Table 2 list of notations
Indices | |
|---|---|
n | Index of the manufacturer’s products (original parts) (n = 1, 2, …, N) |
k | Index of raw materials and related suppliers (k = 1, 2, …, K) |
Parameters | |
\(y_{n}\) | The random variable of demand |
\(p_{n}\) | The selling price of product n (per unit) |
\(v_{n}\) | The variable production cost for product n (per unit) |
\(h_{n}\) | The holding cost for the remaining original parts at the end of the period (per unit) |
\(s_{n}\) | The shortage cost for product n at the end of the period (per unit) |
\(w_{k}\) | The purchasing cost for material k (per unit) |
\(c_{k}\) | The procurement cost of material k by the related supplier (per unit) |
\(m_{nk}\) | The required amount of material k used for each unit production of original part n |
\(tmax_{k}\) | The final due date for the payment to supplier k (in days) |
\(r_{l}\) | The daily interest rate of external financing |
\(r_{m}\) | Rate of return for the manufacturer’s investment |
\(I_{n}\) | Initial inventory of product n |
\(B_{0}\) | Initial budget |
ML | Maximum financing capacity |
Decision variables of the suppliers | |
\(b_{k}\) | The time on or before which the payment of material k will be discounted (in days) |
\(u_{k}\) | The discount rate for early payments |
\(d_{k}\) | The due date for the interest-free period (in days) |
\(\tau_{k}\) | The penalty rate per day delay for payment of material k after the interest-free period |
Decision variables of the manufacturer | |
\(R_{n}\) | Inventory level of product n at the end of the period before shipment to the customers |
\(Q_{n}\) | The production quantity of original part n (\(Q_{n} = R_{n} - I_{n} )\) |
\(Q_{k}\) | The order quantity of raw material k (\(Q_{k} = \mathop \sum \limits_{n} m_{nk} Q_{n}\)) |
\(t_{k}\) | Payment time for material k to the related supplier (in days) |
\(x_{k}^{i}\) | Binary variable related to pay at each time interval (i = 1,2,3) |
\(l\) | The loan amount borrowed from an external source |