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In an FMCG sector we must supply a quantity of product or service that maximizes profits, taking into account cost associated with product returns (excess supply) or product absence (excess demand). We thus forecast demand and its probability, checking it with the cost function, which is highly dynamic over time and different for each company and product.
Given a sales volume prediction (V ), the optimal decision (S1) depends on the uncertainty (1) and the probability of zero remaining stock (P1).
If we introduce a loyalty promotion (coupons, bar code collections, ...) the absence of service cost will increase because of the lost opportunities of future sales (a2 > a0) and decreases the optimal probability of zero remaining stock (P2 < P1), increasing the optimal quantity to be distributed (S2 > S1). However, if we introduce a promotion with added product, and the returning cost thus increases (3 > 0), this makes the optimal probability of zero remaining stock (P3 > P1), decreasing the optimal quantity to distribute (S1 > S3).
