In this paper we study sensitivity analysis of the uncapacitated single level economic lot-sizing problem, which was introduced by Wagner and Whitin about thirty years ago. In particular we are concerned with the computation of the maximal ranges in which the numerical problem parameters may vary individually, such that a solution already obtained remains optimal. Only recently it was discovered that faster algorithms than the Wagner-Whitin algorithm exist to solve the economic lot-sizing problem. Moreover, these algorithms reveal that the problem has more structure than was recognized so far. When performing the sensitivity analysis we exploit these newly obtained insights.

A partial description of the convex hull of solutions to the economic lot-sizing problem with start-up costs (ELSS) has been derived recently. Here a larger class of valid inequalities is given and it is shown that these inequalities describe the convex hull of ELSS. This in turn proves that a plant location formulation as a linear program solves ELSS. Finally a separation algorithm is given.

This dissertation aims to provide models which will help companies make sustainable logistics management and transportation decisions. These models are extensions of the economic lot sizing model with the availability of multiple replenishment modes. The objective of the models is to minimize total replenishment costs and emissions. The study provides applications of these models on contemporary supply chain problems. Initially, the impact of carbon regulatory mechanisms on the replenishment decisions are analyzed for a biomass supply chain under fixed charge replenishment costs. Then, models are extended to consider multiple-setups replenishment costs for age dependent perishable products. For a cost minimization objective, solution algorithms are proposed to solve cases where one, two or multiple replenishment modes are available. Finally, using a bi-objective model, tradeoffs in costs and emissions are analyzed in a perishable product supply chain.