DEVELOPMENT OF A METHOD FOR DETERMINATION OF SHIP'S LOADING TIME DISTRIBUTION UNDER ІRREGULAR CARGO ARRIVAL

A method for determining the time distribution function of ship berthing under loading under the direct option of loading operations (i. e., without the warehouse) in conditions of irregular cargo delivery by rail is developed. In order to take into account uncertainty and risk factors (random arrivals of loaded cars at the terminal and loading volume of cars), it is proposed to use linear Markov processes that describe the dynamics of train arrival and cargo loading on the ship. It is assumed that the intervals between adjacent arrivals of loaded cars at the terminal are exponential random variables. Cargo transshipment from cars on the ship is carried out at a constant rate. The cases when the volume of cargo in cars is a random or constant variable are considered in detail. To find the probability densities and state probabilities of the corresponding Markov process, a system of linear differential equations and initial conditions is derived. A solution to this system of equations in terms of the Laplace transform is found, in particular, the distribution function of the ship berthing time, taking into account possible interruptions while waiting for cargo delivery by cars. For the case of a constant volume of cargo on cars, the corresponding distribution function of the ship berthing time and its asymptotics for a large deadweight tonnage are also found using the central limit theorem. Based on the results obtained, the problem of finding a criterion of expediency of insuring the risk of exceeding the laytime (contractual) of the ship is formulated. It is proved that the results obtained are important for the theory, as well as for the practice of the port operator and shipping companies, since they can reduce the risk of exceeding the ship berthing time under loading operations. A numerical illustration of the proposed method is given