The multi-item capacitated lot-sizing problem with setup times and shortage costs

We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixed integer mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities based on a generalization of Miller et al. [A.J. Miller, G.L. Nemhauser, M.W.P. Savelsbergh, On the polyhedral structure of a multi-item production planning model with setup times, Mathematical Programming 94 (2003) 375–405] and Marchand and Wolsey [H. Marchand, L.A. Wolsey, The 0–1 knapsack problem with a single continuous variable, Mathematical Programming 85 (1999) 15–33] results. We also describe fast combinatorial separation algorithms for these new inequalities. We use them in a branch-and-cut framework to solve the problem. Some experimental results showing the effectiveness of the approach are reported.     

A note on the extensional viscosity of elastic liquids under strong flows

In this article a parametric study based on a balance between viscous drag and restoring Brownian forces is used in order to construct a nonlinear dumbbell model with a finite spring and a drag correction for a dilute polymer solution. The constitutive equations used are reasonable approximation for describing flows of very dilute polymer solutions such as those used in turbulent drag reduction. We investigate the response of an elastic liquid under extensional flows in order to explore the roles of a stress anisotropy and of elasticity in strong flows. It is found that for low Reynolds numbers, the extensional viscosity of a dilute polymer solution is governed by two parameters: a Deborah number representing the importance of the elasticity on the flow and the macromolecule extensibility that accounts for the viscous anisotropic effects caused by the macromolecule orientation. Two different asymptotic regimes are described.The first corresponds to an elastic limit in which the extensional viscosity is a function of the Deborah number and the particle volume fraction. The second is an anisotropic regime with the extensional viscosity independent of Deborah number but strongly dependent on macromolecule aspect ratio. The analysis may explain from a phenomenological point of view why few ppms of macromolecules of high molecule weight or a small volume fraction of long fibres produce important attenuation of the pressure drop in turbulent flows. On the basis of our analysis it is seen that the anisotropic limit of the extensional viscosity caused by extended polymers under strong flows should play a key role in the attenuation of flow instability and in the mechanism of drag reduction by polymer additives.     

Vehicle routing problems with multiple trips

This paper presents a survey on the multi-trip vehicle routing problem (MTVRP) and on related routing problems where vehicles are allowed to perform multiple trips. The first part of the paper focuses on the MTVRP. It gives an unified view on mathematical formulations and surveys exact and heuristic approaches. The paper continues with variants of the MTVRP and other families of routing problems where multiple trips are sometimes allowed. For the latter, it specially insists on the motivations for having multiple trips and the algorithmic consequences. The expected contribution of the survey is to give a comprehensive overview on a structural property of routing problems that has seen a strongly growing interest in the last few years and that has been investigated in very different areas of the routing literature.     

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.     

Vehicle routing problems with multiple trips

This paper presents a survey on the multi-trip vehicle routing problem (MTVRP) and on related routing problems where vehicles are allowed to perform multiple trips and corresponds to the article by Cattaruzza et al. (4OR 14(3):223–259, 2016). The first part of the paper focuses on the MTVRP. It gives an unified view on mathematical formulations and surveys exact and heuristic approaches. The paper continues with variants of the MTVRP and other families of routing problems where multiple trips are sometimes allowed. For the latter, it specially insists on the motivations for having multiple trips and the algorithmic consequences. The expected contribution of the survey is to give a comprehensive overview on a structural property of routing problems that has seen a strongly growing interest in the last few years and that has been investigated in very different areas of the routing literature.     

Models and methods for capacitated lot-sizing problems

This is a summary of the author’s PhD thesis supervised by Philippe Chrétienne and Safia Kedad-Sidhoum and defended in December 2005 at the Université Pierre et Marie Curie (Paris VI). The thesis is written in French and is available from . This work mainly deals with multi-item capacitated lot-sizing problems with setup times, shortages on demand and safety stock deficit costs. We propose a new mathematical model that includes these new constraints. Three solution approaches are considered: branch-and-cut, Lagrangean relaxation and MIP-based heuristics approaches. Experimental results showing the effectiveness and the limit of each approach are presented. This work was financed by the ANRT and DynaSys S.A.     

Simultaneous Determination of Artesunate and Amodiaquine in Fixed-Dose Combination by a RP-HPLC Method with Double UV Detection: Implementation in Interlaboratory Study Involving Seven African National Quality Control Laboratories

The fixed-dose combination artesunate (AS)–amodiaquine (AQ) is one of the most widely used treatments for uncomplicated falciparum malaria. It is currently proposed to the inclusion in the model list of essential medicines of World Health Organization and has been recently prequalified. Until now, no satisfactory method for the simultaneous determination of the two active ingredients had been available. Thus, a reversed phase high performance liquid chromatography for the quantitative determination of AQ and AS was developed and validated. Chromatography was performed using an end-capped octadecylsilyl silica gel column (100?×?4.6?mm, 3?μm) with a binary gradient using aqueous phase containing potassium dihydrogen phosphate (10?mM) and acetonitrile. Taking into consideration the physico-chemical characteristics of the two compounds related to their ionization, the use of a counter ion was necessary to ensure the retention of AQ in a reversed phase system simultaneously to AS. Thus, aqueous mobile phase was adjusted to pH 3.0 and the chosen counter ion was sodium 1-octanesulfonate (100?mM). In these conditions, the retention times were about 4?min for AQ and 10?min for AS with UV detection at 300 and 210?nm, respectively. Method was then validated according to ICH guideline (specificity/linearity/accuracy/precision) and potential interferences with excipients and degradation products were checked. It has also been used for an interlaboratory study involving seven African National Quality Control Laboratories and Afssaps (Agence fran?aise de sécurité sanitaire des produits de santé) laboratory. The results demonstrate that this rapid and simple method can be easily used by official laboratories for routine control, market survey and for the detection of potential substandard medicines which are very frequent in African countries.     

Instability of elastic bodies

The study of the equilibrium of systems constitutes an important chapter of applied mechanics. Since Euler’s works on beam buckling, in 1774, many eminent specialists studied the problem of the elastic instability of structures.An examination of many works published in this field shows a large number of approaches or criteria adopted by various authors. The objective of this study is to show through a classical example the link between the different approaches to provide a multi-level basis and to propose a valid global approach for conservative as well as nonconservative systems.     

Modeling of <Superscript>226</Superscript>Ra behavior in a Spanish estuary affected by the phosphate industry

The Odiel and Tinto rivers, southwest Spain, form a fully mixed estuary. An industrial area that includes a complex dedicated to the production of phosphate fertilizers is located by the Odiel River. This complex released phosphogypsum wastes directly to the Odiel River and also disposed them on open air piles located by the Tinto River. Due to new EU regulations, wastes are not directly released to the Odiel from 1998 on, although they are still disposed on the open air piles. The behavior of ²²⁶Ra in a system like this estuary is complex, since radionuclides are affected by tidal actions and interactions with sediments through adsorption/desorption reactions and erosion/deposition processes. A numerical 2D depth-averaged model of the estuary has been developed, including processes mentioned above. It has been applied to reproduce experimental data measured after a release from the industrial complex in the Odiel River and after an accidental release in the Tinto River from the gypsum piles. The model has also been applied to simulate the self-cleaning process observed in the estuary after the direct releases from the fertilizer complex were stopped.