Optimal and simple approximate solutions to a production-inventory system with two production rates

We consider a production-inventory system in which the facility produces continuously, switching between two production rates: one faster and one slower than the average demand rate. Demand follows a compound Poisson process, and the size of each demand request is an exponential random variable. Unsatisfied demand is backordered. The production-inventory system is controlled by a two-critical number policy (r, R), whereby production switches from the slower rate to the faster rate when inventory drops below level r and from the faster rate to the slower rate when inventory reaches level R. A fixed cost occurs whenever production switches rates. Our analysis covers two cases: r >= 0 and the less studied case of r <= 0. We use a level crossing approach to derive the steadystate distribution of the inventory level. Using the steady-state distribution of the inventory level, we calculate the total expected inventory holding, backorder, and switchover costs for each of the two cases. We outline how to obtain the optimal policy through a search of the expected cost functions. We also propose heuristics that give simple closed-form solutions with near-optimal performance. Through a numerical study, we illustrate the importance of considering the r <= 0 case.

Automated summary

This article discusses a production-inventory system that switches production rates based on demand. It introduces a two-critical number policy for controlling the system and derives the steady-state distribution of the inventory level using a level crossing approach. The total expected costs for two different scenarios are calculated, and simplified solutions are proposed.