## Lot Sizing on a Cycle

Riley Cooper, The University of Newcastle

To accompany my AMSI Vacation Research Scholarship Report here is a brief description of my research topic and report.

How did I choose my research topic for the AMSI VRS Project?

I knew that I wanted to undertake the AMSI Vacation Research Scholarship program but I did not know what I could research or wanted to research. Firstly I emailed many researchers at my university and organised meetings so that I could hear about what they research and see if there was anything of interest to me. After a few meetings I found the topic of Lot Sizing on a Cycle from my supervisor for this project Dr Hamish Waterer. Hamish had previously thought of this interesting problem that hadn’t previously been considered.

What is Lot Sizing and why should it be considered on a cycle rather than a path as has already been studied extensively?

Single Item Lot Sizing is a recurring model in the problem of production planning. The problem is to produce a single stock item over many time periods in order to meet demand of each time period while minimizing the total cost of doing so. In our problem formulation the costs considered are the per unit production cost of the item, over-head production set up costs for each production period and holding costs between time periods. The decisions to be made in the model are: how much stock to produce in each time period, how much stock to hold from one time period to the next and whether or not we should allow for any production in a particular period. In the previous research on this topic, the underlying network has been set up on a path with a clear start and end. In my report we view this problem on a cycle where the stock held from the last period equals the stock entering the first period. The benefits of this formulation is its ability to model a steady state of this problem and to avoid the possible inefficiencies of boundary conditions.

Throughout the 6 weeks of working on this project, as hoped for, we have found that many of the properties proven for Lot Sizing on a Path are also valid for Lot Sizing on a Cycle. To see exactly what has been shown for this variant of the classical path case of this problem, please refer to my Report Lot Sizing on a Cycle.

Riley Cooper was one of the recipients of a 2017/18 AMSI Vacation Research Scholarship.