Autonomous control methods in logistics – A mathematical perspective

We model general autonomously controlled production networks by means of nonlinear differential equations and implement autonomous control methods, where transportation times and disturbances in the transportation times are taken into account. Autonomous control enables intelligent logistic objects to route themselves through a logistic network. Based on this model we investigate a certain scenario of a production network, where we show advantages and disadvantages of the implementation of autonomous control methods from a mathematical perspective in view of robustness and stability.     

HOPS – Hamming-Oriented Partition Search for production planning in the spinning industry

In this paper, we investigate a two-stage lot-sizing and scheduling problem in a spinning industry. A new hybrid method called HOPS (Hamming-Oriented Partition Search), which is a branch-and-bound based procedure that incorporates a fix-and-optimize improvement method is proposed to solve the problem. An innovative partition choice for the fix-and-optimize is developed. The computational tests with generated instances based on real data show that HOPS is a good alternative for solving mixed integer problems with recognized partitions such as the lot-sizing and scheduling problem.     

The aggregate capacity of virtual resources – linear models

This article addresses resource modelling with a specific interest on capacity aggregation. The capacity of a resource with regard to d types of tasks is modelled by a simplex and by a cube in the d-dimensional space. The aggregate capacity model of a virtual resource, that is, of a pool of r resources, is the d-polytope provided by the Minkowski sum of the simplices and cubes modelling the resources. The parametric identification of the d-planes supporting the facets of the polytope is established for r?=?2 and linear simplifications are provided in the (r,?d) general case. Formulated as linear inequalities, the aggregate capacity models fit in with linear programming and quadratic programming optimization techniques.     

On the capacity of boolean graph formulæ

In a recent paper we have solved several well-known combinatorial problems treating them as special cases of our generalization of Shannon's notion of graph capacity. We present a new simple formalism to deal with all such problems in a unified manner, considering graphs or families of graphs as special formulæ the variables of which are pairs of vertices of their common vertex sets. In all of these problems, the maximum size of a set ofn-length sequences from a fixed alphabet is to be determined under various restrictions on the element pairs present in the same coordinate of any two sequences from the set. For sufficiently homogeneous formulæ capacity becomes computable.New applications include generalizations of our result on the maximum number of pairwise qualitatively independentk-partitions of ann-set from independence to various forms of qualitative dependence.Work partially supported by the Italian Ministry of the University and Scientific Research, Project: Algoritmi, Modelli di Calcolo e Strutture Informative.     

Diffusion of methylene blue in glass fibers – Application of the shrinking core model

Diffusion of mass in a solid cylinder with concentration dependent diffusivity (or temperature-dependent thermal conductivity in case of heat diffusion) does not admit of an analytical solution except in special cases. The ‘shrinking core model’ has been used to develop an approximate analytical solution in certain circumstances. The model, generally useful to describe heterogeneous solid–fluid reactions, is applied to theoretically analyze the adsorption–diffusion phenomena of methylene blue dye in a glass fiber in the present work. Theoretical equations have been derived for the case of diffusivity as an exponential function of concentration. The diffusivity parameters are evaluated by global minimization of the error between the experimental and the theoretical concentration history. Other forms of diffusivity, namely constant diffusivity and diffusivity varying linearly with concentration are found to involve larger errors. A parametric sensitivity analysis of the error has been done. The shrinking core model could satisfactorily interpret the experimental dye concentration profile in the substrate.     

Operations Research for green logistics – An overview of aspects,issues, contributions and challenges

The worldwide economic growth of the last century has given rise to a vast consumption of goods while globalization has led to large streams of goods all over the world. The production, transportation, storage and consumption of all these goods, however, have created large environmental problems. Today, global warming, created by large scale emissions of greenhouse gasses, is a top environmental concern. Governments, action groups and companies are asking for measures to counter this threat. Operations Research has a long tradition in improving operations and especially in reducing costs. In this paper, we present a review that highlights the contribution of Operations Research to green logistics, which involves the integration of environmental aspects in logistics. We give a sketch of the present and possible developments, focussing on design, planning and control in a supply chain for transportation, inventory of products and facility decisions. While doing this, we also indicate several areas where environmental aspects could be included in OR models for logistics.     

Sensitivity of the slip rate coefficient in fluid flow – poroelastic coupling conditions

To model flow-induced structural vibrations, an interface to couple fluid flow and poroelastic material in a finite element formulation has been developed. One parameter of this interface condition is the slip rate coefficient, resulting from the so-called Beavers-Joseph-Saffman condition. This condition states that the jump in tangential velocity at a fluid flow – porous interface is proportional to the shear stress. Up to now no a priori determination of this parameter exists, and the known parameter range has been deducted from measurements, i. e., in our case from the results of the pore-resolving simulations. When modeling realistic problems assuming incompressible fluids, vectorial flow velocity and scalar pressure interact with the poroelastic material. As the slip rate coefficient only influences the tangential contributions, its overall influence is not clear. In this work, the sensitivity of the slip rate coefficient regarding the interface's coupling conditions is evaluated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On arithmetic progressions in recurrences – A new characterization of the Fibonacci sequence

We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic progressions is also given.     

Comments on properties of the minmax solutions in goal programming – a reply

This note replies to comments raised by Professor Ogryczak regarding properties of the minmax goal programming and compromise programming solutions. It is shown how the two counterexamples used by Ogryczak to support his views have little validity because they are out of context.     

