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.     

A multiobjective model for forest planning with adjacency constraints

This work presents a nonlinear goal programming model with binary variables used to plan the management of a tree plantation, taking economic and environmental objectives into account. The aims are to stay within the limits of a given harvesting volume, limit the age of basic units targeted for clearcutting, obtain a forest with a balanced age distribution, and surpass the minimum net present value set at each planning period. This has to be achieved bearing in mind technical restrictions regarding treatments, and spatial adjacency constraints that limit the maximum adjacent surface area to which clearcutting can be applied. The outcome is a highly complex problem that is solved by applying a metaheuristic method based on Scatter Search. The proposed model has been validated by applying it to a Cuban plantation located in the region of Pinar del Río.     

A presentation for the singular part of the full transformation semigroup

The (full) transformation semigroup T_n\mathcal{T}_{n} is the semigroup of all functions from the finite set {1,…,n} to itself, under the operation of composition. The symmetric group S_n í T_n{\mathcal{S}_{n}\subseteq \mathcal{T}_{n}} is the group of all permutations on {1,…,n} and is the group of units of T_n\mathcal{T}_{n}. The complement T_n\S_n\mathcal{T}_{n}\setminus \mathcal{S}_{n} is a subsemigroup (indeed an ideal) of T_n\mathcal{T}_{n}. In this article we give a presentation, in terms of generators and relations, for T_n\S_n\mathcal{T}_{n}\setminus \mathcal{S}_{n}, the so-called singular part of T_n\mathcal{T}_{n}.     

A comparison of problem decomposition techniques for the FAP

This paper proposes a problem decomposition approach to solve hard Frequency Assignment Problem instances with standard meta-heuristics. The proposed technique aims to divide the initial problem into a number of easier subproblems, solve them and then recompose the partial solutions into one of the original problem. We consider the COST-259 MI-FAP instances and other Cardiff University test problems in order to simulate larger and more realistic networks. For both benchmarks the standard implementations of meta-heuristics do not generally produce a satisfactory performance within reasonable times of execution. However, the decomposed assignment approach can improve their results, both in terms of solution quality and runtime.     

A method of calculating the critical dimensions of composite operators in the massless nonlinear σ model

For an arbitrary system of composite operators that mix on renormalization, a general scheme is formulated for calculating the critical dimensions directly in the massless model with dimensional and minimal-subtraction type regularization. The critical dimensions of arbitrary powers of the auxiliary field and analogous operators with two additional derivatives are calculated as examples.St Petersburg State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 160–175, April, 1993.     

A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators

We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara’s extremal weight crystals over the Kac–Moody algebra of type A _+∞, and construct a Knuth type correspondence preserving the plactic relations. This bijection yields the Cauchy identity for Schur operators as a homomorphic image of its associated identity for plactic characters of extremal weight crystals, and also recovers Sagan and Stanley’s correspondence for skew tableaux as its restriction.     

On the Existence of Optimal Unions of Subspaces for Data Modeling and Clustering

Given a set of vectors F={f ₁,…,f _m } in a Hilbert space H\mathcal {H}, and given a family C\mathcal {C} of closed subspaces of H\mathcal {H}, the subspace clustering problem consists in finding a union of subspaces in C\mathcal {C} that best approximates (is nearest to) the data F. This problem has applications to and connections with many areas of mathematics, computer science and engineering, such as Generalized Principal Component Analysis (GPCA), learning theory, compressed sensing, and sampling with finite rate of innovation. In this paper, we characterize families of subspaces C\mathcal {C} for which such a best approximation exists. In finite dimensions the characterization is in terms of the convex hull of an augmented set C⁺\mathcal {C}^{+}. In infinite dimensions, however, the characterization is in terms of a new but related notion; that of contact half-spaces. As an application, the existence of best approximations from π(G)-invariant families C\mathcal {C} of unitary representations of Abelian groups is derived.     

A Measure of Non-convexity in the Plane and the Minkowski Sum

In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for “not far from convex” regions this measure does not decrease under the Minkowski sum operation, and guarantees that the Minkowski sum has no “holes”.     

