An optimal replenishment policy for an EOQ model with partial backlogging

We study an inventory system where demand on the stockout period is partially backlogged. The backlogged demand ratio is a mixture of two exponential functions. The shortage cost has two significant costs: the unit backorder cost (which includes a fixed cost and a cost proportional to the length of time for which the backorder exists) and the cost of lost sales. A general procedure to determine the optimal policy and the minimum inventory cost for all the parameter values is developed. This model generalizes several inventory systems analyzed by different authors. Numerical examples are used to illustrate the theoretical results.     

Bifurcations in a predator–prey model in patchy environment with diffusion

In this paper we formulate a predator–prey system in two patches in which the per capita migration rate of each species is influenced only by its own density, i.e. there is no response to the density of the other one. Numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation, i.e. the stable constant steady state loses its stability and spatially non-constant stationary solutions, a pattern emerge.     

Predator invasion in predator–prey model with prey-taxis in spatially heterogeneous environment

We consider a predator–prey model with prey-taxis and Holling-type II functional responses in a spatially heterogeneous environment to analyze the effects of prey-taxis and the heterogeneity of an environment on predator invasion. To achieve our goal, we investigate the stability of semi-trivial solution in which the predator is absent. It is known that both the predator diffusion and the death rate contribute to the predator invasion in a heterogeneous habitat when there is no prey-taxis. In this paper, we show that predator invasion is affected by the prey-taxis and diffusions of the prey-taxis model for a certain range of predator death rates in a heterogeneous environment. Furthermore, in cases where predator invasion by predator diffusion does not occur in a particular death rate range of the predator, predator invasion can occur by prey-taxis in a spatially heterogeneous habitat. In addition, we compare this phenomenon to the corresponding predator–prey model with ratio-dependent functional responses. It is observed that none of the predator’s diffusion and prey-taxis affect the predator’s invasion, and that only the predator’s death rate contributes to predator invasion for the model with ratio-dependent functional responses.     

An outranking-based fuzzy logic model for collaborative group preferences

Some ideas coming from Multi Criteria Decision Aid are here extended to group decision. We present a logical model in order to reflect the degree of truth of the following predicate “group G considers that option x is at least as good as y.” The proposal considers the strength of the majority using its number and the intensity of its preference, and it also acknowledges the importance of the minorities of a certain numerical significance that manifest an intense disagreement with the predicate of the outranking. The effects of the “majority dictatorship” are restricted. Since it considers simultaneously the strength of the majority, the importance of unhappy minorities, and the intensity of the preference/opposition, this model exhibits desirable qualities of the classic methods by Condorcet and Borda. This model can be used to solve problems regarding selection, ranking, classification, and sorting. Various examples are given, which show the quality of the solutions that were obtained.     

Saddle-node-Hopf bifurcation in a modified Leslie–Gower predator-prey model with time-delay and prey harvesting

From the saddle-node-Hopf bifurcation point of view, this paper considers a modified Leslie–Gower predator-prey model with time delay and the Michaelis–Menten type prey harvesting. Firstly, we discuss the stability of the equilibria, obtain the critical conditions for the saddle-node-Hopf bifurcation, and give the completion bifurcation set by calculating the universal unfoldings near the saddle-node-Hopf bifurcation point by using the normal form theory and center manifold theorem. Then we derive the parameter conditions for the existence of monostable coexistence equilibrium and the parameter regions in which both the prey-extinction and the coexistence equilibrium (or coexistence periodic or quasi-periodic solutions) are simultaneously stabilized. We also investigate the heteroclinic bifurcation, and describe the phenomenon that the periodic behavior disappears as through the heteroclinic bifurcation. Finally, some numerical simulations are performed to support our analytic results.     

Voter model in a random environment in ? d

We consider the voter model with flip rates determined by {?? _e , e ?? E _d }, where E _d is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice ? ^d . Suppose that {?? _e , e ?? E _d } are independent and identically distributed (i.i.d.) random variables satisfying ?? _e ? 1. We prove that when d = 2, almost surely for all random environments, the voter model has only two extremal invariant measures: ?? ₀ and ?? ₁.     

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.     

Dynamical behaviors of a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators

In this work, a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators is investigated. By the stroboscopic map of the discrete dynamical system, the prey-extinction periodic solution of the investigated system is proved to be globally asymptotically stable. By the theory of impulsive differential equation, the investigated system is also proved to be permanent. Finally, the numerical analysis is inserted to illustrate the results. Our conclusions provide reliable tactical basis for the practical biological management.     

Bifurcation and Turing pattern formation in a diffusive ratio-dependent predator–prey model with predator harvesting

The ratio-dependent predator–prey model exhibits rich dynamics due to the singularity of the origin. Harvesting in a ratio-dependent predator–prey model is relatively an important research project from both ecological and mathematical points of view. In this paper, we study the temporal, spatial and spatiotemporal dynamics of a ratio-dependent predator–prey diffusive model where the predator population harvest at catch-per-unit-effort hypothesis. For the spatially homogeneous model, we derive conditions for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solution by the center manifold and the normal form theory. For the reaction–diffusion model, firstly it is shown that Turing (diffusion-driven) instability occurs, which induces spatial inhomogeneous patterns. Then it is demonstrated that the model exhibit Hopf bifurcation which produces temporal inhomogeneous patterns. Finally, the existence and non-existence of positive non-constant steady-state solutions are established. Moreover, numerical simulations are performed to visualize the complex dynamic behavior.     

