H. Neil Geismar

Sequencing and Scheduling in Robotic Cells: Recent Developments

A great deal of work has been done to analyze the problem of robot move sequencing and part scheduling in robotic flowshop cells. We examine the recent developments in this literature. A robotic flowshop cell consists of a number of processing stages served by one or more robots. Each stage has one or more machines that perform that stage’s processing. Types of robotic cells are differentiated from one another by certain characteristics, including robot type, robot travel-time, number of robots, types of parts processed, and use of parallel machines within stages. We focus on cyclic production of parts. A cycle is specified by a repeatable sequence of robot moves designed to transfer a set of parts between the machines for their processing.We start by providing a classification scheme for robotic cell scheduling problems that is based on three characteristics: machine environment, processing restrictions, and objective function, and discuss the influence of these characteristics on the methods of analysis employed. In addition to reporting recent results on classical robotic cell scheduling problems, we include results on robotic cells with advanced features such as dual gripper robots, parallel machines, and multiple robots. Next, we examine implementation issues that have been addressed in the practice-oriented literature and detail the optimal policies to use under various combinations of conditions. We conclude by describing some important open problems in the field.

The Integrated Production and Transportation Scheduling Problem for a Product with a Short Lifespan

The integrated production and transportation scheduling problem (PTSP) with capacity constraints is common in many industries. An optimal solution to PTSP requires one to simultaneously solve the production scheduling and the transportation routing problems, which requires excessive computational time, even for relatively small problems. In this study, we consider a variation of PTSP that involves a short shelf life product; hence, there is no inventory of the product in process. Once a lot of the product is produced, it must be transported with nonnegligible transportation time directly to various customer sites within its limited lifespan. The objective is to determine the minimum time required to complete producing and delivering the product to meet the demand of a given set of customers over a wide geographic region. This problem is NP-hard in the strong sense. We analyze the properties of this problem, develop lower bounds on the optimal solution, and propose a two-phase heuristic based on the analysis. The first phase uses either a genetic or a memetic algorithm to select a locally optimal permutation of the given set of customers; the second phase partitions the customer sequence and then uses the Gilmore-Gomory algorithm to order the subsequences of customers to form the integrated schedule. Empirical observations on the performance of this heuristic are reported.

Approximation algorithms for k-unit cyclic solutions in robotic cells

Abstract This paper considers the problem of scheduling operations in bufferless robotic cells that produce identical parts. Finding a multi-unit cyclic solution which minimizes the long-run average time to produce a part is an open problem. Most research has been focused on finding an optimal 1-unit cyclic solution. However, it is known that an optimal multi-unit cyclic solution can be better than an optimal 1-unit cyclic solution for cells with four or more machines. We present polynomial algorithms that produce multi-unit cyclic solutions whose per unit cycle times are within a constant factor of the optimum for the three most common classes of robotic cells viz., additive, constant, and Euclidean travel-time. The approximation guarantees obtained for these three classes of cells are 1.5, 1.5, and 4, respectively. As a by-product, we obtain upper bounds on the difference in the per unit cycle times between an optimal multi-unit cycle and an optimal 1-unit cycle for each of these three classes of cells.

Dominance of Cyclic Solutions and Challenges in the Scheduling of Robotic Cells

We consider the problem of scheduling operations in bufferless robotic cells that produce identical parts. Maximizing the long-term average throughput of parts is an important problem in both theory and practice. We define an appropriate state space required to analyze this problem and show that cyclic schedules which repeat a fixed sequence of robot moves indefinitely are the only ones that need to be considered. For the different classes of robotic cells studied in the literature, we discuss the current state of knowledge with respect to cyclic schedules. Finally, we discuss the importance of two fundamental open problems concerning optimal cyclic schedules, special cases for which these problems have been solved, and attempts to solve the general case.