How to get the timing right. A computational model of the effects of the timing of contacts on team cohesion in demographically diverse teams

Lau and Murnighan’s faultline theory explains negative effects of demographic diversity on team performance as consequence of strong demographic faultlines. If demographic differences between group members are correlated across various dimensions, the team is likely to show a “subgroup split” that inhibits communication and effective collaboration between team members. Our paper proposes a rigorous formal and computational reconstruction of the theory. Our model integrates four elementary mechanisms of social interaction, homophily, heterophobia, social influence and rejection into a computational representation of the dynamics of both opinions and social relations in the team. Computational experiments demonstrate that the central claims of faultline theory are consistent with the model. We show furthermore that the model highlights a new structural condition that may give managers a handle to temper the negative effects of strong demographic faultlines. We call this condition the timing of contacts. Computational analyses reveal that negative effects of strong faultlines critically depend on who is when brought in contact with whom in the process of social interactions in the team. More specifically, we demonstrate that faultlines have hardly negative effects when teams are initially split into demographically homogeneous subteams that are merged only when a local consensus has developed.     

A New Regularity Criterion in Terms of the Direction of the Velocity for the MHD Equations

In this paper we obtain a new regularity criterion for weak solutions to the 3D MHD equations. It is proved that if div( \fracu|u|) \mathrm{div}( \frac{u}{|u|}) belongs to L^\frac21-r( 0,T;[(X)\dot]_r( \mathbbR³) ) L^{\frac{2}{1-r}}( 0,T;\dot{X}_{r}( \mathbb{R}^{3}) ) with 0≤r≤1, then the weak solution actually is regular and unique.     

The self-dual point of the two-dimensional random-cluster model is critical for q?≥ 1

We prove a long-standing conjecture on random-cluster models, namely that the critical point for such models with parameter q?≥?1 on the square lattice is equal to the self-dual point ${p_{sd}(q) = \sqrt{q} / (1+\sqrt{q})}$ . This gives a proof that the critical temperature of the q-state Potts model is equal to ${\log (1+\sqrt q)}$ for all q?≥ 2. We further prove that the transition is sharp, meaning that there is exponential decay of correlations in the sub-critical phase. The techniques of this paper are rigorous and valid for all q?≥ 1, in contrast to earlier methods valid only for certain given q. The proof extends to the triangular and the hexagonal lattices as well.     

A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

We are interested in locations of multiple facilities in the plane with the aim of minimizing the sum of weighted distance between these facilities and regional customers, where the distance between a facility and a regional customer is evaluated by the farthest distance from this facility to the demand region. By applying the well-known location-allocation heuristic, the main task for solving such a problem turns out to solve a number of constrained Weber problems (CWPs). This paper focuses on the computational contribution in this topic by developing a variant of the classical Barzilai-Borwein (BB) gradient method to solve the reduced CWPs. Consequently, a hybrid Cooper type method is developed to solve the problem under consideration. Preliminary numerical results are reported to verify the evident effectiveness of the new method.     

Martingale Approximation and Optimality of Some Conditions for the Central Limit Theorem

Let (X _i ) be a stationary and ergodic Markov chain with kernel Q and f an L ² function on its state space. If Q is a normal operator and f=(I?Q)^1/2 g (which is equivalent to the convergence of \(\sum_{n=1}^{\infty}\frac{\sum_{k=0}^{n-1}Q^{k}f}{n^{3/2}}\) in L ²), we have the central limit theorem [cf. (Derriennic and Lin in C.R. Acad. Sci. Paris, Sér. I 323:1053–1057, 1996; Gordin and Lif?ic in Third Vilnius conference on probability and statistics, vol. 1, pp. 147–148, 1981)]. Without assuming normality of Q, the CLT is implied by the convergence of \(\sum_{n=1}^{\infty}\frac{\|\sum_{k=0}^{n-1}Q^{k}f\|_{2}}{n^{3/2}}\), in particular by \(\|\sum_{k=0}^{n-1}Q^{k}f\|_{2}=o(\sqrt{n}/\log^{q}n)\), q>1 by Maxwell and Woodroofe (Ann. Probab. 28:713–724, 2000) and Wu and Woodroofe (Ann. Probab. 32:1674–1690, 2004), respectively. We show that if Q is not normal and f∈(I?Q)^1/2 L ², or if the conditions of Maxwell and Woodroofe or of Wu and Woodroofe are weakened to \(\sum_{n=1}^{\infty}c_{n}\frac{\|\sum_{k=0}^{n-1}Q^{k}f\|_{2}}{n^{3/2}}<\infty\) for some sequence c _n ↘0, or by \(\|\sum_{k=0}^{n-1}Q^{k}f\|_{2}=O(\sqrt{n}/\log n)\), the CLT need not hold.     

