The objective of this thesis is to develop models and algorithms to plan the purchasing of reusable containers in a closed-loop supply chain where the demand is increasing. We restrict our study to a periodic review process between a single manufacturer and a single supplier. Each item is transported either in a reusable container or in a single-use disposable. Furthermore, a setup cost is paid every time new containers are purchased. Consequently, our model is similar to a lot-sizing problem with return of every item after a fixed duration. We study both cases of a deterministic demand as well as a stochastic demand. In the deterministic setting, we use dynamic programming and minimum linear-cost flows to generate polynomial time algorithms. When the demand is stochastic, we use the Markov decision process framework to develop pseudo-polynomial time heuristics for four different strategies. We show the L-natural-convexity of the cost functions for three strategies to speed up the computations. The thesis concludes with an application on a real-life supply chain.
