http://repub.eur.nl/res/aut/1790/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/6680/ 1994-12-22T00:00:00Z In this paper we consider a generalization of the Fixed Job Schedule Problem (FJSP) which appears in the aircraft maintenance process at an airport. A number of jobs must be carried out where each job requires processing from a fixed time to a fixed finish time. These jobs must be carried out by a number of machines which are available in specific shifts only. The jobs must be carried out in a non-preemptive way, although at the end of a shift preemption of a job is allowed sometimes. The problem is to choose the number of machines in each of the shifts in such a way that all jobs can be carried out and that the total costs of the machines or the total number of machines are minimum. In this paper we present an analysis of the computational complexity of these problems. We also analyse the worst case behaviour of the preemptive variant versus the non-preemptive variant. http://repub.eur.nl/res/pub/2306/ 1994-11-15T00:00:00Z When jobs have to be processed on a set of identical parallel machines so as to minimize the makespan of the schedule, list scheduling rules form a popular class of heuristics. The order in which jobs appear on the list is assumed here to be determined by the relative size of their processing times; well-known special cases are the LPT rule and the SPT rule, in which the jobs are ordered according to non-increasing and non-decreasing processing time respectively. When all processing times are exactly known, a given list scheduling rule will generate a unique assignment of jobs to machines. However, when there exists a priori uncertainty with respect to one of the processing times, then there will be, in general, several possibilities for the assignment that will be generated once the processing time is known. This number of possible assignments may be viewed as a measure of the sensitivity of the list scheduling rule that is applied. We derive bounds on the maximum number of possible assignments for several list scheduling heuristics, and we also study the makespan associated with these assignments. In this way we obtain analytical support for the intuitively plausible notion that the sensitivity of a list scheduling rule increases with the quality of the schedule produced. http://repub.eur.nl/res/pub/6679/ 1993-01-01T00:00:00Z In this paper we consider a generalization of the Fixed Job Scheduling Problem (FSP) which appears in a natural way in the aircraft maintenance process at an airport. A number of jobs has to be carried out, where the main attributes of a job are: a fixed start time, a fixed finish time and a value representing the priority of the job. For carrying out these jobs a number of machines is available. These machines are available in specific time intervals (shifts) only. A job can be carried out by a machine only if the interval between the start time and the finish time of the job is a subinterval of the shift of the machine. Furthermore, the jobs must be carried out in a non-preemptive way and each machine can be carrying out at most one job at the same time. http://repub.eur.nl/res/pub/6683/ 1992-12-24T00:00:00Z In this paper a generalization of the Fixed Job Scheduling Problem (FSP) is considered, which appears in the aircraft maintenance process at an airport. A number of jobs have to be carried out, where the main attributes of a job are a fixed start time, a fixed finish time and an aircraft type. For carrying out these jobs a number of engineers are available. An engineer is allowed to carry out a specific job only if he has a license for the corresponding aircraft type. Furthermore, the jobs must be carried out in a non-preemptive way and each engineer can be carrying out at most one job at the same time. Within this setting natural questions to be answered ask for the minimum number of engineers required for carrying out all jobs or, more generally, for the minimum total costs for hiring engineers. In this paper a complete classification of the computational complexity of two classes of mathematical problems related to these practical questions is given. Furthermore, it is shown that the polynomially solvable cases of these problems can be solved by a combination of Linear Programming and Network Flow algorithms. http://repub.eur.nl/res/pub/14357/ 1992-01-01T00:00:00Z http://repub.eur.nl/res/pub/1481/ 1992-01-01T00:00:00Z In this paper we present a general framework for shortest path algorithms, including amongst others Dijkstra's algorithm and the A* algorithm. By showing that all algorithms are special cases of one algorithm in which some of the nondeterministic choices are made deterministic, termination and correctness can be proved by proving termination and correctness of the root algorithm. Furthermore, several invariants of the algorithms are derived which improve the insight with respect to the operations of the algorithms. http://repub.eur.nl/res/pub/2310/ 1992-01-01T00:00:00Z We consider the n-period economic lot sizing problem, where the cost coefficients are not restricted in sign. In their seminal paper, H. M. Wagner and T. M. Whitin proposed an O(n[sup 2]) algorithm for the special case of this problem, where the marginal production costs are equal in all periods and the unit holding costs are nonnegative. It is well known that their approach can also be used to solve the general problem, without affecting the complexity of the algorithm. In this paper, we present an algorithm to solve the economic lot sizing problem in O(n log n) time, and we show how the Wagner-Whitin case can even be solved in linear time. Our algorithm can easily be explained by a geometrical interpretation and the time bounds are obtained without the use of any complicated data structure. Furthermore, we show how Wagner and Whitin's and our algorithm are related to algorithms that solve the dual of the simple plant location formulation of the economic lot sizing problem. http://repub.eur.nl/res/pub/6681/ 1991-09-05T00:00:00Z In this paper we consider several generalizations of the Fixed Job Scheduling Problem (FSP) which appear in a natural way in the aircraft maintenance process at an airport: A number of jobs have to be carried out, where the main attributes of a job are: a fixed start time, a fixed finish time, a value representing the job's priority and a job class. For carrying out these jobs a number of machines are available. These machines can be split up into a number of disjoint machine classes. For each combination of a job class and a machine class it is known whether or not it is allowed to assign a job in the job class to a machine in the machine class. Furthermore the jobs must be carried out in a non-preemptive way and each machine can be carrying out at most one job at the same time. Within this setting one can ask for a feasible schedule for all jobs or, if such a schedule does not exist, for a feasible schedule for a subset of the jobs of maximum total value. In this paper we present a complete classification of the computational complexity of two classes of combinatorial problems related this operational job scheduling problem. http://repub.eur.nl/res/pub/2312/ 1991-06-17T00:00:00Z A linear description for the economic lot-sizing problem consisting of exponentially many linear inequalities was given by Barany, Van Roy and Wolsey in 1984. Using this formulation we present a dual algorithm for the economic lot-sizing problem, which is of the same complexity as the Wagner and Whitin dynamic programming algorithm. Besides its use in sensitivity analysis the dual algorithm also provides an alternative proof of the fact that the linear description is complete.