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

Table 3

The optimal length of replenishment cycle time 𝑇₁₂ under various cases.

Situation	Condition	TC12(𝑇12)	𝑇12
𝑀>𝑁	2𝐴≥Δ1(1,𝑘)	TC12-2(𝑇12-2),	𝑇12-2
	2𝐴<Δ1(1,𝑘)	TC12-1(𝑇12-1),	𝑇12-1
𝑀≤𝑁		TC12-3(𝑇12-3)	𝑇12-3

where 𝑇_12-1=[2𝐴+(𝑘−ℎ)𝐷𝑇²_𝑊]/(𝑘+𝑝𝐼_𝑒)𝐷, 𝑇_12-2=[2𝐴+(𝑐𝐼_𝑐−𝑝𝐼_𝑒)𝐷(𝑀−𝑁)²+(𝑘−ℎ)𝐷𝑇²_𝑊]/[(𝑘+𝑐𝐼_𝑐)𝐷], and 𝑇_12-3=[2𝐴+(𝑘−ℎ)𝐷𝑇²_𝑊]/[(𝑘+𝑐𝐼_𝑐)𝐷].