Introduction to convex optimization

In this thesis, we touched upon the concept of convexity which is one of the essential topics in optimization. There exist many real world problems that mathematically modelling these problems and trying to solve them are the focus point of many researchers. Many algorithms are proposed for solving such problems. Almost all proposed methods are very efficient when the modelled problems are convex. Therefore, convexity plays an important role in solving those problems. There are many techniques that researchers use to convert a non-convex model to a convex one. Also, most of the algorithms that are suggested for solving non-convex problems try to utilize the notions of convexity in their procedures. In this work, we begin with important definitions and topics regarding convex sets and function. Next, we will introduce optimization problems in general, then, we will discuss convex optimization problems and give important definitions in relation with the topic. Furthermore, we will touch upon Linear Programming which is one of the most famous and useful cases of Convex Optimization problems. Finally, we will discuss the Generalized Inequalities and their application in vector optimization problem

The Value of Supply Chain Visibility when Yield is Random

This dissertation focuses on supply chains with uncertainty due to random yields. A common assumption in such systems is that the yields are observable only after all transportation or production steps are completed. The actual yield realization however happens earlier during the process. Technological advances and stronger supply chain collaboration make it possible to observe yield realization in real time and therefore close the time gap between the event and the observation. Within this thesis optimal and heuristic policies are developed that make use of this new type of information in various supply chain settings. These policies are used to identify conditions under which real time yield information is particularly beneficial