Table of Content

30 September 2016, Volume 4 Issue 3

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Stochastic Optimization

Monitoring and Limiting Deceptive Counterfeiting:a Two-Stage Model

Fang Liu,Ke Liu,Xin-Li Xie

2016, 4(3):  265.  doi:10.1007/s40305-016-0130-6

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Over past decades, deceptive counterfeits which cannot be recognized by ordinary consumers when purchasing, such as counterfeit cosmetics, have posed serious threats on consumers’ health and safety, and resulted in huge economic loss and inestimable brand damages to the genuine goods at the same time. Thus, how to effectively control and eliminate deceptive counterfeits in the market has become a critical problem to the local government. One of the principal challenges in combating the cheating action for the government is how to enhance the enforcement of relative quality inspection agencies like industrial administration office (IAO). In this paper,we formulate a two-stage counterfeit product model with a fixed checking rate from IAO and a penalty for holding counterfeits. Tominimize the total expected cost over two stages,the retailer adopts optimal ordering policies which are correlated with the checking rate and penalty. Under certain circumstances, we find that the optimal expected cost function for the retailer is first-order continuous and convex. The optimal ordering policy in stage two depends closely on the inventory level after the first sales period. When the checking rate in stage one falls into a certain range, the optimal ordering policy for the retailer at each stage is to order both kinds of products. Knowing the retailer’s optimal ordering policy at each stage, IAO can modify the checking rate accordingly to keep the ratio of deceptive counterfeits on the market under a certain level.

Management Science

Analysis of a Joint Pricing and Seat Allocation Model in a Hub-to-Hub Airline Network

Hong-Zhi He

2016, 4(3):  309.  doi:10.1007/s40305-016-0121-7

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In airline revenue management, after differentiating products on each itinerary according to various restrictions, management needs to set the prices for the products. A deterministic joint pricing and seat allocation model is proposed. It is reduced to a separable concave programming problem and thus readily solvable. Focusing on a special hub-to-hub airline network, monotonicity of the pricing decisions is explored. Using a nonlinear primal–dual technique, it is shown that some itineraries’ optimal prices are decreasing, while some other itineraries’ optimal prices are increasing with a capacity change in either a side leg or the middle leg. Such structural properties add important managerial insights into the pricing model for revenue managers in an airline company.

Stochastic Optimization

Tail Asymptotics of Two Parallel Queues with Transfers of Customers

Tao Jiang,Li-Wei Liu

2016, 4(3):  335.  doi:10.1007/s40305-016-0127-1

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This paper studies a system consisting of two parallel queues with transfers of customers. In the system, one queue is called main queue and the other one is called auxiliary queue. The main queue is monitored at exponential time instances. At a monitoring instant, if the number of customers in main queue reaches L (> K), a batch of L−K customers is transferred from the main queue to the auxiliary queue, and if the number of customers in main queue is less than or equal to K, the transfers will not happen. For this system, by using a Foster-Lyapunov type condition, we establish a sufficient stability condition. Then, we provide a sufficient condition under which,for any fixed number of customers in the auxiliary queue, the stationary probability of the number of customers in the main queue has an exact geometric tail asymptotic as the number of customers in main queue increases to infinity. Finally, we give some numerical results to illustrate the impact of some critical model parameters on the decay rate.

Continuous Optimization

A Variant of the Dual Face Algorithm Using Gauss-Jordan Elimination for Linear Programming

Ping-Qi Pan

2016, 4(3):  347.  doi:10.1007/s40305-015-0106-y

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Using Cholesky factorization, the dual face algorithm was described for solving standard Linear programming (LP) problems, as it would not be very suitable for sparse computations. To dodge this drawback, this paper presents a variant using Gauss-Jordan elimination for solving bounded-variable LP problems.

Discrete Optimization

Approximation Randomized Strategy-Proof Mechanisms in Obnoxious Facility Game withWeighted Agents

Lan Xiao, Xiao-Zhi Zhang

2016, 4(3):  357.  doi:10.1007/s40305-016-0117-3

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In this paper, we investigate the obnoxious facility location game with weighted agents. First, we design a randomized group strategy-proof mechanism with approximation ratio 3Wmax/2Wmin when the weighted agents are located on a line; then, on the cycle metric, we also discuss the strategy-proofness and the approximation ratios of a class of group strategy-proof deterministic mechanisms.

An Optimal Online Algorithm for Scheduling on Two Parallel Machines with GoS Eligibility Constraints

Jia Xu， Zhao-Hui Liu

2016, 4(3):  371. 

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We consider the online scheduling problem on two parallel machines with the Grade of Service (GoS) eligibility constraints. The jobs arrive over time, and the objective is to minimize the makespan. We develop a (1 + α)-competitive optimal algorithm, where α ≈ 0.555 is a solution of α3 − 2α2 − α + 1 = 0.

Complexities of Some Problems on Multi-agent Scheduling on a Single Machine

Jin-Jiang Yuan

2016, 4(3):  379. 

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We study the computational complexities of three problems on multi-agent scheduling on a single machine. Among the three problems, the computational complexities of the first two problems were still open and the last problem was shown to be unary NP-hard in the literature. We show in this paper that the first two problems are unary NP-hard. We also show that the unary NP-hardness proof for the last problem in the literature is invalid, and so, the exact complexity of the problem is still open.

Continuous Optimization

Two-Phase-SQP Method with Higher-Order Convergence Property

Suvra Kanti Chakraborty， Geetanjali Panda

2016, 4(3):  385.  doi:10.1007/s40305-016-0122-6

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We propose a two-phase-SQP (Sequential Quadratic Programming) algorithm for equality-constrained optimization problem. In this paper, an iteration process is developed, and at each iteration, two quadratic sub-problems are solved. It is proved that, under some suitable assumptions and without computing further higher-order derivatives, this iteration process achieves higher-order local convergence property in comparison to Newton-SQP scheme. Theoretical advantage and a note on l1 merit function associated to the method are provided.