A comparison of feasible direction methods for the stochastic transportation problem

The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.     

Existence and global stability of periodic solution for impulsive predator-prey model with diffusion and distributed delay

In this paper, the nonlinear nonautonomous predator-prey model with impulsive effect is considered. By using the method of coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solution, and by the means of a suitable Lyapunov function, the uniqueness and global attractivity of positive periodic solution are presented. An example shows the feasibility of our main results.     

Exact asymptotics for the stationary distribution of a Markov chain: a production model

We derive rough and exact asymptotic expressions for the stationary distribution π of a Markov chain arising in a queueing/production context. The approach we develop can also handle “cascades,” which are situations where the fluid limit of the large deviation path from the origin to the increasingly rare event is nonlinear. Our approach considers a process that starts at the rare event. In our production example, we can have two sequences of states that asymptotically lie on the same line, yet π has different asymptotics on the two sequences.     

Airfreight forwarder shipment planning: A mixed 0–1 model and managerial issues in the integration and consolidation of shipments

The planning and management of air cargo logistics is a complex endeavor, involving collaboration of multiple logistics agents to deliver shipments timely, safely and economically. Airfreight forwarders are third-party brokers/operators who coordinate and manage cargo shipments for their clients. It is important for a forwarder to develop a shipment plan to evaluate the possible integrations and consolidations, to assess whether shipments can meet their respective target delivery dates, and to estimate the amount of costs involved. In this paper, we formulate a forwarder’s shipment planning problem as a mixed 0–1 LP. Effects of integration and consolidation – on the timely delivery of shipments during any phase of the shipping process – are explicitly addressed. A forwarder’s in-house capacity, as well as the available capacity of its partners and sub-contracting agents, are incorporated. We also consider the target cost for a shipment. Based on the special characteristics of the model, we design a customized tabu-search algorithm. We also provide an illustrative case to examine several managerial issues.     

Existence and multiplicity of periodic solutions for the ordinary p-Laplacian systems

Some existence and multiplicity results are obtained for periodic solutions of the ordinary p-Laplacian systems: $$\left\{\begin{array}{@{}l@{\quad{}}l}(|u'(t)|^{p-2}u'(t))'=\nabla F(t,u(t)),&\mbox{a.e. }t\in[0,T],\\[4pt]u(0)-u(T)=u'(0)-u'(T)=0\end{array}\right.$$ by using the Saddle Point Theorem, the least action principle and the Three-critical-point Theorem.     

Dynamical behavior for an eco-epidemiological model with discrete and distributed delay

In this paper, the dynamical behavior of an eco-epidemiological model with discrete and distributed delay is studied. Sufficient conditions for the local asymptotical stability of the nonnegative equilibria are obtained. We prove that there exists a threshold value of the feedback time delay τ beyond which the positive equilibrium bifurcates towards a periodic solution. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.     

A transient stochastic simulation–optimization model for operational fuel planning in-theater

Army fuel planners are responsible for developing daily loading plans that specify which tankers to load, with what fuel, and where to send the loaded tankers. The tools used to accomplish this task are custom built spreadsheets which require large amounts of time and effort to use, update, and keep free of errors. This research presents a transient stochastic simulation–optimization model of the in-theater bulk fuel supply chain, where the simulation model is used to simulate the performance of the fuel supply chain under a particular fuel distribution policy and the optimization portion is used to update the policy so that it results in the performance desired by the Army fuel planner. The fuel distribution policy can then be used to derive the daily loading plan. Due to the multi-objective nature of the problem, the set of policies that form the efficient frontier are all candidate policies for the Army fuel planner to select from. Results of experimentation with a wide variety of supply chain scenarios indicate that, for a given supply chain scenario, the optimization portion of the model identifies a set of fuel distribution policies that address the objectives of the Army fuel planner. In addition, the simulation–optimization model comfortably solves the largest supply chain scenarios the Army fuel planner would reasonably be expected to encounter.