The freight consolidation and containerization problem

In today’s global free market, third-party logistics providers (3PLs) are becoming increasingly important. This paper studies a problem faced by a 3PL operating a warehouse in Shanghai, China, under contract with a major manufacturer of children’s clothing based in the United States. At the warehouse, the 3PL receives textile parcel shipments from the suppliers located in China; each shipment is destined for different retail stores located across the United Sates. These shipments must be consolidated and loaded into containers of varying sizes and costs, and then sent along shipping routes to different destination ports. An express company, such as UPS and FedEx, unloads the shipments from the containers at the destination ports and distributes them to their corresponding stores or retailers by parcel delivery. The objective is to find an allocation that minimizes the total container transportation and parcel delivery costs. We formulate the problem into an integer programming model, and also propose a memetic algorithm approach to solve the problem practically. A demonstration of a good solution to this problem was a decisive factor in the awarding of the contract to the 3PL in question.  

Hopf bifurcation in a predator-prey system with Holling type III functional response and time delays

This paper is concerned with a delayed predator-prey system with modified Leslie-Gower and Holling type III schemes. By analyzing the associated characteristic equation, its local stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. Based on the normal form method and center manifold theorem, the formulaes for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, some numerical simulations to illustrate the theoretical analysis are also carried out.  

A memetic algorithm for the multiperiod vehicle routing problem with profit

In this paper, we extend upon current research in the vehicle routing problem whereby labour regulations affect planning horizons, and therefore, profitability. We call this extension the multiperiod vehicle routing problem with profit (mVRPP). The goal is to determine routes for a set of vehicles that maximizes profitability from visited locations, based on the conditions that vehicles can only travel during stipulated working hours within each period in a given planning horizon and that the vehicles are only required to return to the depot at the end of the last period. We propose an effective memetic algorithm with a giant-tour representation to solve the mVRPP. To efficiently evaluate a chromosome, we develop a greedy procedure to partition a given giant-tour into individual routes, and prove that the resultant partition is optimal. We evaluate the effectiveness of our memetic algorithm with extensive experiments based on a set of modified benchmark instances. The results indicate that our approach generates high-quality solutions that are reasonably close to the best known solutions or proven optima, and significantly better than the solutions obtained using heuristics employed by professional schedulers.  

The single vehicle routing problem with toll-by-weight scheme: A branch-and-bound approach

Expressways in China make use of the toll-by-weight scheme, in which expressway tolls are collected based on the weight and traveling distance of the vehicle. Most vehicle routing models assume that the cost of traversing each edge is equivalent to edge length or some constant; as a result, such models cannot be practically applied to the Chinese expressway transportation system. This study addresses a new single vehicle routing problem that takes the vehicle’s (laden and unladen) weight into account. To solve this problem exactly, we provide a branch-and-bound algorithm with a provably valid lower bound measure, along with five dominance checkers for additional pruning. We analyze our algorithm using instances generated from standard TSP test cases, as well as two new sets of test cases based on real expressway information from the Gansu and Jiangxi provinces in China. The algorithm can be applied to any toll scheme in which the toll per unit distance monotonically increases with weight, even if the toll function is non-linear.  

SVEIRS epidemic model with delays and partial immunization for internet worms

A delayed SVEIRS model for the transmission of worms in internet with partial immunization is proposed. The impact of the possible combination of the two delays on the model is investigated. By analyzing the corresponding characteristic equations and regarding the possible combination of the two delays as the bifurcation parameter, local stability of the endemic equilibrium and existence of local Hopf bifurcation at the viral equilibrium are addressed, respectively. Further, explicit formulas that determine direction and stability of the Hopf bifurcation are derived with the help of the normal form theory and the center manifold theorem. Finally, some numerical simulations are carried out to verify the obtained theoretical findings.  

柱黑洞的熵

采用由广义测不准关系得到的新的态密度方程,研究了具有柱对称时空背景下黑柱的 熵．利用新的态密度方程后,不通过截断可以消除brick-wall模型中无法克服的发散项,并且 同样可得到黑柱的熵与视界面积成正比的结论．计算结果表明,黑柱熵是视界面上量子态的 熵,是一种量子效应,是黑洞的内禀性质．在计算中我们直接应用量子统计的方法,求柱黑洞 背景下玻色场与费米场的配分函数,避开了求解各种粒子波动方程的困难,为研究各种时空黑 洞熵提供了一条简捷的新途经．