A stochastic maritime transportation-inventory problem with gamma, exponential, and uniform demand distributions

Abstract

We examine a maritime transportation-inventory problem under three daily demand distributions, namely gamma, exponential and uniform. This is essentially an extension of the problem of Soroush and Al-Yakoob (2018) in which case daily demands are assumed to be normally distributed. The principle thrust of this research effort is to find an optimal vessel schedule with the objective of minimising the expected overall cost consisting of the vessels' operational expenses, expected penalties for violating some pre-specified lower and upper storage levels, and vessels' chartering expenses, while meeting the stochastic demand requirements at each destination with acceptable reliability levels. We formulate each problem scenario as a stochastic optimisation model, which using chance-constrained programming, is converted into an exact mixed-integer nonlinear program. Our results show that different demand distributions lead to significantly different vessel schedules and associated costs. Sensitivity analyses are also performed. [Received 18 November 2018; Revised 17 May 2019; Revised 7 August 2019; Revised 3 November 2019; Accepted 21 January 2020]