Stochastic models for asynchronous automated material handling systems

In this thesis we consider analytical models for asynchronous automated material handling systems that explicitly incorporate the stochastic nature of the demand process. An asynchronous automated material handling system consists of two major components, an automated guided vehicle system (AGVS) and an automated storage and retrieval system (AS/RS). We develop and solve analytical design models for multiple load AGVSs and derive optimal storage assignment policies for a single command mode AS/RS.;The multiple load AGVSs we consider operate under a go-when-filled dispatching policy. They deliver material from a central depot to workcenters throughout the factory. To optimize system performance, the workcenters are partitioned into zones for the purpose of material delivery. We consider two AGVS design models. In the first model a single automated guided vehicle (AGV) is dedicated to each zone while in the second model a common pool of AGVs is used to service workcenters in all zones. The workcenter demands are stochastic. We derive analytical expressions for mean delivery times and use them as constraints in non-linear binary integer programs. The objective is to find the optimal partitioning of workcenters into zones, the optimal number of AGVs to purchase and the optimal subset of workcenters to service by the AGVS, in order to maximize the monetary benefit of the systems. We present efficient branch-and-bound algorithms that solve the AGVS design problems optimally by exploiting their special structures. To determine the optimal AGVS designs without using the analytical solution methods, one would have to simulate the systems for all zoning options, all possible numbers of AGVs, and all combinations of open and closed workcenters. This approach would be computationally infeasible for most problems.;The single command mode AS/RS we consider operates under a periodic review, order-up-to level inventory policy. It stores and retrieves items that are used in a manufacturing process where timeliness of delivery is important. Our objective is to find an assignment of items to storage cells that minimizes expected storage and retrieval time or, equivalently, maximizes throughput. We consider a discrete and a continuous representation of the storage rack, and derive an optimal assignment policy and an improved class-based assignment policy that take the stochastic nature of the demand process into account. Computational results show that our assignment policies achieve significant savings in expected storage and retrieval time over assignment policies that are based on deterministic demand assumptions.