An MILP approximation for ordering perishable products with non-stationary demand and service level constraints

Abstract

We study the practical production planning problem of a food producer facing a non-stationary erratic demand for a perishable product with a fixed life time. In meeting the uncertain demand, the food producer uses a FIFO issuing policy. The food producer aims at meeting a certain service level at lowest cost. Every production run a setup cost is incurred. Moreover, the producer has to deal with unit production cost, unit holding cost and unit cost of waste. The production plan for a finite time horizon specifies in which periods to produce and how much.We formulate this single item—single echelon production planning problem as a stochastic programming model with a chance constraint. We show that an approximate solution can be provided by an MILP model. The generated plan simultaneously specifies the periods to produce and the corresponding order-up-to levels. The order-up-to level for each period is corrected for the expected waste by explicitly considering for every period the expected age-distribution of the products in stock. The model assumes zero lead time and backlogging of shortages. The viability of the approach is illustrated by numerical experiments. Simulation shows that in 96.4% of the periods the service level requirements are met with an error tolerance of 1%.