Table 3 Summary of notations
Indices | |
j | Index of final products at the auto manufacturer (j = 1, 2, …, J) |
n | Index of OEM's products (n = 1, 2, …, N) |
k | Index of components purchased from supplier \(S_{k}\) by the OEM (k = 1, 2, …, K) |
Parameters related to the suppliers’ decisions | |
\(S_{k}\) | The supplier of component k for the OEM |
\(D_{k}\) | Demand for component k |
\(T_{{S_{k} }}\) | Cycle time of replenishment for supplier k |
\(s_{k}^{\prime}\) | The unit storage cost of component k for supplier \(S_{k}\) |
\(h_{k}^{\prime}\) | The unit holding cost of component k for supplier \(S_{k}\), representing the cost of capital, excluding the storage cost |
\(A_{k}^{\prime}\) | The fixed ordering cost of component k by supplier \(S_{k}\) |
\(c_{k}\) | The unit cost of component k purchased from external sources by the supply chain suppliers |
\(r_{k}\) | Rate of return for supplier \(S_{k}\) |
Parameters related to the OEM’s decisions | |
\(D_{n}\) | Demand for part n |
\(T_{{OEM_{k} }}\) | Cycle time of replenishment for OEM |
\(F_{n}\) | Fixed cost of producing part n at the OEM |
\(v_{n}\) | Variable production cost for each unit of part n at the OEM |
\(p_{n}\) | The unit price of part n produced by the OEM |
\(w_{k}\) | The unit cost of component k purchased from suppliers in the supply chain by the OEM |
\(N_{nk}\) | The quantity of component k needed for producing each unit of part n |
\(s_{k}\) | The unit storage cost of component k for the OEM |
\(h_{k}\) | The unit holding cost of component k for the OEM, representing the cost of capital, excluding the storage cost |
\(H_{k}\) | The opportunity cost of the capital tied up in the inventories |
\(A_{k}\) | The fixed ordering cost of component k by the OEM |
\(r_{OEM}\) | Rate of return (ROR) for the OEM |
i | The interest rate of external financing |
\(\gamma_{k}\) | Penalty rate for the delay in payment to supplier \(S_{k}\) |
\(tmax_{k}\) | Maximum deadline for payment to supplier \(S_{k}\) |
\({\text{M}}\) | Maximum limit for external financing (Debt) |
B | Initial budget |
L | Minimum cash level at the OEM, determined by the manager |
Parameters related to the auto manufacturer’s decisions | |
\(D_{j}\) | Total demand for final product j |
\(m_{jn}\) | The quantity of part n needed for producing each unit of final product j |
\(p_{j}\) | The unit price of product j produced by the auto manufacturer |
\(r_{AM}\) | Rate of return for the auto manufacturer |
Decision variables | |
OEM | |
\(Q_{k}\) | Order quantity for component k ordered by the OEM to the supplier \(S_{k}\) |
\(\alpha_{n}\) | The service level of original part n |
\(t_{k}\) | The OEM’s payment time to supplier \(S_{k}\) |
Dbt | The required amount of external financing for the OEM |
Suppliers | |
\(d_{k}\) | The due date of the interest-free period |
\({\uplambda }_{k}\) | The coefficient of replenishment for supplier \(S_{k}\) |
Auto manufacturer | |
\(\beta\) | The prepayment rate of the auto manufacturer |