The asymptotic variance rate of the output process of finite capacity birth-death queues

We analyze the output process of finite capacity birth-death Markovian queues. We develop a formula for the asymptotic variance rate of the form λ ^*+∑v _i where λ ^* is the rate of outputs and v _i are functions of the birth and death rates. We show that if the birth rates are non-increasing and the death rates are non-decreasing (as is common in many queueing systems) then the values of v _i are strictly negative and thus the limiting index of dispersion of counts of the output process is less than unity. In the M/M/1/K case, our formula evaluates to a closed form expression that shows the following phenomenon: When the system is balanced, i.e. the arrival and service rates are equal, is minimal. The situation is similar for the M/M/c/K queue, the Erlang loss system and some PH/PH/1/K queues: In all these systems there is a pronounced decrease in the asymptotic variance rate when the system parameters are balanced. Research supported in part by Israel Science Foundation Grant 249/02 and 454/05 and by European Network of Excellence Euro-NGI.     

Value of supplier’s capacity information in a two-echelon supply chain

In traditional supply chain models it is generally assumed that full information is available to all parties involved. Although this seems reasonable, there are cases where chain members are independent agents and possess different levels of information. In this study, we analyze a two-echelon, single supplier-multiple retailers supply chain in a single-period setting where the capacity of the supplier is limited. Embedding the lack of information about the capacity of the supplier in the model, we aim to analyze the reaction of the retailers, compare it with the full-information case, and assess the value of information and the effects of information asymmetry using game theoretic analysis. In our numerical studies, we conclude that the value of information is highly dependent on the capacity conditions and estimates of the retailers, and having information is not necessarily beneficial to the retailers.     

Analytic first integrals of the FitzHugh – Nagumo systems

We study the analytical integrability of the FitzHugh–Nagumo systems in with parameters      

Supply network planning in the forest supply chain with bucking decisions anticipation

We consider a two-echelon timber supply chain in which the first echelon consists of several stands to be harvested and the second echelon consists of mills to be supplied with logs of different length. This problem aims at minimizing harvesting and transportation costs for one production period, while satisfying demand expressed as a mix of volumes of specific log types. Harvesting cost, which includes felling, bucking and hauling to roadside, depends upon the number of log type to be produced and sorted. Each stand to be harvested is modeled individually with a limited number of trees of various classes of diameter and total length, which affects the productivity factors of the bucking patterns to be used. To take these characteristics into account, we propose heuristics based on columns generation to solve the supply network problem at the forest level with an anticipation of bucking operations at the stand level.     

A Bilevel p-median model for the planning and protection of critical facilities

The bilevel p-median problem for the planning and protection of critical facilities involves a static Stackelberg game between a system planner (defender) and a potential attacker. The system planner determines firstly where to open p critical service facilities, and secondly which of them to protect with a limited protection budget. Following this twofold action, the attacker decides which facilities to interdict simultaneously, where the maximum number of interdictions is fixed. Partial protection or interdiction of a facility is not possible. Both the defender’s and the attacker’s actions have deterministic outcome; i.e., once protected, a facility becomes completely immune to interdiction, and an attack on an unprotected facility destroys it beyond repair. Moreover, the attacker has perfect information about the location and protection status of facilities; hence he would never attack a protected facility. We formulate a bilevel integer program (BIP) for this problem, in which the defender takes on the leader’s role and the attacker acts as the follower. We propose and compare three different methods to solve the BIP. The first method is an optimal exhaustive search algorithm with exponential time complexity. The second one is a two-phase tabu search heuristic developed to overcome the first method’s impracticality on large-sized problem instances. Finally, the third one is a sequential solution method in which the defender’s location and protection decisions are separated. The efficiency of these three methods is extensively tested on 75 randomly generated instances each with two budget levels. The results show that protection budget plays a significant role in maintaining the service accessibility of critical facilities in the worst-case interdiction scenario.     

A tactical model for planning the production and distribution of fresh produce

We present an integrated tactical planning model for the production and distribution of fresh produce. The main objective of the model is to maximize the revenues of a producer that has some control over the logistics decisions associated with the distribution of the crop. The model is used for making planning decisions for a large fresh produce grower in Northwestern Mexico. The decisions obtained are based on traditional factors such as price estimation and resource availability, but also on factors that are usually neglected in traditional planning models such as price dynamics, product decay, transportation and inventory costs. The model considers the perishability of the crops in two different ways, as a loss function in its objective function, and as a constraint for the storage of products. The paper presents a mixed integer programming model used to implement the problem as wells as the computational results obtained from it.     

On the sphericity of the subgroup PSL2(ℝ) in the group of diffeomorphisms of the circle

It is shown that the group PSL₂(?) is a spherical subgroup in the group of C³-diffeomorphisms of the circle.     

Clustering motions in N-body systems – free-fall motions in the Gaussian three-body problem

Clustering motions are typical and universal phenomena in N-body systems. Basic mechanisms leading to escaping and/or to trapping of particles are pursued in the analysis of a global structure for the three-body problem. The global structure of the three-body problem is numerically studied under the short range Gaussian interaction potential. As the Gaussian potential does not have any singularities at zero distance, we can avoid the computational errors in the long time simulations. Main concerns are the analysis of the collinear three-body problem, and the result compared with the case of gravitational potential. The distributions of periodic orbits are precisely searched and their stability is determined by the linear stability analysis. The collapsing of quasi-periodic motions is correlated to the destabilization of the three-body cluster in the case of the free-fall motions, and that the boundary for the collapsing tori displays fractal curves. Finally the escape diagram for two-dimensional three-body problems are discussed in comparison with the case of gravitational potential, where the remarkable difference near the triple collision is pointed out.