Abstract
A stochastic model of work of inventory management system at a ship repair yard (SRY) has been developed. In order to account for factors related to uncertainties and risks (random moments of arrival of ships at SRY, random volumes of repairs), it has been proposed to apply the apparatus of Markov drift processes for modeling. These processes make it possible to take into consideration the discrete character of change in the number of vessels at SRY, as well as the ongoing character of fluctuation in the inventory level of materials in warehouse. In this case, docks at SRY are interpreted as a queueing system. It is also assumed that the restocking of materials at a warehouse and their utilization during repair of ships is carried out continuously, at constant intensities, but depending on the availability of a material in warehouse. The result of this study is the stated problem on stochastic optimization of intensities in the resupply of materials based on the criterion of minimum cumulative average current expenses of the yard, which also take into consideration the losses associated with additional downtime of ships due to the lack of materials in warehouse during repair. It has been shown that the results obtained are important to the practical operation of SRY supply department as they make it possible to build a strategy for the replenishment of materials in stock at SRY under conditions of time-dependent non-uniformity in the need for ship repairs. From a theoretical point of view, the obtained results demonstrate a possibility of using the apparatus of Markov drift processes to solve various problems on optimal inventory control under conditions of random fluctuations in the demand for materials in warehouse.
Highlights
From an applied point of view, a discrete set describes the dynamics of queueing system (QS) states, defined by discrete variables, while the continuum set can describe, for example, a fluctuation of inventory levels at a warehouse over time
The aim of this study is to state mathematically, and solve, the problem on the optimal inventory control over materials required to repair ships, under conditions of uncertainty about the time of ships arrival at SRY and the volumes of repair operations
The present study shows that the proposed approach to optimizing inventory control at SRY makes it possible to minimize the expected operating costs of SRY under conditions of the random arrivals of ships at SRY and the randomness in the volumes of repair operations at each ship
Summary
Ship repair is a complex and low mechanized industrial sector. Ship repair yards (plants) perform a dock repair, as well as repair of bottom-overboard fittings, pipelines, propeller-rudder system, they replace hull’s steel structures, they manufacture fuel equipment for ICE, spare parts for ship equipment and devices, etc. From an applied point of view, a discrete set describes the dynamics of QS states, defined by discrete variables (the number of ships at docks and in queues to them), while the continuum set can describe, for example, a fluctuation of inventory levels at a warehouse over time This circumstance makes it possible to state and solve a variety of tasks on optimal inventory management under conditions of uncertainty and risk. This approach could be used in order to solve the problem related to examining an influence of the level of materials stocks at SRY on the dynamics of change in the number of vessels at the yard, and to the construction of an optimization method for the replenishment policy regarding the specified stocks
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