A genetic algorithm for multi-level, multi-machine lot sizing and scheduling

This contribution introduces a mixed-integer programming formulation for the multi-level, multi-machine proportional lot sizing and scheduling problem. It also presents a genetic algorithm to solve that problem. The efficiency of that algorithm is due to an encoding of solutions which uses a two-dimensional matrix representation with non-binary entries rather than a simple bitstring. A computational study reveals that the proposed procedura works amazingly fast and competes with a tabu search approach that has recently been published

Balancing u-shaped assembly lines heuristically

While balancing straight assembly lines is a well-studied problem, the Situation where the assembly line has a U-shaped Iayout is a still emerging research field. The advantage of these lines is that workers may simply turn around to operate at two legs of the line. Hence, there is an additional degree of freedom for assigning Operations to stations. This bears the hope that U-lines are more efficient than straight lines. Since work on this NP-hard problem has mainly focused on exact algorithms, we study priority rule heuristics. We adapted 16 priority rules which have been applied to the straight line case before and examine their Performance with a computational study

Zum Problem der taktisch-operativen Entscheidung zwischen Eigen- oder Fremdfertigung

Die Entscheidung zwischen Eigenerstellung oder Fremdbezug bestimmter Erzeugnisse wird in der Betriebswirtschaftslehre traditionell anhand kostenorientierter Kriterien gefällt, die die Mehrkosten des Fremdbezugs betrachten. In diesem Beitrag wurde gezeigt, daß dieses Entscheidungskriterium nicht hinreichend ist, um realisierbare Produktionspläne zu garantieren. Darüber hinaus konnte gezeigt werden, daß eine ganzheitliche Betrachtung von Fremdbezugsund Produktionskosten zu insgesamt kostengünstigeren Lösungen fuhrt. Ein gemischt-ganzzahliges Modell präzisiert erstmals dieses Problem. Lösungsverfahren, die auf bekannten Methoden aus der Literatur basieren, liegen auf der Hand.Make-or-buy decisions are traditionally made on the basis of cost-oriented criteria which measure the additional expenses when items are bought instead of being self-produced. This contribution turned out, that this is not sufficient to guarantee feasible production plans. Fur-thermore, it has been shown that an overall point of view that simultaneously concerns about prices and production costs does indeed decrease total costs. For the first time in literature, a mixed-integer model is given to provide a precise definition of the problem. Moreover, hints are given to construct Solution approaches which are based on already available methods

Lagrangean relaxation for scheduling projects under resource constraints to maximize the net present value

Resource-constrained project scheduling under a net present value objective attracts growing interest. Because this is an NP-hard problem, it is unlikely that optimum solutions can be computed for large instances. Thus, heuristics have become a popular research field. Up to now, however, tight upper bounds have not been proposed. Therefore, most researchers evaluate their heuristics on the basis of a best known lower bound, but it is unclear how good the performance really is. With this contribution we close this gap and derive tight upper bounds on the basis of a Lagrangean relaxation of the resource constraints. We also use this approach as a basis for a heuristic and show that our heuristic as well as the cash flow weight heuristic proposed by Baroum and Patterson yield solutions very close to the optimum result. Furthermore, we discuss the proper choice of a test-bed, and, by reviewing the literature, emphasize that discount rates must be carefully chosen to give realistic instances

Standardization in information systems

On a very abstract level, an information system consists of a set of system elements which communicate with each other. Communication is an unproductive operation, so the time needed to communicate data should be kept as short as possible and, to put it in monetary terms, the opportunity costs for communication should be kept small. Now, communicating data is more than just transmitting it, but it consists in large parts of converting data structures that are used by one system element into data structures that are used by another system element. Such conversion can be avoided, if the system elements use a common standard of data structures. Since establishing a standard at a system element incurs standardization costs, a decision maker has to check, if the cost savings gained by standardized communication outweigh the costs for installing the standard. In a recent paper, it is claimed that this so-called standardization problem is an NP-hard optimization problem. We will demonstrate that this is not true, but in fact the standardization problem can be solved in polynomial time by solving a minimum cut problem

Minimal investment budgets for flow line configuration

A flow line consists of a sequence of work places (or stations) through which one or more producta (or models) move one-way in order to be processed. Each model requires specific Operations which must be performed in a predefined Order. To be able to do so, the stations must be equipped with machines, robots, and workers having a certain skill such that it is guaranteed that each model passing through the system can be completely processed. The number of stations and the equipment of these stations is called the configuration of the flow line. In this paper we deal with the NP-hard problem of finding a configuration such that the net present value of cash outflows for installing and maintaining the flow line is minimized. As a special case, minimizing the number of stations is treated as well. Lower bounds are derived using column generation. Also, two heuristics are presented. One heuristic is based on the result of the column generation procedura while the other is adapted from the so-called majority merge heuristic. A computational study proves that the feasible Solution obtained on the basis of column generation requires a decidedly lower investment budget

Improved lower bounds for the proportional lot sizing and scheduling problem

Where standard MLP-solvers fail to compute optimum objective function values for certain MLP-model formulations, lower bounds may be used as a point of reference for evaluating heuristics. In this paper, we compute lower bounds for the multi-level proportional lot sizing and scheduling problem with multiple machines (PLSP-MM). Four approaches are compared: Solving LP-relaxations of two different model formulations, solving a relaxed MLP-model formulation optimally, and solving a Lagrangean relaxation. Keywords

Proportional lot sizing and scheduling: Some extensions

This contribution generalizes the work of Drexl and Haase about the so-called proportional lot sizing and scheduling problem which was published in 1995. While the early paper considers single-level cases only, the paper at hand describes multi-level problems. 1t provides mixed-integer programs for several important extensions which differ in the allocation of resources. A generic solution method is presented and, following the preceding paper, a randomized regret based sampling method is tested. A computational study proves that, even for the multi-level case which is far more complex than the single-level problem, promising results are gained

A cellular automaton based heuristic for multi-level lot sizing and scheduling

Cellular automata were used to model and to simulate phenomena in the area of physics, biology and medicine. In this paper it is now shown how the idea of cellular automata can be applied to optimization problems as well. As an example a cellular automaton is used as a basis for solving multi-level lot sizing and scheduling problems to suboptimality. We will furthermore give an outline of a proof that any genetic algorithm can be interpreted as a cellular automaton

Minimizing total weighted completion times subject to precedence constraints by dynamic programming

In this paper we present a polynomial time dynamic programming algorithm for solving a scheduling problem with a (total) weighted completion time objective function where the weights are activity- and time-dependent. We highlight application areas for this type of problem to underscore the relevance of it. A computational study proves that large instances with up to 120 activities can be solved