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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.

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.

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.

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.

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 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.

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.

The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.

Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

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.

The purpose of this paper is to manage the demand uncertainty considered as lower and upper levels for a medium-scale industrial distribution planning problem in a biobjective inventory routing problem (IRP). In order to achieve this, the grey system theory is applied since no statistical distribution from the past data and incomplete information.

This study is investigated with optimizing the distribution plan, which involves 30 customers of 12 periods in a manufacturing company under demand uncertainty that is considered as lower and upper levels for a biobjective IRP with using grey demand parameters as a grey integer programming model. In the data set, there are also some missing demand values for the customers. So, the seven different grey models are developed to eliminat the effects on demand uncertainties in computational analysis using a piece of developed software considering the logistical performance indicators such as total deliveries, total cost, the total number of tours, distribution capacity, average remaining capacity and solution time.

Results show that comparing the grey models, the cost per unit and the maximum number of vehicle parameters are also calculated as the new key performance indicator, and then results were ranked and evaluated in detail. Another important finding is the demand uncertainties can be managed with a new approach via logistics performance indicators using alternative solutions.

The results enable logistics managers to understand the importance of demand uncertainties if more reliable decisions are wanted to make with obtaining a proper distribution plan for effective use of their expectations about the success factors in logistics management.

The study is the first in terms of the application of grey models in a biobjective IRP with using interval grey demand data. Successful implementation of the grey approaches allows obtaining a more reliable distribution plan. In addition, this paper also offers a new key performance indicator for the final decision.