Wenqiang Dai

Competitive Strategies for On-line Production Order Disposal Problem

In this paper we study the on-line production order disposal problem considering preemption and abortion penalty. We discuss the cases when orders have uniform and nonuniform lengths. For the case of uniform order length, the GR strategy is proved to be \(2\rho + 2\sqrt{(1+\rho)^2 + \rho + 3}\) -competitive, where ρ ≥ 0 is the coefficient of the punishment. For the case of nonuniform order lengths, GR is \(2(\lambda + \lambda\rho) + 2\sqrt{(\lambda+\lambda\rho)^2 + \lambda\rho + 1}\) -competitive where λ is the ratio of length between the longest and shortest orders. When abortion penalty is not counted, the ER strategy is proposed and proved to be eλ + e + 1 -competitive, where e ≈ 2.718. The result is much better than that of GR. We show that ER is not competitive when abortion penalty is counted.

A note: An improved upper bound for the online inventory problem with bounded storage and order costs

This work gives an improved competitive analysis for an online inventory problem with bounded storage and order costs proposed by Larsen and Wohlk (2010). We improve the upper bound of the competitive ratio from (2+1k)Mmto less than 45(2+1k)Mm,where k, M and m are parameters of the given problem. The key idea is to use linear-fractional programming and primal-dual analysis methods to find the upper bound of a central inequality.

The Optimal Order Policy for a Capacitated Multiple Product Inventory System under Symmetry

Although many researches have conjectured the optimality of the hedging point policy for the multiple-product stochastic capacitated periodic review problem, it is still a challenge to prove the hypothesis. This paper considers a special case of the capacitated multiple-product periodic review problem where stochastic demand distribution, production rate, unit production cost and periodic expected inventory cost are the same for all different products. For this symmetric problem, we prove an optimal policy where ordering and non-ordering regions for every product are defined. Our research provides significant implications to the characterization of the optimal policy for the general problem.

On the edge l ∞ radius of Saitou and Nei's method for phylogenetic reconstruction

In this paper, we study the performance of Saitou and Neis neighbor-joining method for phylogenetic reconstruction. We show that the edge l∞ radius of the method is 1/4. This improves an result by Atteson [The performance of neighbor-joining methods of phylogenetic reconstruction, Algorithmica 25 (1999) 251-278] and Xu et al. [A lower bound on the edge l∞ radius of Saitou and Neis method for phylogenetic reconstruction, Inform. Process. Lett. 94(5) (2005) 225-230]. Previously, only an upper bound 1/4 and a lower bound 1/6 were known.

A lower bound on the edge l ∞ radius of Saitou and Nei's method for phylogenetic reconstruction

In this paper, we study the performance of Saitou and Neis neighbor-joining method for phylogenetic reconstruction. We show that the edge linfin; radius of the method is at least 1/6. This partially answers a question by Atteson (1999). Previously, only an upper bound of 1/4 was known.

Competitive analysis of the online financial lease problem

The financial lease is an important financing tool by which the lessee can acquire ownership of equipment upon the expiration of the lease after making a series of rent payments for the use of the equipment. In this paper, we consider an online version of this financial lease decision problem in which the decision maker (the lessee) does not know how long he/she will use the equipment. By assuming, the lessee can use the equipment through two options: financial lease or lease; we define and solve this online financial lease decision problem using the competitive analysis method. The optimal online strategies are discussed in each financial lease case with or without down payment. Finally, the optimal strategies are summarized as simple decision rules.

A bi-objective model for hazard materials location and routing problem

This paper mainly focuses on the hazard materials optimal management problem, which involves the questions such as following: where to open treatment centers and with which technologies, where to open disposal centers, how to route different types of hazardous materials to the treatment centers which have compatible treatment technologies at the treatment center, how to route residues to disposal centers and how to route recycle matters to the recycling centers. A new bi-objective location-routing model is proposed, with some practical constraints which are not considered previously. Finally an experiment result is also reported.

Fuzzy Multi-objective Programming Approach to Hazard Materials Treatment Center Location

This paper mainly focus on the hazard materials treatment center location problem using the fuzzy multi-objective programming approach. We consider the factor of treating volume of each treatment center into the classical MAX-MIN model. The problem is formulated as a bi-objective problem, which is rarely studied previously. Additionally, to provide a more realistic model structure, decision maker’s imprecise aspiration levels for the goals are incorporated into the model through fuzzy modelling approach. In the decision process, a fuzzy goal programming method is developed. We also discuss the computing approach and prove that the fuzzy optimal solution has a good performance.

Triangulating a convex polygon with small number of non-standard bars

For a given convex polygon with inner angle no less than

A 16-competitive algorithm for hierarchical median problem

\frac{2}{3}\pi