Optimal workforce assignment to operations of a paced assembly line

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation’s processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.     

Near-Boundary Asymptotics for Correlation Kernels

We discuss asymptotic formulas for the correlation kernel corresponding to a (more or less) general potential Q in the plane. If K _n is such a kernel, there is a known asymptotic formula K _n (z,z)=nΔQ(z)+B ₁(z)+n ^?1 B ₂(z)+? valid for z in the interior of a certain compact set known as the “droplet” corresponding to Q (on which ΔQ>0). On the other hand, if z is in the exterior of the droplet, K _n (z,z) converges to zero exponentially in n. Results of this type are useful in random matrix theory and conformal field theory; they have recently been used to prove the Gaussian field convergence in the interior of the droplet for fluctuations of eigenvalues of random normal matrices. To be able to extend such results beyond the interior, it becomes necessary to have a certain uniformity of estimates as z approaches the boundary either from the interior or from the exterior. Such estimates have to our knowledge hitherto not been known on a rigorous level. This note intends to fill this gap. We will consider applications in later publications. Our treatment of the (interior) asymptotics relies in an essential way on previous work due to Berman, Berndtsson, and Sjöstrand (Ark. Mat. 46, 2008), and Berman (Indiana Univ. Math. J. 58, 2009). We hope that this note can to some extent be regarded as a contribution to that work.     

Hydrogeochemical modeling for groundwater management in arid and semiarid regions using MODFLOW and MT3DMS: A case study of the Jeffara of Medenine coastal aquifer,South-Eastern Tunisia

The study of water quality and the quantification of reserves and their variations according to natural and anthropogenic forcing is necessary to establish an adequate management plan for groundwater resources. For this purpose, a modeling approach is a useful tool that allows, after calibration phase and verification of simulation, and under different scenarios of forcing and operational changes, to estimate and control the groundwater quantity and quality. The main objective of this study is to collect all available data in a model that simulates the Jeffara of Medenine coastal aquifer system functioning. To achieve this goal, a conceptual model was constructed based on previous studies and hydrogeological investigations. The regional groundwater numerical flow model for the Jeffara aquifer was developed using MODFLOW working under steady-state and transient conditions. Groundwater elevations measured from the piezometric wells distributed throughout the study area in 1973 were selected as the target water levels for steady state (head) model calibration. A transient simulation was undertaken for the 42 years from 1973 to 2015. The historical transient model calibration was satisfactory, consistent with the continuous piezometric decline in response to the increase in groundwater abstraction. The developed numerical model was used to study the system's behavior over the next 35 years under various constraints. Two scenarios for potential groundwater extraction for the period 2015–2050 are presented. The predictive simulations show the effect of the increase of the exploitation on the piezometric levels. To study the phenomenon of salinization, which is one of the most severe and widespread groundwater contamination problems, especially in coastal regions, a solute transport model has been constructed by using MT3DMS software coupled with the groundwater flow model. The best calibration results are obtained when the connection with the overlying superficial aquifer is considered suggesting that groundwater contamination originates from this aquifer. Recommendations for water resource managers

• The results of this study show that Groundwater resources of Jeffara of Medenine coastal aquifer in Tunisia are under immense pressure from multiple stresses.
• The water resources manager must consider the impact of economic and demographic development in groundwater management to avoid the intrusion of saline water.
• The results obtained presented some reference information that can serve as a basis for water resources planning.
• The model runs to provide information that managers can use to regulate and adequately control the Jeffara of Medenine water resources.

     

Correlation between chemical composition and antibacterial activity of essential oils from fifteen Eucalyptus species growing in the Korbous and Jbel Abderrahman arboreta (North East Tunisia)

The essential oils of fifteen Eucalyptus species harvested from the Jbel Abderrahman and Korbous arboreta (North East Tunisia) were screened for their antibacterial activities by the agar disc diffusion method. Eighteen major components as identified by GC/FID and GC/MS were selected for a study of the chemical and biological activity variability. The main one was 1,8-cineole, followed by spathulenol, trans-pinocarveol, α-pinene, p-cymene, globulol, cryptone, β-phellandrene, viridiflorol, borneol, limonene and isospathulenol. The chemical principal component analysis identified five species groups and subgroups, where each group constituted a chemotype, however that of the values of zone diameter of the inhibition (zdi) identified six groups of Eucalyptus oils, characterized by their antibacterial inhibition ability. The strongest activity was shown by E. platypus oil against Enterococcus faecalis and by E. lamannii oil against Staphylococcus aureus, Pseudomonas aeruginosa and Escherichia coli. A correlation between the levels of some major components and the antibacterial activities was observed.     

Cavity identification in linear elasticity and thermoelasticity

The aim of this paper is an analysis of geometric inverse problems in linear elasticity and thermoelasticity related to the identification of cavities in two and three spatial dimensions. The overdetermined boundary data used for the reconstruction are the displacement and temperature on a part of the boundary. We derive identifiability results and directional stability estimates, the latter using the concept of shape derivatives, whose form is known in elasticity and newly derived for thermoelasticity. For numerical reconstructions we use a least‐squares formulation and a geometric gradient descent based on the associated shape derivatives. The directional stability estimates guarantee the stability of the gradient descent approach, so that an iterative regularization is obtained. This iterative scheme is then regularized by a level set approach allowing the reconstruction of multiply connected shapes. Copyright © 2007 John Wiley & Sons, Ltd.     

On the K-divisibility constant for some special finite-dimensional Banach couples

We prove new estimates of the K-divisibility constants for some special Banach couples. In particular, we prove that the K-divisibility constant for a couple of the form (UV,U) where U and V are non-trivial Hilbert spaces equals . We also prove estimates for the K-divisibility constant of the two-dimensional version of the couple (L₂,L_∞), proving in particular that this couple is not exactly K-divisible. There are also several auxiliary results, including some estimates for relative Calderón constants for finite-dimensional couples.     

A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines

This paper deals with a scheduling problem of independent tasks with common due date where the objective is to minimize the total weighted tardiness. The problem is known to be ordinary NP-hard in the case of a single machine and a dynamic programming algorithm was presented in the seminal work of Lawler and Moore [E.L. Lawler, J.M. Moore, A functional equation and its application to resource allocation and sequencing problems, Management Science 16 (1969) 77–84]. In this paper, this algorithm is described and discussed. Then, a new dynamic programming algorithm is proposed for solving the single machine case. These methods are extended for solving the identical and uniform parallel-machine scheduling problems.     

Transformation of an elliptic into a circular beam using a diffractive binary optic

We propose a new method for transforming an elliptic Gaussian beam, in the near field, into a circular Gaussian beam in the far field. For that, we consider the use of a simple binary diffractive optic which is able to circularize an elliptic beam of 2:1 aspect ratio.