Nathalie Sauer

Perturbation analysis for continuous and discrete flow models: a study of the delivery time impact on the optimal buffer level

In this paper, a manufacturing system composed of a single-product machine, a buffer and a stochastic demand is considered. Two models are presented: continuous and discrete flow models including constant delivery times, machine failures and random demands. The objective is to determine the value of the optimal buffer level, for a hedging point policy which minimises the total average cost function. The cost function is the sum of inventory, transportation and lost sales costs. Infinitesimal perturbation analysis is used for optimisation of the failure-prone manufacturing system. The trajectories of buffer level are studied for the continuous and discrete cases and the infinitesimal perturbation analysis estimators are evaluated. These estimators are shown to be unbiased and then they are implemented in an optimisation algorithm which determines the optimal buffer level in the presence of constant delivery time. Numerical results are presented for continuous and discrete flow models and then compared in order to evaluate the application of the infinitesimal perturbation analysis on the discrete flow model.

NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract

In this paper, we study the single-item lot sizing problem under a capacity reservation contract. A manufacturer is replenished by an external supplier with batch deliveries and a certain capacity is reserved at the supplier level with an advantageous cost. In addition to the classical ordering and inventory holding costs, for each batch ordered under the reserved capacity a fixed cost per batch is incurred; and for batches exceeding this capacity a higher fixed cost per batch is paid, typically through the purchase from the spot market. We identify various NP-hard cases, propose a pseudo-polynomial time dynamic programming algorithm under arbitrary parameters, show that the problem admits an FPTAS and give polynomial time algorithms for special cases. We finally state a list of open problems for further research.

Dynamic Models for Green Logistic Networks Design

Abstract Nowadays, the relationship industry-environment plays a significant role in business and supply chain management. Due to legislation pressures, consumer awareness and economic interest in used products, the concept of Green Supply Chain Management was born, with Reverse Logistics as principal driver. Designing a green logistic network consists in integrating environmental aspects in strategic decision making towards the location of logistic facilities. In this work mixed integer linear programming models are proposed for the design of a reverse logistic network. The innovative aspects of this study are: the assumption of a dynamic, multi-product environment and the uncertainty of used products returns. CPLEX software is used to formulate and solve the models. A results analysis is presented as well as possible research avenues.

Online assignment strategies for emergent, urgent and work-in-cases surgeries in an operating theatre

Optimization issues in Heath care have become noticeably important keen interest, for more than three decades, for the operational research community. The planning of operating rooms is a difficult process. Its real complexity results from various sources of variability. In this work, we consider one of the key sources of variability, specifically emergencies. Due to non-elective surgeries arrival, the operating room schedule has to be adjusted. Thus, need for a decision support tool, guiding the operating room manager, to handle this unpredictable flow of patients, arises. The main contribution of this work is to provide online assignment strategies, taking into account three non-elective patients categories. The proposed assignments are riskless on patients health. According to the non-elective surgery category, the proposed adjusted schedule minimizes different criteria, such as patients waiting time, deviation from the scheduled start time of a surgery and the amount of resulting overtime.

Mathematical model and lower bounds for multi stage jobshop scheduling problem with special blocking constraint

Abstract This paper deals with multi stage jobshop scheduling problem. At each stage, either a fix or a variable number of identical parallel machines are available to execute jobs operations. As often in industrial environment, no space is available between machines, a specific blocking constraint is taken into account. A linear integer mathematical model is proposed and executed in XPress-MP optimization software to solve short size instances of this problem and to validate proposed model. In order to be able to evaluate future heuristics solutions quality, four lower bounds are proposed, computed and evaluated with benchmark for symmetric and asymmetric machines repartition cases.

Dispersion optimisation using a genetic algorithm

The presented works concern the traceability phenomenon implementation within the production organisation, particularly in the field of raw materials management in the food industry. This project aims to minimise the raw materials dispersion in the manufactured products. We seek to solve the problem of raw materials allocation into finished products, in order to minimise its dispersion and moreover, the products recall if needed. The dispersion criteria are afterwards used to determine productions criticality in terms of sanitary risk, from which it is possible to optimise the processes of picking and dispatching. The final objective is to reduce the number of recalls in case of a crisis using the traceability information and the decision making tools. To solve the first part of the problem, a genetic algorithm is proposed.