“…Recently, Pal et al [54] considered a two-echelon competitive supply chain with trade credit policy. Alternative production-inventory models that have investigated various aspects of the coordination of supply chains are as follows: Goyal [55], Yao and Chiou [56], Chung and Wee [57], Chang et al [58], Lin and Lin [59], C ardenas-Barr on et al [60], Lin et al [61], Su [62], Sana [63], Das et al [64], Ouyang et al [65], Giri and Sharma [66], Ouyang et al [67], Sana [68], Sarkar [69], Mahata et al [70], and their references.…”