The Study On Speed Optimization Of Containership Considering Empty Container Repositioning

The imbalance of the developing international trade makes the contradiction between supply and demand of empty containers increasingly intensified,which are mainly transported by containers,and the cost of empty container repositioning accounts for a large proportion of the operating cost of shipping companies.At the same time,as another major operating cost of shipping companies,fuel consumption cost also increases the economic burden of shipping companies in recent years because of the high fuel price.However,the shipping industry has been in the doldrums for more than ten years.As a result,many shipping companies have encountered operational difficulties,even bankruptcy.In the face of the fact that the supply of shipping capacity exceeds the demand,how to operate at low cost and improve the revenue under the condition of meeting the requirements of customers has become the key to the sustainable operation of shipping companies.From the perspective of container shipping companies,this paper establishes a nonlinear model of speed optimization with the objective of maximizing the average daily profit of container shipping including the cost of empty container repositioning.In order to solve the problem conveniently,the original objective function of the maximum value is changed into minimum value of the objective function.First calculating the partial derivative of the transformed objective function,then the convexity and concavity of the transformed objective function are judged.It is found to be similar the saddle face,so the optimal solution is obtained at the boundary value of empty container transportation volume,and the KKT condition is applied to obtain the optimal solution of sailing speed;.Finally,we select two containerships in a shipping company which capacity is 3000 TEU and 5000 TEU,and put these two containerships into Los Angeles Yantian direct route and Hong Kong Singapore direct route respectively for example analysis.The results show that the two routes have two kinds of extreme phenomena: the ships in one route sail at the maximum speed without empty container repositioning,while the ships in the other route sail at the lowest speed with the maximum amount of empty container repositioning.In order to further study the reasons,sensitivity analysis is made on the heavy container transportation volume,fuel price and empty container transportation volume.The results show that: the increase of heavy container transportation volume or freight rate can not only make the ship speed up,but also make the ship give up empty container transportation.This is because the increase of ship speed makes the average daily handling cost exceed the empty container storage fee plus charter fee saved by empty container repositioning;while the increase of fuel price will make the ship slow down and reduce the average daily profit of the ship,which is mainly due to the increase of fuel consumption cost.When the ship decelerates to a certain extent,the low freight rate and low volume allow the shipping company to make up for more losses by dispatching empty containers.Therefore,shipping companies can speed up their navigation when the shipping industry is booming,and it is a different way to increase their revenue to carry out empty container repositioning under the condition of shipping industry downturn and shipping companies operating at a loss.