Robotic Cells with Parallel Machines: Throughput Maximization in Constant Travel-Time Cells

We present a general analysis of the problem of sequencing operations in bufferless robotic cell flow shops with parallel machines. Our focus will be cells that produce identical parts. The objective is to find a cyclic sequence of robot moves that maximizes the steady state throughput. Parallel machines are used in the industry to increase throughput, most typically at bottleneck processes having larger processing times.Efficient use of parallel machines requires that several parts be processed in one cycle of robot movements. We analyze such cycles for constant travel-time robotic cells. The number of cycles that produce several parts is very large, so we focus on a subclass called blocked cycles. In this class, we find a dominating subclass called LCM Cycles.The results and the analysis in this paper offer practitioners (i) guidelines to determine whether parallel machines will be cost-effective for a given implementation, (ii) a simple formula for determining how many copies of each machine are required to meet a particular throughput rate, and (iii) an optimal sequence of robot moves for a cell with parallel machines under a certain common condition on the processing times.

A Framework to Analyze Cash Supply Chains

The Federal Reserve System of the United States is making changes to its cash recirculation policy to reduce depository institutions’ (banks’) overuse of its cash processing services. These changes will affect operating policies and costs at many institutions having large cash businesses and, in turn, impact cash transportation and logistics providers. This study provides the framework to study the cash supply chain structure and analyzes it as a closed-loop supply chain. Additionally, it describes the cash flow management system used by banks in the U.S.

Robotic cells with parallel machines and multiple dual gripper robots: a comparative overview

The combination of parallel machines and multiple dual gripper robots has become increasingly prevalent in modern manufacturing with robotic cells. However, there has been no previous study of the design and scheduling challenges faced by managers who employ these complex cells. The benefit of implementing dual grippers in cells with multiple robots over cells with the same number of single gripper robots is quantified in this paper. Configuration decisions are addressed by comparing different implementations of multi-robot cells to show that the method of exchanging parts between robots (shared machines versus transfer stations) has little bearing on the throughput. In contrast, it is demonstrated that the assignment of processing stages to robots can have a significant effect on a cells potential throughput. A scheme that allows multiple robots to cooperate without colliding or suffering gridlock is described; this is realized with minimal impact on throughput. The optimality is analytically established, under conditions that are very common in practice, for a particular cyclic sequence of robot moves in robotic cells with one or more dual gripper robots, parallel machines and transfer stations.

Productivity Improvement From Using Machine Buffers in Dual-Gripper Cluster Tools

Cluster tools (also referred to as robotic cells) are extensively used in semiconductor wafer fabrication. We consider the problem of scheduling operations in an m -machine cluster tool that produces identical parts (wafers). Each machine is equipped with a unit-capacity input buffer and a unit-capacity output buffer. The machines and buffers are served by a dual-gripper robot. Each wafer is processed on each of the m machines, and the objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes the throughput. We first obtain a tight upper bound on the optimal throughput and then use this bound to obtain an asymptotically optimal sequence under conditions that are common in practice. Next, we quantify the improvement in productivity that can be realized from the use of unit-capacity input and output buffers at the machines. Finally, we illustrate our analysis on cluster tools with realistic parameters, based on our work with a Dallas-based semiconductor equipment manufacturer.

Integrated production and distribution scheduling with a perishable product

This research focuses on the practical problem of a perishable product that must be produced and distributed before it becomes unusable but at minimum cost. The problem has some features of the integrated production and distribution scheduling problem in that we seek to determine the fleet size and the trucks’ routes subject to a planning horizon constraint. In particular, this research differs because the product has a limited lifetime, the total demand must be satisfied within a planning horizon, multiple trucks can be used, and the production schedule and the distribution sequence are considered. A mixed integer programming model is formulated to solve the problem and, then, heuristics based on evolutionary algorithms are provided to resolve the models.

Throughput optimization in robotic cells with input and output machine buffers: A comparative study of two key models

We consider the problem of scheduling operations in a robotic cell processing a single part type. Each machine in the cell has a one-unit input buffer and a one-unit output buffer. The machines and buffers are served by one single gripper robot. The domain considered is free-pickup cells with additive inter-machine travel time. The processing constraints specify the cell to be a flow shop. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes throughput. Bufferless robotic cells have been studied extensively in the literature. However, the few studies of robotic cells with output buffers at each machine have shown that the throughput can be improved by such a configuration. We show that there is no throughput advantage in providing machine input buffers in addition to output buffers. The equivalence in throughput between the two models has significant practical implications, since the cost of providing additional buffers at each machine is substantial.