Stochastic production planning with internal and external storage and ordering costs

Abstract

This paper aims to compare different models to support decision making in production planning (and, consequently, in sales and inventory), in an environment where product demands are variable and uncertain, it is possible to produce at normal hours and overtime, loss of sales is consequence of stockouts, there is limit to internal storage, with possible and more expensive external storage, and ordering costs are non-negligible. At first, we present a linear and deterministic model, with known demand and without shortage. In the second model, safety stocks are calculated to meet a probabilistic demand, but it is not yet considered the possibility of shortage. The third model includes shortage calculation as a consequence from demand uncertainty. The last two models use an iterative process to re-estimate the unit cost of storage, needed to calculate safety stocks in each period of the planning horizon. The models were implemented in MSExcel, making use of linear programming and search functions available in the software. As the original problem, data of the examples are based on real companies. The study allows concluding that, in the problem analyzed, linear models, simpler and faster to execute, may be sufficient to support good decisions.