A Stochastic Vessel Scheduling Transportation-Inventory Problem With Gamma And Uniform Demands
This paper addresses a stochastic scheduling transportation-inventory problem to transport crude oil from a source to adestination over a finite time horizon via a fleet of heterogeneous vessels. The demands have either gammaor uniform distribution, and a penalty structure isimposed on the shortages and excesses in daily storage levels at the destination. The expected overall cost of such a fleet operation is composed of the total vessels’ operational expenses, expected total penalties incurred for violating pre-specified lower and upper on storage levels, and vessel chartering expenses.The objective is to optimize the fleet schedules and to minimize the total expected cost, which can be achieved by simultaneously maintaining desirable storage levels and meeting the stochastic demands with acceptable reliability levels. For each demand distribution, the problem is formulatedas a stochastic optimization model and then chance constrained programming is used to convert the model into an exact mixed-integer nonlinear program. Some computational results are reported.
Keywords: Stochastic scheduling, inventory/shortages, transportation, chance constraints, integer nonlinear programming, gamma, uniform