some suitable conditions.

2016, 12(3): 1153-1172
doi: 10.3934/jimo.2016.12.1153

*+*[Abstract](1174)*+*[PDF](1784.9KB)**Abstract:**

This paper presents production-inventory model for deteriorating items with constant demand under the effect of inflation and time-value of money. Models are developed without shortages while using two production cost functions. In the first case, production cost is divided into two parts: an initial cost which occurs at the beginning of each cycle and is applied to the entire quantity produced during the cycle and a running cost that is incurred as production progresses and is applied to the initial units produced. In the second case, the production cost is incurred at the beginning of the cycle. Numerical examples are given to illustrate the theoretical results and made the sensitivity analysis of parameters on the optimal solutions. The validation of this model's result was coded in Microsoft Visual Basic 6.0

2017 Impact Factor: 0.994

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