Mixed financing strategies for a supply chain with a financially distressed seller: combination of equity financing and debt financing

Abstract This work discusses a supply chain composed of one third‐party logistics (3PL) firm and one capital‐constrained seller. To cover the seller's ordering and logistics costs, two distinct mixed financing schemes are considered to address the funding needs: (i) equity financing and bank credit financing (EBF) and (ii) equity financing and 3PL firm financing (ELF). We examine how the equity financing ratio influences equilibrium outcomes and derive the financing preference for each member. The results reveal that a large equity financing ratio prompts the seller to buy more. Interestingly, the seller's profit under EBF either monotonically decreases or exhibits a concave relationship with respect to the equity financing ratio. By contrast, the seller's profit under ELF is consistently concave with respect to the equity financing ratio. Additionally, a Pareto zone of the 3PL firm's interest rate exists in which a win–win situation can be achieved. The seller tends to opt for ELF when the sum of the unit transportation fee and ordering cost is high but the equity financing ratio is moderate. Comparatively, the 3PL firm is reluctant to offer financing when both the sum of the unit transportation fee and ordering cost, and the sum of the unit transportation cost and ordering cost are high, while the equity financing ratio is low. Finally, we investigate an endogenous equity financing ratio and further discuss the effect of the seller's initial working capital.