Modeling Conveyor Merges in Zone Picking Systems

In many order picking and sorting systems conveyors are used to transport products through the system and to merge multiple flows of products into one single flow. In practice, conveyor merges are potential points of congestion, and consequently can lead to a reduced throughput. In this paper, we study merges in a zone picking system. The performance of a zone picking system is, for a large part, determined by the performance of the merge locations. We model the system as a closed queueing network that describes the conveyor, the pick zones, and the merge locations. The resulting model does not have a product-form stationary queue-length distribution. This makes exact analysis practically infeasible. Therefore, we approximate the behavior of the model using the aggregation technique, where the resulting subnetworks are solved using matrix-geometric methods. We show that the approximation model allows us to determine very accurate estimates of the throughput when compared with simulation. Furthermore, our model is in particular well suited to evaluate many design alternatives, in terms of number of zones, zone buffer lengths, and maximum number of totes in the systems. It also can be used to determine the maximum throughput capability of the system and, if needed, modify the system in order to meet target performance levels

Analysis of Class-based Storage Strategies for the Mobile Shelf-based Order Pick System

Mobile Shelf-based Order Pick (MSOP) systems are gaining significant in- terest for e-commerce fulfillment due to their rapid deployment capability and dynamic organization of storage pods based on item demand profiles. In this research, we model the MSOP system with class-based storage strategies and alternate pod storage policies using multi-class closed queuing networks. We observe that though closest-open location pod storage policy do not allow to efficiently use the storage spaces in comparison to random location pod storage policy in an aisle, it increases the system throughput for all item classes

Analyzing Order Throughput Times in a Milkrun Picking System

E-commerce fulfillment competition evolves around cheap, speedy, and time-definite delivery. Milkrun order picking systems have proven to be very successful in providing handling speed for a large, but highly variable, number of orders. In this system, an order picker picks orders that arrive in real time during the picking process; by dynamically changing the stops on the picker’s current picking route. The advantage of milkrun picking is that it reduces order picking set-up time and worker travel time compared to conventional batch picking systems. This paper is the first in studying order throughput times of multi-line orders in a milkrun picking system. We model this system as a cyclic polling system with simultaneous batch arrivals and determine the mean order throughput time. These results allow us to study the effect of different product allocations. For a real world application we show that milkrun order picking reduces the order throughput time significantly compared to conventional batch picking

Merck Animal Health Uses Operations Research Methods to Transform Biomanufacturing Productivity for Lifesaving Medicines

Merck Animal Health offers veterinarians, farmers, pet owners, and governments a wide range of veterinary pharmaceuticals, vaccines, health management solutions and services, and an extensive suite of connected technology that includes identification, traceability, and monitoring products. Biomanufacturing uses living organisms (i.e., viruses and bacteria) to grow the active ingredients in vaccines, pharmaceuticals, and therapeutics. This high-tech manufacturing process generates unique challenges not found in many other industries. For example, biomanufacturing operations include high levels of uncertainty and batch-to-batch variability in production yield, lead times, and costs. Additionally, the high cost of equipment and labor-intensive nature of operations preclude the ability to flexibly add capacity. Facing these challenges, we decided that harnessing the power of operations research and advanced analytics to complement our rich life sciences and biomanufacturing expertise was critical. After four years of collaboration with the Eindhoven University of Technology, we developed a portfolio of optimization models and decision support applications that substantially improved our biomanufacturing effectiveness. The implementation of the developed models had a significant impact by generating $200 million of additional revenue without the need for additional raw materials, energy resources, or new equipment. The developed models are widely adopted across the firm, thus enhancing its core function

A finite compensation procedure for a class of two-dimensional random walks

Motivated by queueing applications, we consider a class of two-dimensional random walks, the invariant measure of which can be written as a linear combination of a finite number of product-form terms. In this work, we investigate under which conditions such an elegant solution can be derived by applying a finite compensation procedure. The conditions are formulated in terms of relations among the transition probabilities in the inner area, the boundaries as well as the origin. A discussion on the importance of these conditions is also given

Deep Reinforcement Learning for Optimal Planning of Assembly Line Maintenance

Discovering the optimal maintenance planning strategy can have a substantial impact on production efficiency, yet this aspect is often overlooked in favor of production planning. This is a missed opportunity as maintenance and production activities are deeply intertwined. Our study sheds light on the significance of maintenance planning, particularly in the dynamic setting of an assembly line. By maximizing the average production rate and incorporating flexible planning windows, buffer content, and machine production states, a unique problem is addressed in which a policy for planning maintenance on the final machine of a serial assembly line is developed. To achieve this, novel average-reward deep reinforcement learning techniques are employed and pitted against generic dispatching methods. Using a digital twin with real-world data, experiments demonstrate the immense potential of this new deep reinforcement learning technique, producing policies that outperform generic dispatching strategies and practitioner policies

The Mn/Gn/1 queue with vacations and exhaustive service

We consider the Mn/Gn/1 queue with vacations and exhaustive service in which the server takes (repeated) vacations whenever it becomes idle, the service time distribution is queue length dependent, and the arrival rate varies both with the queue length and with the status of the server, being busy or on vacation. Using a rate balance principle, we derive recursive formulas for the conditional distribution of residual service or vacation time given the number of the customers in the system and the status of the server. We also derive a closed-form expression for the steady-state distribution as a function of the probability of an empty system. As an application of the above, we provide a recursive computation method for Nash equilibrium joining strategies to the observable M/G/1 queue with vacations