Fabien Chauny

Probabilistic satisfiability with imprecise probabilities

Abstract Treatment of imprecise probabilities within the probabilistic satisfiability approach to uncertainty in knowledge-based systems is surveyed and discussed. Both probability intervals and qualitative probabilities are considered. Analytical and numerical methods to test coherence and bound the probability of a conclusion are reviewed. They use polyhedral combinatorics and advanced methods of linear programming.

A two-phase heuristic for strip packing: Algorithm and probabilistic analysis

The strip packing problem consists in laying out a specified list of rectangular pieces on a rectangular strip of fixed width but infinite length, in such a way as to minimized the length of strip used. We present a novel heuristic algorithm for this problem, based on a two-phase approach: the strategic and the tactical; the former has a global view of the problem and proposes a list of patterns to the latter, which in turn is in charge of actually laying out these patterns. The strategic module is based on a linear programming relaxation of the problem, whereas the tactical module is a recursive algorithm based on repeated knapsack operations. The performance of the algorithm is analyzed through a probabilitic analysis on its relative deviation from the (unknown) optimal solution; the deviation is found to converge to zero as problem size increases under some conditions on the problem data.

Sequencing Punch Operations In A Flexible Manufacturing Cell A Three-Dimensional Space-Filling Curve Approach

AbstractA Travelling Salesman Problem in a three-dimensional spatial domain js associated with a sclieduling problem encountered in a flexible manufacturing cell including a computer-controlled punching machine. The heuristic recently proposed by Bartholdi and Platzman, which uses a space-filling curve as a quick way to organize a tour of a set of locations to visit in a unit square, is tested and generalized to the spatial domain describing the punch operations. A new recursive procedure is proposed for the construction of open space-filling curves in the unit cube and in a parallelopiped. Numerical experimentations show that the 3-dimensional space-filling curve heuristic becomes attractive when the number of punches executed by each tool is relatively small and when the turret rotation speed is relatively high.

Dynamic programming solution to the stochastic multiple lot dispatching in an FMS

The production scheduling problem considered is related to the planning of operations of a flexible manufacturing cell composed of a punch press and a shear that produce parts from metal plates. A stochastic control problem is identified, to optimize the expected discounted cost of the system. The control consists in dispatching n bins to a processor unit which can process only one bin at a time. A dynamic programming approach is used, and numerical techniques are applied for the solution of the two-bin case. Numerical results are presented and discussed.<<ETX>>

Lp-Based Method For The Multi-Sheet Cutting Stock Problem

AbstractThe rectangular cutting-stock problem consists in laying out a specified list of rectangular pieces on a minimum number of rectangular sheets. A pattern is a way to put some rectangles from the list on a sheet. The heuristic presented in this paper associates to each pattern a variable equal to the number of times the pattern is selected, and then tries to minimize the sum of the variables. Constraints are used to insure that all rectangles from the list are laid out. The linear relaxation of a reduced problem is considered and solved, and the result is then rounded off according to a special process. The solution can then be improved via an adapted branch and bound procedure. The heuristic is tested on a number of real problems arising in the metal industry, and evaluated using lower and upper bounds.

Nursing care demand prediction based on a decomposed semi-markov population model

The semi-markovian population model introduced by Kao for the planning of progressive care hospitals is adapted to the prediction of nursing care demand at the level of a care unit in a general hospital. Assuming a feedback admission policy which refills the unit as soon as discharges occur, it is shown that the care unit can be decomposed into B independent subsystems corresponding to each of the B beds in the unit. For each bed the semi-Markov model permits the computation of the expected care demand and its variance for each of the seven forthcoming days. The model permits also the prediction of admissions of new patients. A prediction formula can thus be obtained where the expected care demand is expressed as a linear function of the expected number of admissions in the forthcoming days. Finally this methodology is illustrated on real data obtained in the gynaecology department of the Montreal Jewish General Hospital.

A Class of Asymptotically Optimal Strip-Packing Heuristics

The strip-packing problem consists in laying out a specified list of rectangular pieces on a rectangular strip of infinite length, in such a way as to minimize the length of strip used. We present a novel heuristic algorithm for this problem, based on a two-phased approach: the strategic and the tactical; the former has a global view of the problem and proposes a list of patterns to the latter, which in turn is in charge of actually laying out these patterns. The strategic module is based on a linear programming relaxation of the problem, whereas the tactical module is a recursive algorithm based on repeated knapsack operations. The performance of the algorithm is analyzed through a probabilistic analysis on its relative deviation from the (unknown) optimal solution; the deviation is found to converge to zero as problem size increases under some conditions on the problem data.

Clamps positioning and optimal holding positions in a DNC punch press

A process planning problem typically encounted in flexible manufacturing systems (FMS) treating laminated material (e.g. metal sheets) is modeled and solved. In such production systems, computer-controlled clamps hold the material on a work table. Sheet repositioning represents an important proportion of the processing time. Models are developed that give, under various operational conditions, a minimal set of repositionings. The first formulation of the model calls for a medium-size mixed-integer programming problem. In a subsequent reformulation, the real-life problem is reduced to a set of simpler linear programming problems. Illustrations of the method, as currently implemented on a FMS, are provided. >

Clamps positioning and optimal holding positions in a FMS

A process planning problem typically encountered in flexible manufacturing systems treating laminated material (e.g. metal sheets) is modelled and solved. In such production systems computer controlled clamps hold the material on a work table. Sheet repositioning represents an important proportion of the processing time. The models developed in this paper give, under various operational conditions, a minimal set of repositionings. The first formulation of the model calls for a medium-size mixed-integer programming problem. In a subsequent reformulation, the real life problem is reduced to a set of simpler linear programming problems. Illustrations of the method, as currently implemented on a FMS are provided.