Impact of uncertainty ascribed to defective products on supply chains

• The uncertainty of defective products in supply chains affects order quantities and profits for retailers and manufacturers.
• Compensation contracts between manufacturers and retailers can mitigate losses due to defective products.
• Mathematical modeling and game theory provide frameworks for assessing and addressing these uncertainties.

Traditional inventory management primarily addresses the uncertainty of demand, but the uncertainty in the supply, mainly due to defective products, is equally crucial. Including defective products introduces variability in supply chains, affecting order quantities and leading to overstock or shortages. This paper formulates a supply chain model incorporating defective products to understand their impact on order quantities and profits for retailers and manufacturers.

Historical studies have mainly focused on the direct impact of defective products, such as compensation costs and quality improvement efforts. However, this paper focuses on the latent loss caused by the uncertainty of faulty products. It proposes a method to quantify this latent loss in monetary terms and suggests compensation contracts wherein manufacturers compensate retailers to maintain a healthy supply chain partnership. By employing contract techniques and game theory, the paper illustrates that fair compensation can incentivize retailers to order appropriately, even when defective products are anticipated.

The model demonstrates that when defective products are expected, retailers must order more than usual to offset potential losses from faulty items. However, despite full-price refunds for defective products, retailers still face losses due to uncertainty. The paper proposes a compensation fee higher than the wholesale price to cover these latent losses, ensuring retailers’ profits are not adversely affected. This fee acts as a risk mitigation tool and encourages cooperation between manufacturers and retailers.

Numerical examples and mathematical proofs show the conditions under which compensation contracts can be mutually beneficial. The Nash bargaining approach, among other methods, is used to determine fair compensation, ensuring that the profits from increased order quantities are shared equitably between manufacturers and retailers. This equitable sharing fosters a cooperative partnership, incentivizing manufacturers to maintain high product quality and improve their processes, thus reducing future uncertainties.

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