Single item lot-sizing with non-decreasing capacities

We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lot-sizing problem is polynomially solvable using dynamic programming. When the capacities are non-decreasing, we derive a compact mixed integer programming reformulation whose linear programming relaxation solves the lot-sizing problem to optimality when the objective function satisfies i) and ii). The formulation is based on mixing set relaxations and reduces to the (known) convex hull of solutions when the capacities are constant over time. We illustrate the use and effectiveness of this improved LP formulation on a new test instances, including instances with and without Wagner-Whitin costs, and with both non-decreasing and arbitrary capacities over time.lot-sizing, mixing set relaxation, compact reformulation, production planning, mixed integer programming

Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs

This paper presents a new class of valid inequalities for the single-item capacitated lotsizing problem with step-wise production costs (LS-SW). We first provide a survey of different optimization methods proposed to solve LS-SW. Then, flow cover and flow cover inequalities derived from the single node flow set are described in order to generate the new class of valid inequalities. The single node flow set can be seen as a generalization of some valid relaxations of LS-SW. A new class of valid inequalities we call mixed flow cover, is derived from the integer flow cover inequalities by a lifting procedure. The lifting coefficients are sequence independent when the batch sizes (V) and the production capacities (P) are constant and if V divides P. When the restriction of the divisibility is removed, the lifting coefficients are shown to be sequence independent. We identify some cases where the mixed flow cover inequalities are facet defining. A cutting plane algorithmis proposed for these three classes of valid inequalities. The exact separation algorithmproposed for the constant capacitated case runs in polynomial time. Finally, some computational results are given to compare the performance of the different optimization methods including the new class of valid inequalities.single-item capacitated lot sizing problem, flow cover inequalities, cutting plane algorithm

An integrated model for warehouse and inventory planning

We propose a tactical model which integrates the replenishment decision in inventory management, the allocation of products to warehousing systems and the assignment of products to storage locations in warehousing management. The purpose of this article is to analyse the value of integrating warehouse and inventory decisions. This is achieved by proposing two methods for solving this tactical integrated model which differ in the level of integration of the inventory and warehousing decisions. A computational analysis is performed on a real world database and using multiple scenarios differing by the warehouse capacity limits. Our observation is that the total cost of the inventory and warehousing systems can be reduced drastically by taking into account the warehouse capacity restrictions in the inventory planning decisions, in an aggregate way. Moreover additional inventory and warehouse savings can be achieved by using more sophisticated integration methods for inventory and warehousing decisions

A tighter continuous time formulation for the cyclic scheduling of a mixed plant

Abstract In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides [22], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide quite good feasible solutions quickly

X-ray magnetic circular dichroism in (Ge,Mn) compounds: experiments and modeling

X-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra at the L$_{2,3}$ edges of Mn in (Ge,Mn) compounds have been measured and are compared to the results of first principles calculation. Early \textit{ab initio} studies show that the Density Functional Theory (DFT) can very well describe the valence band electronic properties but fails to reproduce a characteristic change of sign in the L$_{3}$ XMCD spectrum of Mn in Ge$_3$Mn$_5$, which is observed in experiments. In this work we demonstrate that this disagreement is partially related to an underestimation of the exchange splitting of Mn 2$p$ core states within the local density approximation. It is shown that the change in sign experimentally observed is reproduced if the exchange splitting is accurately calculated within the Hartree-Fock approximation, while the final states can be still described by the DFT. This approach is further used to calculate the XMCD in different (Ge,Mn) compounds. It demonstrates that the agreement between experimental and theoretical spectra can be improved by combining state of the art calculations for the core and valence states respectively.Comment: 8 page

Transcriptional Profiling of Plasmodium falciparum Parasites from Patients with Severe Malaria Identifies Distinct Low vs. High Parasitemic Clusters

Background: In the past decade, estimates of malaria infections have dropped from 500 million to 225 million per year; likewise, mortality rates have dropped from 3 million to 791,000 per year. However, approximately 90% of these deaths continue to occur in sub-Saharan Africa, and 85% involve children less than 5 years of age. Malaria mortality in children generally results from one or more of the following clinical syndromes: severe anemia, acidosis, and cerebral malaria. Although much is known about the clinical and pathological manifestations of CM, insights into the biology of the malaria parasite, specifically transcription during this manifestation of severe infection, are lacking. Methods and Findings: We collected peripheral blood from children meeting the clinical case definition of cerebral malaria from a cohort in Malawi, examined the patients for the presence or absence of malaria retinopathy, and performed whole genome transcriptional profiling for Plasmodium falciparum using a custom designed Affymetrix array. We identified two distinct physiological states that showed highly significant association with the level of parasitemia. We compared both groups of Malawi expression profiles with our previously acquired ex vivo expression profiles of parasites derived from infected patients with mild disease; a large collection of in vitro Plasmodium falciparum life cycle gene expression profiles; and an extensively annotated compendium of expression data from Saccharomyces cerevisiae. The high parasitemia patient group demonstrated a unique biology with elevated expression of Hrd1, a member of endoplasmic reticulum-associated protein degradation system. Conclusions: The presence of a unique high parasitemia state may be indicative of the parasite biology of the clinically recognized hyperparasitemic severe disease syndrome

A tighter continuous time formulation for the cyclic scheduling of a mixed plant

In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides [22], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide quite good feasible solutions quickly