Mixed gated/exhaustive service in a polling model with priorities

In this paper we consider a single-server polling system with switch-over times. We introduce a new service discipline, mixed gated/exhaustive service, that can be used for queues with two types of customers: high and low priority customers. At the beginning of a visit of the server to such a queue, a gate is set behind all customers. High priority customers receive priority in the sense that they are always served before any low priority customers. But high priority customers have a second advantage over low priority customers. Low priority customers are served according to the gated service discipline, i.e. only customers standing in front of the gate are served during this visit. In contrast, high priority customers arriving during the visit period of the queue are allowed to pass the gate and all low priority customers before the gate. We study the cycle time distribution, the waiting time distributions for each customer type, the joint queue length distribution of all priority classes at all queues at polling epochs, and the steady-state marginal queue length distributions for each customer type. Through numerical examples we illustrate that the mixed gated/exhaustive service discipline can significantly decrease waiting times of high priority jobs. In many cases there is a minimal negative impact on the waiting times of low priority customers but, remarkably, it turns out that in polling systems with larger switch-over times there can be even a positive impact on the waiting times of low priority customers.     

On the optimality of threshold control in queues with model uncertainty

We consider a single-stage queuing system where arrivals and departures are modeled by point processes with stochastic intensities. An arrival incurs a cost, while a departure earns a revenue. The objective is to maximize the profit by controlling the intensities subject to capacity limits and holding costs. When the stochastic model for arrival and departure processes are completely known, then a threshold policy is known to be optimal. Many times arrival and departure processes can not be accurately modeled and controlled due to lack of sufficient calibration data or inaccurate assumptions. We prove that a threshold policy is optimal under a max–min robust model when the uncertainty in the processes is characterized by relative entropy. Our model generalizes the standard notion of relative entropy to account for different levels of model uncertainty in arrival and departure processes. We also study the impact of uncertainty levels on the optimal threshold control.     

A bioeconomic differential algebraic predator–prey model with nonlinear prey harvesting

In this paper, we propose a bioeconomic differential algebraic predator–prey model with Holling type II functional response and nonlinear prey harvesting. As the nonlinear prey harvesting is introduced, the proposed model displays a complex dynamics in the predator–prey plane. Taking into account of the economic factor, our predator–prey system is established by bioeconomic differential algebraic equations. The effect of economic profit on the proposed model is analyzed by viewing it as a bifurcation parameter. By jointly using the normal form of differential algebraic models and the bifurcation theory, the stability and bifurcations (singularity induced bifurcation, Hopf bifurcation) are discussed. These results obtained here reveal richer dynamics of the bioeconomic differential algebraic predator–prey model with nonlinear prey harvesting, and suggest a guidance for harvesting in the practical word. Finally, numerical simulations are given to demonstrate the results.     

Supply chain DEA: production possibility set and performance evaluation model

Performance evaluation is of great importance for effective supply chain management. The foundation of efficiency evaluation is to faithfully identify the corresponding production possibility set. Although a lot of researches have been done on supply chain DEA models, the exact definition for supply chain production possibility set is still in absence. This paper defines two types of supply chain production possibility sets, which are proved to be equivalent to each other. Based upon the production possibility set, a supply chain CRS DEA model is advanced to appraise the overall technical efficiency of supply chains. The major advantage of the model lies on the fact that it can help to find out the most efficient production abilities in supply chains, by replacing or improving inefficient subsystems (supply chain members). The proposed model also directly identifies the benchmarking units for inefficient supply chains to improve their performance. A real case validates the reasonableness and acceptability of this approach.     

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.     

Ejection chain and filter-and-fan methods in combinatorial optimization

The design of effective neighborhood structures is fundamentally important for creating better local search and metaheuristic algorithms for combinatorial optimization. Significant efforts have been made to develop larger and more powerful neighborhoods that are able to explore the solution space more effectively while keeping computation complexity within acceptable levels. The most important advances in this domain derive from dynamic and adaptive neighborhood constructions originating in ejection chain methods and a special form of a candidate list design that constitutes the core of the filter-and-fan method. The objective of this paper is to lay out the general framework of the ejection chain and filter-and-fan methods and present applications to a number of important combinatorial optimization problems. The features of the methods that make them effective in these applications are highlighted to provide insights into solving challenging problems in other settings.     

Analysis of a plankton–fish model with external toxicity and nonlinear harvesting

Ricerche di Matematica - In this paper, we consider a three species plankton–fish system that incorporates external toxicity and nonlinear harvesting. We consider that the growth of species...     

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.     

Optimal harvesting policy of a stochastic predator–prey model with time delay

This paper concerns the optimal harvesting of a stochastic delay predator–prey model. Sufficient and necessary conditions for the existence of an optimal control are established. The optimal harvesting effort and the maximum value of the cost function are obtained as well. Some numerical tests are given to illustrate the main results.     

On the Markov-modulated insurance risk model with tax

In this paper, we consider the Markov-modulated insurance risk model with tax. We assume that the claim inter-arrivals, claim sizes and premium process are influenced by an external Markovian environment process. The considered tax rule, which is the same as the one considered by Albrecher and Hipp [Blätter DGVFM 28(1):13–28, 2007], is to pay a certain proportion of the premium income, whenever the insurer is in a profitable situation. A system of differential equations of the non-ruin probabilities, given the initial environment state, are established in terms of the ruin probabilities under the Markov-modulated insurance risk model without tax. Furthermore, given the initial state, the differential equations satisfied by the expected accumulated discounted tax until ruin are also derived. We also give the analytical expressions for them by iteration methods.