دانلود کتاب مقدمه‌ای بر برنامه‌نویسی ریاضی و مثال‌های علوم شبکه با نظریه و پایتون

The real-world evolves rapidly—it is important to reorganize labour, manufacturing outputs, shipping distribution networks, supervisory and other managerial responsibilities accordingly. A particular challenge is to allocate resources in an effective and efficient way. Achieving a scientific approach to studying and addressing such real-world challenges is one aim of Mathematical Programming and Network Science. The idea is to employ mathematical tools to achieve an optimal allocation of resources. For example, consider the case of a company that wishes to maximize its profits while at the same time minimizing its emissions outputs. Some typical phases of a modelling and programming work cycle include – defining a suitable optimization problem that is informed by relevant real-world problems and data; – formulating a relevant mathematical optimization model to represent a given real-world problem; – developing a computer-based procedure for deriving solutions to the mathematically formulated optimization problem; testing the mathematical model to see if the mathematically obtained solution is actually practical for the given real-world problem; and – implementing conclusions and/or revising the model as required. Mathematical programming and network science are very rich and difficult fields. They seek to solve mathematical optimization problems with the intent to apply such solutions to make informed real-world decisions for business, industry, government, non-profit and other organizational contexts. In doing so, they employ deep mathematical tools from linear algebra, combinatorial and convex analysis. At the same time, there are ethical reflections that become relevant. For example, given knowledge of an optimal solution, is it socially responsible to act on it? For instance, will maximizing profits inflict undue harm on a particular workforce? Similarly, will minimizing emissions outputs have undue harm on economic productivity? Not withstanding such considerations, knowledge of and/or the ability to find, at least some optimal solutions to mathematical programming problems are of clear strategic interest to entities of all sizes and flavours. A detailed understanding, of even at least some subset, of the optimal and/or feasible solutions allows leaders and individuals to make informed socially responsible and scientifically guided decisions.