StevenSlimstock/r_Q_optimization

When using or sharing the app or its source code IN ANY WAY, please use the following citation:

Steven R. Pauly, (r,Q)-optimization, (2025).

This app implements the (r, Q)-calculation based on the paper "The Square Root Algorithm for Single Item Lot Sizing" of 2017 by M. Farvid & K. Rosling.

Besides that, you have the ability to use different lead time demand distributions (both discrete and continous ones). For this, we use the paper "Loss Functions for Inventory Control" of 2025 by Steven R. Pauly (the author of this page).

Lastly, you can choose to compare the optimal solution to simple, sequential models that are easy to implement in practice. The "closed stochastic EOQ model" comes, for the backorder cost per unit per time unit and the fill rate constraint from the paper "Simple Economic Order Quantity heuristics for stochastic inventory control", published in 2025 by Ruud H. Teunter, M. Zied Babai and Aris A. Syntetos. The "closed stochastic EOQ model" for the backorder cost per unit was derived by the author of this page (using the same technique as in the previously mentioned paper). The "Gallego" EOQ formula comes from the paper "New bounds and heuristics for (Q, r) policies" by Guillermo Gallego, published in 1998. Then, the vanilla en backorder EOQ formula appear numerously in literature and the "Platt" EOQ formula is a formula that was derived in the paper "Tractable (Q, R) heuristic models for constrained service levels." by David E. Platt, Lawrence W. Robinson and Robert B. Freund in 1997.

Research has been done on checking the optimality gap of the EOQ model with backordering in a system where a backorder cost per unit per time unit is used and lead time demand is normally distributed. This app allows you check the optimality gap for both a backorder cost per unit per time unit as for a backorder cost per unit and a fill rate constraint, but also check the optimality gap for different lead time demand distributions. The source code can be used to do an analysis on a large scale. You do have to adjust the code to work with parallelization if you want to run a large number of instances.