Bernard Penz

Lot Sizing with Carbon Emission Constraints

This paper introduces new environmental constraints, namely carbon emission constraints, in multi-sourcing lot-sizing problems. These constraints aim at limiting the carbon emission per unit of product supplied with different modes. A mode corresponds to the combination of a production facility and a transportation mode and is characterized by its economical costs and its unitary carbon emission. Four types of constraints are proposed and analyzed in the single-item uncapacitated lot-sizing problem. The periodic case is shown to be polynomially solvable, while the cumulative, global and rolling cases are NP-hard. Perspectives to extend this work are discussed.

An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints

In this paper, we study the single machine total completion scheduling problem subject to a period of maintenance. We propose an approximation algorithm to solve the problem with a worst case error bound of 3/17. Furthermore, an example is provided to show that the bound is tight. Computational experiments and an analysis are given afterwards.

A bounded dynamic programming approach to schedule operations in a cross docking platform

Cross docking is a logistic technique employed to reduce the inventory holding, order picking, transportation costs as well as the delivery time. Products arriving to the cross dock are unloaded from inbound trailers, possibly reconsolidated with other products arriving from different destinations and loaded into outbound trailers within less than 24h. In this study, we consider a multiple receiving and shipping door cross dock environment. The objective is to find optimal (for reasonably small cross docks) or near optimal (for larger cross docking facilities) scheduling policies which minimizes the total costs related to the transshipment operations at the facility.

Scheduling cross docking operations under full, partial and no information on inbound arrivals

Cross docking is a logistic technique which seeks to reduce the inventory holding, order picking, transportation costs and delivery time. Little attention has been given to the transshipment operations inside a cross dock. In this article, we study the transshipment scheduling problem in a single receiving and a single shipping door cross dock under three scheduling policies: In the first policy, we assume to have complete information on the order of arrivals and the contents of all inbound trucks. The second and the third policies assume the availability of partial and no information on the sequence of upcoming trucks. An optimal graph based model is proposed for the full information case, and a polynomial time algorithm is given. Heuristics are developed for the other two cases. The comparison of the costs associated to each policy helps evaluating the value of information in cross dock scheduling problems.

Sensitivity analysis of scheduling algorithms

Abstract We are interested in this work in studying the performances of static scheduling policies in presence of on-line disturbances. In the general case, the sensitivity of the schedules, i.e., the degradation of the performance of the solution due to the disturbances, is linear in the magnitude of the perturbation. Our main result within this paper is to show that in some scheduling contexts, namely the case of independent tasks, the sensitivity can be guaranteed not to exceed the square root of the magnitude of the perturbation.

Minimizing the makespan in the two-machine no-wait flow-shop with limited machine availability

Abstract This paper deals with the two-machine no-wait flow-shop problem with limited machine availability. In this model, we assume that machines may not always be available, for example because of preventive maintenance. We only consider the deterministic case where the unavailable periods are known in advance. The objective function considered is the maximum completion time (C max ). We prove that the problem is NP -Hard even if only one unavailability period occurs on one single machine, and NP -Hard in the strong sense for arbitrary numbers of unavailability periods. We also provide heuristic algorithms with error bounding analysis.

An experimental study for the selection of modules and facilities in a mass customization context

To design an efficient product family, designers have to anticipate the production process and, more generally, the supply chain costs. But this is a difficult problem, and designers often propose a solution which is subsequently evaluated in terms of logistical costs. This paper presents a design problem in which the product and the supply chain design are considered at the same time. It consists in selecting a set of modules that will be manufactured at distant facilities and then shipped to a plant close to the market for final, customized assembly under time constraints. The goal is to obtain the bill of materials for all the items in the product family, each of which is made up of a set of modules, and specifying the location where these modules will be built, in order to minimize the total production costs for the supply chain. The objective of the study is to analyze both, for small instances, the impact of the costs (fixed and variable) on the optimal solutions, and to compare an integrated approach minimizing the total cost in one model with a two-phases approach in which the decisions relating to the design of the products and the allocation of modules to distant sites are made separately.

Collaboration for a two-echelon supply chain in the pulp and paper industry: the use of incentives to increase profit

In our research, we study the case of a pulp and paper producer who decides to establish a partnership with one buyer. Using two different types of relationship, namely a traditional system without any collaboration scheme and Collaborative Planning, Forecasting and Replenishment, we develop decision models describing the producer and the buyer planning processes. We also identify which approach is more profitable for each actor as well as for the network, based on real costs and parameters obtained from the industrial case. We then test how different incentives can improve the traditional system and provide higher gains for each partner. Our results show that using incentives increases the systems profit by up to 4% if parameters are well defined.

Complexity results and approximation algorithms for the two machine no-wait flow-shop with limited machine availability

The scheduling problems studied in this paper concern a two-machine no-wait flow shop problem with limited machine availability. In this model, we assume that machines may not always be available, for example because of preventive maintenance. We only consider the deterministic case where the unavailable periods are known in advance. The objective function considered is the maximum completion time (Cmax). We prove that the problem is NP-hard even if only one non-availability period occurs on one of machines, and NP-hard in the strong sense for arbitrary numbers of non-availability periods. We also provide heuristic algorithms with error bounding analysis.

The single-item green lot-sizing problem with fixed carbon emissions

We consider in this paper a single-item lot sizing problem with a periodic carbon emission constraint. In each period, the carbon emission constraint defines an upper limit on the average emission per product. Different modes are available, each one is characterized by its own cost and carbon emission parameters. The problem consists in selecting the modes used in each period such that no carbon emission constraint is violated, and the cost of satisfying all the demands on a given time horizon is minimized. This problem has been introduced in Absi et al. (2013), and has been shown polynomially solvable when only unit carbon emissions are considered. In this paper, we extend the analysis for this constraint to the realistic case of a fixed carbon emission associated with each mode, in addition to its unit carbon emission. We establish that this generalization renders the problem NP-hard. Several dominant properties are presented, and two dynamic programming algorithms are proposed. We also establish that the problem can be solved in polynomial time for a fixed number of modes when carbon emission parameters are stationary.