Multiseason Production Planning under Export Quotas

An export quota is a direct restriction on the quantity of certain goods that can be exported and is an important instrument in international trade policy. In this study, we focus on an exporting firm and examine the implication of export quotas on its production and inventory policies. In particular, the firm applies for an exporting license every season (eg, year) and the amount it can sell is unknown for certainty in advance. The firm must determine its production quantity every period (eg, month) under a production capacity constraint. The presence of quotas decouples inventory from sales: the firm can sell its goods if and only if the quota permits, and this changes the way it manages its production and inventory. We show that the firm in general benefits from stockpiling-produce up to an inventory level higher than current quota. Stockpiling happens if and only if the remaining quota for the current season is smaller than a threshold value. It is more likely to happen when it is closer to the end of a season or when the quotas in future seasons are larger. Although the inventory in excess of current quota cannot be used to fill the demand in the current season, they will be needed in future seasons when new quotas are released and the firm cannot increase production quickly enough due to capacity constraints. Our numerical studies show that the cost of limiting production only to current quota can be substantial.