Marie-Claude Portmann

Branch and bound crossed with GA to solve hybrid flowshops

This article deals with an optimal methods for solving a k-stage hybrid flowshop scheduling problem. This problem is known to be NP-hard. In 1991, Brah and Hunsucker proposed a branch and bound algorithm to solve this problem. However, for some medium size problems, the computation time is not acceptable. The aim of this article is to present an improvement of this algorithm. As a matter of fact, we prove that the value of their lower bound (LB) may decrease along a path of the search tree. First of all, we present an improvement of their LB. Then, we introduce several heuristics at the beginning of the search in order to compute an initial upper bound and genetic algorithm (GA) to improve during the search the value of the upper bound. More precisely, our GA takes into account the set of partial decisions made by the branch and bound and builds a series of populations of complete solutions with the aim of improving the upper bound (the best found criterion value corresponding to a complete solution). Experimentation show that the optimality of branch and bound is more often reached and the value of criterion is improved when our improvements are taken into account.

Single machine batch scheduling with resource dependent setup and processing times

Abstract Jobs are processed by a single machine in batches. A batch is a set of jobs processed contiguously and completed together when the processing of all jobs in the batch is finished. Processing of a batch requires a machine setup time common for all batches. Both the job processing times and the setup time can be compressed through allocation of a continuously divisible resource. Each job uses the same amount of the resource. Each setup also uses the same amount of the resource, which may be different from that for the jobs. Polynomial time algorithms are presented to find an optimal batch sequence and resource values such that either the total weighted resource consumption is minimized, subject to meeting job deadlines, or the maximum job lateness is minimized, subject to an upper bound on the total weighted resource consumption. The algorithms are based on linear programming formulations of the corresponding problems.

Permutation flowshop scheduling problems with maximal and minimal time lags

In this paper, we study permutation flowshop problems with minimal and/or maximal time lags, where the time lags are defined between couples of successive operations of jobs. Such constraints may be used to model various industrial situations, for instance the production of perishable products. We present theoretical results concerning two-machine cases, we prove that the two-machine permutation flowshop with constant maximal time lags is strongly NP-hard. We develop an optimal branch and bound procedure to solve the m-machine permutation flowshop problem with minimal and maximal time lags. We test several lower bounds and heuristics providing upper bounds on different classes of benchmarks, and we carry out a performance analysis.

A splitting-up approach to simplify job-shop scheduling problems

In this paper we propose a scheduling algorithm based on splitting up the problem into separate yet linked subproblems. We develop a heuristic algorithm to manage the remaining links between the scheduling subproblems obtained as a result of the splitting process. The complexity of the computation and the performance of the algorithms are examined and numerical examples are given to illustrate these algorithms.

An Efficient Proactive-Reactive Scheduling Approach to Hedge Against Shop Floor Disturbances

We consider the single machine scheduling problem with dynamic job arrival and total weighted tardiness and makespan as objective functions. The machine is subject to disruptions related to late raw material arrival and machine breakdowns. We propose a proactive—reactive approach to deal with possible perturbations. In the proactive phase, instead of providing only one schedule to the decision maker, we present a set of predictive schedules. This set is characterized by a partial order of jobs and a type of associated schedules, here semi-active schedules. This allows us to dispose of some flexibility in job sequencing and flexibility in time that can be used on-line by the reactive algorithm to hedge against unforeseen disruptions. We conduct computational experiments that indicate that our approach outperforms a predictive reactive approach particularly for disruptions with low to medium amplitude.

Some new efficient methods to solve the n/1/ri/ϵTi scheduling problem

Abstract In this paper, we prove a sufficient condition for local optimality to solve the n /1/ r i / ϵT i scheduling problem which is known to be NP-hard. We then define a new dominant subset of schedules on the basis of this condition and propose several new approximate algorithms to construct schedules belonging to this subset. Numerical experiments enable us to compare them with classical approximate algorithms.

Planification de systèmes d'assemblage avec approvisionnements aléatoires en composants

ABSTRACT We are interested in the management of an assembly system. Some components can be used for assembling different products. Each product need several components of various types to be manufactured. Components are ordered to companies which usually cannot guarantee a fix delivery time. In other words, the delivery times are random. The costs to be taken into account are the inventory costs of the components and the backlogging costs of the products. The production capacity is not bounded. A rolling horizon approach, which involves a linear programming model, forecasting and simulation, is used.

Technical note: New results for the capacitated lot sizing problem with overtime decisions and setup times

The capacitated lot sizing problem with overtime and setup times (CLSPOS) consists of planning the lot sizes of multiple families over a planning horizon with the objective of minimizing overtime and inventory holding costs. Each time that an items lot size is positive, capacity is consumed by a setup. Capacity is limited and includes regular time capacity as well as overtime. It is assumed that setups do not incur costs other than lost production capacity and therefore, setups contribute to total costs implicitly via overtime costs whenever capacity bottlenecks occur. The CLSPOS is more complicated than the standard capacitated lot sizing problem (CLSP) which involves explicit setup costs, no capacity consuming setups and only regular time capacity. Here is described a genetic algorithm (GATA) integrated with tabu search (TS) and simulated annealing (SA) to solve CLSPOS. GATA integrates the powerful characteristics of all three search algorithms, GAs, TS and SA. The results are compared with the ones reported in a previous study and demonstrate that GATA outperforms other heuristics.

Optimal testing and repairing a failed series system

We consider a series repairable system that includes n components and assume that it has just failed because exactly one of its components has failed. The failed component is unknown. Probability of each component to be responsible for the failure is given. Each component can be tested and repaired at given costs. Both testing and repairing operations are assumed to be perfect, that is, the result of testing a component is a true information that this component is failed or active (not failed), and the result of repairing is that the component becomes active. The problem is to find a sequence of testing and repairing operations over the components such that the system is always repaired and the total expected cost of testing and repairing the components is minimized. We show that this problem is equivalent to minimizing a quadratic pseudo-boolean function. Polynomially solvable special cases of the latter problem are identified and a fully polynomial time approximation scheme (FPTAS) is derived for the general case. Computer experiments are provided to demonstrate high efficiency of the proposed FPTAS. In particular, it is able to find a solution with relative error ɛ = 0.1 for problems with more than 4000 components within 5 minutes on a standard PC with 1.2 Mhz processor.

Maximization Problems in Single Machine Scheduling

Problems of scheduling n jobs on a single machine to maximize regular objective functions are studied. Precedence constraints may be given on the set of jobs and the jobs may have different release times. Schedules of interest are only those for which the jobs cannot be shifted to start earlier without changing job sequence or violating release times or precedence constraints. Solutions to the maximization problems provide an information about how poorly such schedules can perform. The most general problem of maximizing maximum cost is shown to be reducible to n similar problems of scheduling n−1 jobs available at the same time. It is solved in O(mn+n2) time, where m is the number of arcs in the precedence graph. When all release times are equal to zero, the problem of maximizing the total weighted completion time or the weighted number of late jobs is equivalent to its minimization counterpart with precedence constraints reversed with respect to the original ones. If there are no precedence constraints, the problem of maximizing arbitrary regular function reduces to n similar problems of scheduling n−1 jobs available at the same time.