Integrated Production-Inventory Supply Chain Model

Read this article. An integrated production-inventory model is constructed to address supplier, manufacturer, and retailer uncertainties. According to the author, what are the three types of uncertainties in supply chain management?

Model description and diagrammatic representation

The integrated inventory model (Figure 1) starts when t = 0 and stock is zero. At that time, the suppliers start their production with the rate p_s unit per unit time and purchase at the rate p_m unit per unit time to the manufacturer. When t = t_s , suppliers stop their production, and at t = T_s , the inventory level of suppliers become zero. The total time of the integrated model is T, so the idle time for suppliers is T−T_s. Similarly, the manufacturers start their production at the same time t = 0 with the production rate p_m unit per unit time and purchase this production D_r unit to the retailer in the time gap T_R, which is the bulk pattern. At time t=T_s (=[ \dfrac{T_s}{T_R}]), manufacturers stop their production, and at t = (n + 1)T _R ( n=[\dfrac{p_mT_s}{D_r}]), the stock of manufacturer is zero. Thus, idle period for the manufacturer is T − (n + 1)T_r. Retailers start selling this product to the customers at time t = T_r and end selling at  T=(n+1)T_r+\dfrac{{p_m}^{T_s−nD_nr}
}{D_c} . The idle period for retailers is T_r.

Figure 1 Inventory level for the integrated model.