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In a companion paper (1) a general mathematical model for the allocation of touristic investments was developed. In this paper a solution methodology for the model is developed based on the principles of dynamic programming. At each stage of the dynamic program an integer program is solved to limit the range of values of the state variable which must explicitly be considered. The algorithm is illustrated through an example, and the advantages of the solution procedure are explained by considering the solution as a base for the strategic decision making in the touristic sector.

Negative effects of habitat isolation that arise from landscape fragmentation can be mitigated, by connecting natural areas through a network of habitat corridors. To increase the permeability of a given network, i.e. to decrease the resistance to animal movements through this network, often many developments can be made. The available financial resources being limited, the most effective developments must be chosen. This optimization problem, suggested in Finke and Sonnenschein, can be treated by heuristics and simulation approaches, but the method is heavy and the obtained solutions are sub‐optimal. The aim of the paper is to show that the problem can be efficiently solved to optimality by mathematical programming.

The moves of the individual in the network are modeled by an absorbing Markov chain and the development problem is formulated as a mixed‐integer quadratic program, then this program is linearized, and the best developments to make are determined by mixed‐integer linear programming.

First, the approach allows the development problem to be solved to optimality contrary to other methods. Second, the definition of the mathematical program is relatively simple, and its implementation is immediate by using standard, commercially available, software. Third, as it is well known with mixed‐integer linear programming formulation it is possible to add new constraints easily if they are linear (or can be linearized).

With a view to propose a simple and efficient tool to solve a difficult combinatorial optimization problem arising in the improvement of permeability across habitat networks, the approach has been tested on simulated habitat networks. The research does not include the study of some precise species movements in a real network.

The results provide a simple and efficient decision‐aid tool to try to improve the permeability of habitat networks.

The joint use of mathematical programming techniques and Markov chain theory is used to try to lessen the negative effects of landscape fragmentation.

This paper seeks to construct a model for inventory management for multiple periods. The model considers not only the usual parameters, but also price quantity discount, storage and batch size constraints.

Mixed 0‐1 integer programming is applied to solve the multi‐period inventory problem and to determine an appropriate inventory level for each period. The total cost of materials in the system is minimized and the optimal purchase amount in each period is determined.

The proposed model is applied in colour filter inventory management in thin film transistor‐liquid crystal display (TFT‐LCD) manufacturing because colour filter replenishment has the characteristics of price quantity discount, large product size, batch‐sized purchase and forbidden shortage in the plant. Sensitivity analysis of major parameters of the model is also performed to depict the effects of these parameters on the solutions.

The proposed model can be tailored and applied to other inventory management problems.

Although many mathematical models are available for inventory management, this study considers some special characteristics that might be present in real practice. TFT‐LCD manufacturing is one of the most prosperous industries in Taiwan, and colour‐filter inventory management is essential for TFT‐LCD manufacturers for achieving competitive edge. The proposed model in this study can be applied to fulfil the goal.

The purpose of this paper is to use α‐dense curves for solving Boolean equations, 0‐1 integer programming problems such as the shortest path problem or the knapsack problem.

The paper's aim is to present the applications in Boolean algebra and 0‐1 integer programming of a new method based on α‐dense curves first developed at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. The α‐dense curves generalize the space filling curves (Peanocurves,…) and fractal curves. The main idea consists in expressing n variables by means of a single one.

Apply the method to Boolean algebra and 0‐1 integer programming.

The paper presents a new method based on α‐dense curves for solving Boolean equations and 0‐1 integer programming problems.

This chapter presents application of multi-criteria mathematical programming models by integer and mixed-integer programming for optimal allocation of workers among supporting services in a hospital. The services include logistics, inventory management, financial management, operations management, medical analysis, etc. The optimality criteria of the problem are minimization of operational costs of supporting services subject to some specific constraints. The constraints represent specific conditions for resource allocation in a hospital. The overall problems are formulated as assignment models, where the decision variables represent the assignment of people to various jobs. Numerical examples are presented. Some computational results modeled on a real data from a hospital in Poland are reported.

In practical environments, machines subject to maintenance are prevalent in many production systems. This paper aims to find a schedule that minimizes the completion time (or equivalently, the total setup time) subject to maintenance and due dates.

An efficient heuristic is presented to provide the near‐optimal solution for the problem. The performance of the heuristic is evaluated by comparing its solution with the optimal solution obtained from the integer linear programming model.

In many production systems, the sequence‐dependent setup time of a job cannot be ignored when a switch between two different jobs occurs. The paper studies the sequence‐dependent setup time problem with periodic maintenance, where several maintenances are required. Computational results show that problems with larger time interval and smaller maintaining time can produce a smaller completion time.

Here an efficient heuristic is developed to provide the near‐optimal schedule for the problem. The proposed integer linear programming model is also presented to provide the optimal schedule. However, the proposed heuristic and the integer linear programming model developed in the paper are appropriate for those companies where maintenance is performed periodically and the sequence‐dependent setup times of their jobs are required.

The paper presents the heuristic and the integer linear programming model to deal with sequencing and maintenance problems.

Addresses the problem of maintenance planning and scheduling and reviews pertinent literature. Discusses the characteristics and the complexity of the problem. Advocates mathematical programming approaches for addressing the maintenance scheduling problem. Gives examples to demonstrate the utility of these approaches. Proposes expansion of the state‐of‐the‐art maintenance management information system to utilize the mathematical programming approaches and to have better control over the maintenance scheduling problem.

This study proposes strategies for vaccine center allocation for coronavirus disease (COVID) vaccine by determining the number of vaccination stations required for the vaccination drive, location of vaccination station, assignment of demand group to vaccination station, allocation of the scarce medical professional teams to station and number of optimal days a vaccination station to be functional in a week.

The authors propose a mixed-integer nonlinear programming model. However, to handle nonlinearity, the authors devise a heuristic and then propose a two-stage mixed-integer linear programming (MILP) formulation to optimize the allocation of vaccination centers or stations to demand groups in the first stage and the allocation of vaccination centers to cold storage links in the second stage. The first stage optimizes the cost and average distance traveled by people to reach the vaccination center, whereas the second stage optimizes the vaccine’s holding and storage and transportation cost by efficiently allocating cold storage links to the centers.

The model is studied for the real-world case of Chandigarh, India. The results obtained validate that the proposed approach can immensely help government agencies and policymaking body for a successful vaccination drive. The model tries to find a tradeoff between loss due to underutilized medical teams and the distance traveled by a demand group to get the vaccination.

To the best of our knowledge, there are hardly any studies on a vaccination program at such a scale due to sudden outbreaks such as Covid-19.

Scheduling is defined by Baker as, “the allocation of resources over time to perform a collection of tasks”. The term facilities is often used instead of resources and the tasks to be performed may involve a variety of different operations.