Gerd Finke

An Integrated Model for an Industrial Production–Distribution Problem

In this paper, we are interested in a multi-facility, multi-product and multi-period industrial problem. In this problem, both production and distribution costs are significant and they are inter-related. Therefore they should be considered simultaneously in a cost optimization problem. We model this combined production–distribution problem in the form of a network flow problem with relatively few additional 0–1 variables describing the linking constraints between periods. Computational experiments show that the real size problems we encountered can be solved in reasonable time using commercial linear programming codes like CPLEX.

Scheduling tasks and vehicles in a flexible manufacturing system

Due to their increasing applicability in modern industry, flexible manufacturing systems (FMSs), their design, and their control have been studied extensively in the recent literature. One of the most important issues that has arisen in this context is the FMS scheduling problem. This article is concerned with a new model of an FMS system, motivated by the practical application that takes into account both machine and vehicle scheduling. For the case of a given machine schedule, a simple polynomial-time algorithm is presented that checks the feasibility of a vehicle schedule and constructs it whenever one exists. Then a dynamic programming approach to construct optimal machine and vehicle schedules is proposed. This technique results in a pseudopolynomialtime algorithm for a fixed number of machines.

Cycles and permutations in robotic cells

We consider a robotic cell, consisting of a flow-shop in which the machines are served by a single central robot. We concentrate on the case where only one part type is produced and analyze the validity of the so-called one-cycle conjecture by Sethi, Sriskandarajah, Sorger, Blazewicz and Kubiak. This conjecture claims that the repetition of the best one-unit production cycle will yield the maximum throughput rate in the set of all possible cyclic robot moves. We present a new algebraic approach, unifying the former rather tedious proofs for the known results on pyramidal one-cycles and two- and three-machine cells. In this framework, counterexamples will be constructed, showing that the conjecture is not valid for four and more machines. We first present examples for a general four-machine cell, for which the two-unit production cycles dominate the one-unit cycles. Then we consider in particular the so-called regular cells, where all machines are equidistant, since the one-cycle conjecture has originally been formulated for this case. Here, we prove that for four-machine cells, two-unit production cycles are still dominated by one-unit production cycles. Then we describe a counterexample with a three-unit production cycle, thus, settling completely the one-cycle conjecture.

New trends in machine scheduling

Abstract This review is concerned with new directions in deterministic machine scheduling theory. We study: resource constrained scheduling, scheduling tasks that require more than one machine at a time, scheduling with nonlinear speed-resource alloted functions, and scheduling in flexible manufacturing systems. The two features that distinguish the above problems are the use of resources in addition to the machines and new models for the processing of tasks. The study of these models was primarily motivated by their practical importance. In each case, we overview the existing results and present solution strategies for particularly chosen problems.

On A Conjecture About Robotic Cells: New Simplified Proof For The Three-Machine Case

AbstractWe consider a robotic cell, consisting of a flow-shop in which the machines are served by a single central robot. We concentrate on the case where only one part type is produced and want to analyze the conjecture of Sethi, Sriskandarajah, Sorger, Blazewicz and Kubiak. This well-known conjecture claims that the repetition of the best one-unit production cycle will yield the maximum throughput rate in the set of all possible robot moves. The conjecture holds for two and three machines, but the existing proof by van de Klundert and Crama for the three-machine case is extremely tedious.We adopt the theoretical background developed by Crama and van de Klundert. Using a particular state graph, the k-unit production cycles are represented as special paths and cycles for which general properties and bounds for the m-machine robotic cell can be obtained. By means of these concepts, we shall give a concise proof for the validity of the conjecture for the three-machine case.

Minimizing mean weighted execution time loss on identical and uniform processors

Abstract The problem of minimizing mean weighted execution time loss was formulated by the present author in 1984; there the preemptive case for identical as well as for a fixed number of uniform processors was solved via a linear programming approach. In this paper, we propose a strongly polynomial algorithm based on a network flow technique, which minimizes the above criterion for an arbitrary number of identical as well as uniform processors. The upper bounds on the number of preemptions in both cases are also given.

Complexity of one-cycle robotic flow-shops

We study the computational complexity of finding the shortest route the robot should take when moving parts between machines in a flow-shop. Though this complexity has already been addressed in the literature, the existing attempts made crucial assumptions which were not part of the original problem. Therefore, they cannot be deemed satisfactory. We drop these assumptions in this paper and prove that the problem is NP-hard in the strong sense when the travel times between the machines of the cell are symmetric and satisfy the triangle inequality. We also impose no restrictions on the times of robot arrival at and departure from machines as it is the case in the related, but different, hoist scheduling problem. Our results hold for processing times equal on all machines in the cell. However, the equidistant case for equal processing times can be solved in O(1) time.

Merging and Sorting Applied to the Zero-One Knapsack Problem

Branch-and-bound algorithms are adequate for the solution of a wide range of 0-1 knapsack problems. It is shown that the simplest method of branching is as good as any. However, problems with highly correlated large weights and values quickly become unsolvable in a reasonable time. This paper develops algorithms that are aimed specifically at the hardest possible examples. The new methods use merging and sorting ideas and require a moderate amount of additional memory space. They are, however, faster by factors far in excess of 1,000 in many cases, thereby extending considerably the range of practically solvable 0-1 knapsack problems.

Vehicle scheduling in two-cycle flexible manufacturing systems

Flexible manufacturing systems (FMSs) have received much attention recently due to their importance for designing modern factories producing small lots of complicated products to specific customer orders. One of the most important problems arising in this context is scheduling parts on machines and, connected with it, an appropriate routing of automated guided vehicles (AGVs) ensuring on-time delivery of parts to particular machines. This paper generalizes a new approach to model flexible manufacturing systems, motivated by the practical application. The objective is to develop algorithmic procedures that integrate the production schedules with the routing of automated guided vehicles in FMS. The transportation system of the FMS model consists of two cycles, leading to two separate machining centers. These cycles are interconnected, with a common stretch at the inspection and retrieval area, so that the AGVs can switch between the cycles to obtain a higher routing flexibility. In order to keep a complex system simple, a routing strategy is proposed that maintains a steady, regular, cyclic flow of all available vehicles. We develop, by means of a number theoretic concept, vehicle schedules that are collision-free for any cycle sequence. For a given production plan, we then present an efficient dynamic programming approach to check whether or not the required raw material (for machining parts) can be supplied in time to the various NC-machines. This method also solves an open problem in processor scheduling where a set of jobs with a restricted number of distinct processing times is to be scheduled before deadlines on m parallel processors.

Scheduling with resource management in manufacturing systems

Abstract Modern manufacturing technology has made it possible to concentrate the total production process on very few NC-machines. In the metal cutting industry, mechanical parts are often produced on a single machine, as a sequence of machining operations requiring different tools. In this way, time consuming set-ups and transfers are avoided. However, the required resources, like tools, fixtures and pallets, have greatly increased in varieties and numbers. This increase imposes difficult control and management problems. A new problem area seems to emerge with this development; namely the need for techniques to solve simultaneously two linked scheduling problems: the part-machine scheduling problem and the resource alloction and sequencing problem. It is the objective of this paper to expose the problems arising in connection with these two-level nested scheduling problems and describe some concrete models and solution procedures.