Presenter: Sandra Transchel, Kühne Logistics University

Link to personal website: Sandra Transchel · KLU

Title: Sorting as a Strategic Bottleneck: Contract Design in Multi-Producer Closed-Loop Supply Chains

Host: Christian Larsen

Abstract:

Deposit-refund systems (DRS) have proven effective in stimulating consumer returns of reusable packaging. However, in multi-producer environments with heterogeneous, brand-specific containers, a critical operational bottleneck arises after collection: returned items arrive mixed and must be sorted before reuse. Sorting is costly, affects net return rates, and directly determines the need for new packaging injection. Existing closed-loop supply chain models focus on collection or remanufacturing effort but do not endogenize sorting effort as a strategic decision of an intermediary.

We develop a game-theoretic model of a closed-loop supply chain consisting of multiple producers and a single wholesaler operating under a DRS. Producers use differentiated reusable packaging and rely on the wholesaler’s costly sorting effort to reduce return inefficiency. Sorting effort increases the net return rate through a concave recovery technology and affects both deposit reimbursements and replacement production costs. In a benchmark setting without contractual coordination, we show that the wholesaler exerts positive effort only if the deposit exceeds a critical threshold; otherwise, equilibrium sorting effort collapses to zero, generating systemic underinvestment.

To address this coordination failure, we analyze two contract classes: a per-unit transfer-fee contract and a cost-sharing contract. For each mechanism, we characterize the wholesaler’s best response and derive the unique symmetric Nash equilibrium among producers in closed form. Both contracts exhibit threshold structures in market size: beyond a critical number of producers, equilibrium contributions vanish due to free-riding, even though sorting remains socially valuable. Comparative statics reveal that equilibrium incentives increase in replacement and sorting costs but decrease in deposit levels and the number of producers. Sorting inefficiency has opposite effects across contracts, strengthening transfer-fee incentives while weakening cost-sharing contributions. A further numerical analysis shows that cost-sharing dominates transfer fees in reducing total system cost and increasing net return rates, particularly in fragmented markets with high replacement costs.

Organisers: Surabhi Verma and Hartanto Wong