Optimal Replenishment Decisions under Two-Level Trade Credit with Partial Upstream Trade Credit Linked to Order Quantity and Limited Storage Capacity

Table 1

The optimal length of replenishment cycle time 𝑇₂₂ under various cases.

Situation	Case	Condition	TC22(𝑇22)	𝑇22
𝑀>𝑁	Δ1(𝛼,𝑘)>Δ3(𝛼,𝑘)	2𝐴>Δ2(𝛼,𝑘)	TC22-3(𝑇22-3)	𝑇22-3
		Δ2(𝛼,𝑘)≥2𝐴≥Δ1(𝛼,𝑘)	minTC22-2𝑇22-2,TC22-3𝑇22-3	𝑇22-2 or 𝑇22-3
		Δ1(𝛼,𝑘)≥2𝐴≥Δ3(𝛼,𝑘)	minTC22-1𝑇22-1,TC22-3𝑇22-3	𝑇22-1 or 𝑇22-3
		2𝐴<Δ3(𝛼,𝑘)	minTC22-1(𝑇22-1),TC22-3((𝑀−𝑁)/𝑣)	𝑇22-1 or (𝑀−𝑁)/𝑣
	Δ1(𝛼,𝑘)<Δ3(𝛼,𝑘)	2𝐴≥Δ2(𝛼,𝑘)	TC22-3(𝑇22-3)	𝑇22-3
		Δ2(𝛼,𝑘)>2𝐴>Δ3(𝛼,𝑘)	minTC22-2𝑇22-2,TC22-3𝑇22-3	𝑇22-2 or 𝑇22-3
		Δ3(𝛼,𝑘)≥2𝐴≥Δ1(𝛼,𝑘)	minTC22-2(𝑇22-2),TC22-3((𝑀−𝑁)/𝑣)	𝑇22-2 or (𝑀−𝑁)/𝑣
		2𝐴<Δ1(𝛼,𝑘)	minTC22-1(𝑇22-1),TC22-3((𝑀−𝑁)/𝑣)	𝑇22-1 or (𝑀−𝑁)/𝑣
𝑀≤𝑁			TC22-3(𝑇22-3)	𝑇22-3