16:00-16:45

Integrated queueing-inventory models and their connection with robotic mobile fulfillment systems

Sonja Otten (Leuphana University of Lüneburg, Germany)

Abstract

Production processes are usually investigated using models and methods from queueing theory. Control of warehouses and their optimization rely on models and methods from inventory theory. Both theories are fields of Operations Research, but they comprise quite different methodologies and techniques. In classical Operations Research queueing and inventory theory are considered as disjoint research areas. Today’s emergence of complex supply chains (= production-inventory networks) calls for integrated production-inventory models as well as for adapted techniques and evaluation tools.

We consider several networks of production-inventory systems. More precisely, production-inventory systems at several locations are connected by a supplier. Demand of customers arrives at each production system. If the local inventory is depleted, arriving customers are lost. To satisfy a customer’s demand each server needs exactly one unit of raw material from the associated local inventory. The supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy.

We develop Markov process models for these production-inventory systems and derive the steady state distribution of the global system. For most of the production-inventory systems the obtained steady state is of product form. This enables us to analyse the long term average

costs with the aim to find the optimal base stock levels.

These integrated production-inventory models can be placed within the context of robotic mobile fulfillment systems (RMFS). In an RMFS, robots bring shelves with storage items from the storage area to pick stations, where the items are picked according to customers’ demands.

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16:45-17:30

Shelf Repositioning in a Robotized Warehouse

Ruslan Krenzler (Leuphana University of Lüneburg, Germany)

Abstract

Often, when you order things online, robots will bring your things from some storage area to a human employee for packing. Both, the robots and the humans, are parts of an efficient very complex modern warehouse. To better understand the real-world warehouse and to develop optimization algorithms, we develop a simple mathematical model. We critically analyze our results with regard to their real-world application.

In this talk we focus on a special type of the robotized warehouses: “parts-to-picker”. There, robots move shelves between a storage area and output stations. At every output station there is a person — the picker — who takes things from the shelves and packs them into boxes according to customers’ orders. The content of each shelf is different. The customers’ orders are random. As a result, some shelves are used more frequently than the others. When the picker does not need the shelf any more, a robot carries this shelf back to the storage area. In the storage area, there are several free places and we need to decide where to put this shelf. Every decision influences the next one. And the sequence of these decisions influences the overall efficiency of the warehouse. We look for an optimal sequence.