Multiple items procurement under stochastic nonstationary demands

In the consumer goods wholesaling and retailing industry, a large number of stock keeping units must be managed on a regular basis. The items are typically purchased in families, each family being associated with a specific external vendor, and usually there are some constraints on family order quantities and there are frequent opportunities to buy at a temporary low price. The demand for an item is often stochastic and not stationary. In this paper, by computing procurement plans over rolling planning horizons, we transform this difficult sequential decision problem into a multi-period static decision problem under risk. The problem is initially formulated as a stochastic program with simple recourse and a branch and bound algorithm is designed to solve an equivalent deterministic program. A piecewise concave approximation is proposed to reduce this program to a linear program with one 0–1 variable per planning period. The performances of the algorithms are studied in two simulation experiments. The simulations show that, when planning over a rolling horizon, the approach proposed yields excellent results.