The thesis at hand includes eight chapter and is structured as follows: Following a brief introduction of the topic in Chapter 1, Chapter 2 provides a survey of literature reviews in the area of lot sizing. Its intention is to show which streams of research emerged from Harris' seminal lot size model, and which major achievements have been accomplished in the respective areas. It first develops the methodology and then descriptively analyzes the sample. Subsequently, a content-related classification scheme for lot sizing models is developed, and the reviews contained in the sample are discussed in light of this classification scheme. The analysis reveals that various extensions of Harris' lot size model have been developed over the years, such as lot sizing models that include multi-stage inventory systems, incentives, or productivity issues. The aims of such a tertiary study are the following: firstly, it helps primary researchers to position their own work in the literature, to reproduce the development of different types of lot sizing problems, and to find starting points if they intend to work in a new research direction. Secondly, the study identifies several topics that offer opportunities for future secondary research apart from the ones covered in this thesis.

In the presence of a progressive payment scheme, the supplier offers a sequence of credit periods, where the interest rate that is charged on the outstanding balance usually increases from period to period. If a buyer faces a progressive trade credit scheme, various options for settling the unpaid balance exist, where the financial impact of each option depends on the current credit interest structure and the alternative investment conditions. Chapter 3 takes up this issue by generalizing the trade credit inventory model with progressive interest scheme by considering a) the case where the credit interest rate of the buyer may (but not necessarily has to) exceed the interest rate charged by the supplier, b) where the buyer has the option to settle the outstanding balance continuously within the credit periods, c) where compound interest accrues at the retailer, and d) bank loans are available as a substitute for the trade credit. In addition, some inaccuracies in earlier formulations of the effective interest cost are corrected.

Subsequently, Chapter 4 studies and extends solution algorithms for deriving the optimal ordering and payment policies of a retailer on the condition that the supplier provides a progressive interest scheme. Based on the finding that the piecewise total cost functions are convex but not necessarily continuous, a modified solution algorithm is developed and collated with existing ones in the course of a simulation experiment. The results indicate that the modified algorithm can locate all optimal solutions and outperforms existing approaches.

Chapters 5 and 6 further extend the scope of the analysis by considering models aimed at finding ordering and payment policies for a buyer with stock-dependent demand and a supplier that offers a progressive payment scheme. Such a setting can frequently be observed in retail stores where the demand rate is usually influenced by the amount of inventories displayed on the shelves. These chapters correct some errors in the formulation of previously published approaches and extend those works by assuming that the credit interest rate of the retailer may exceed the interest rate charged by the supplier. Several numerical examples illustrate the benefits of the suggested modifications. The results also illustrate the close linkage between operational and financial aspects in supply chain management, which should be considered by employing more integrated planning approaches.

As decisions on the working capital structure of the company defined by an appropriate inventory and payment policy significantly influence future cash-flows and thus the temporal allocation of payments, they should also be evaluated in terms of long-term profitability by considering their net present value or equivalent measures. Especially in situations where trade credit agreements are used over a long period of time and where discount rates are varying, explicitly considering the time-value of money in inventory models helps to make them more realistic. This aspect is considered in Chapter 7 that studies the optimal ordering and payment policies of a buyer assuming that the supplier offers a progressive interest scheme. The models proposed enable decision makers to improve decision making and the results reveal that taking into account the temporal allocation of payments, the prevailing interest relation influences replenishment policies significantly.

Finally, Chapter 8 studies a buyer sourcing a product from multiple suppliers under stochastic demand. The buyer uses a (Q,s) continuous review, reorder point, order quantity inventory control system to determine the size and timing of orders. Lead time is assumed to be deterministic and to vary linearly with the lot size, wherefore lead time and the associated stock-out risk may be influenced both by varying the lot size and the number of contracted suppliers. After presenting several mathematical models for a multiple supplier single buyer integrated inventory problem with stochastic demand and variable lead time, the impact of different delivery structures on the risk of incurring a stock-out during lead time and the required inventories is analyzed.