## 3 Method
### Problem Definition and Notations  
In this part, the production-logistics problem and corresponding notations are given as follows. Generally, an FMS consists of a set of computer numerically controlled machines and a material-handling system. AGVs are widely used to facilitate the transport of raw materials, work in process (WIP), finished products, and waste materials between warehouses and production cells. Consider an FMS that contains a set of machines and a set of AGVs. A set of jobs is to be processed on a list of machines in a predetermined order. A machine can perform one operation once. The warehouse and every production cell has an input buffer and an output buffer served as the unloading point and the loading point respectively. Both the number and the loading space of AGVs are limited.  
The notations used in the problem statement, algorithm description, and throughout the paper are as follows:  
\(i,h\): machine  
\(j\): job  
\((i,j)\): an operation that job \(j\) is processed on machine \(i\)  
\((i,j)\rightarrow(h,j)\): job \(j\) should be firstly processed on machine \(i\) and then on machine \(h\)  
\(t\): current time  
\(y_{ij}\): starting time of operation \((i,j)\)  
\(p_{ij}\): processing time of operation \((i,j)\)  
\(\Delta T_{ij}^{R}\): remaining time of operation \((i,j)\)  
\(p_{ibj}\): priority of logistics task between operation \((i,j)\) and operation \((h,j)\)  
\(Q_{ih}\): volume of parts transported from machine \(i\) to machine \(h\)  
\(Q_{k}^{A}(t)\): remaining space of AGV \(k\) at time \(t\)  
\(L_{r}\): path length of road segment \(r\)  
\(v_{k}\): speed of AGV \(k\)  
\(T_{ik}^{(r)}\): time cost of AGV \(k\) passing road segment \(r\)  
\(T_{ik}\): time cost of AGV \(k\) arriving at machine \(i\)  
\(\Delta T_{ik}^{A}\): time cost of AGV \(k\) going from machine \(i\) to machine \(h\)  
\(\Delta T_{total}\): total waiting time  
\(\Delta T_{ibj}\): waiting time between operation \((i,j)\) and operation \((h,j)\)  
\(\Delta T_{ij}^{\text{W}A}\): waiting time of job \(j\) on machine \(i\) before processing  
\(\Delta T_{ij}^{\text{W}A}\): waiting time of job \(j\) on machine \(i\) after processing  
\(C_{\text{max}}\): makespan  
\(C_{j}\): completion time of job \(j\)  
\(C_{ij}\): completion time of operation \((i,j)\)  
\(E_{total}\): total electricity consumption  
\(E_{M^{\prime}}^{(i)}\): electricity consumption of machine \(i\)  
\(E_{AGV}^{(k)}\): electricity consumption of AGV \(k\)  
\(P_{M^{\prime}}^{(i)}\): average power of machine \(i\) when processing  
\(P_{MI}^{(i)}\): average power of machine \(i\) when idle  
\(P_{AGV}^{(k)}\): average power of AGV \(k\)  
Assuming that a feasible schedule plan is given as in Figure 2, first, the job \(j\) is processed on the machine \(i\). The starting time of operation \((i,j)\) is \(y_{ij}\). The processing time of operation \((i,j)\) is \(P_{ij}\). The completion time of operation \((i,j)\) is \(C_{ij}\). The remaining time of operation \((i,j)\) is \(\Delta T_{ij}^{R}\). Then, after the operation \((i,j)\), the WIP is transported to the next machine \(h\). The waiting time between operation\((i,j)\) and operation \((h,j)\) is \(\Delta T_{ijl}\). The waiting time of the job \(j\) on machine \(i\) before processing is \(\Delta T_{ij}^{WB}\). The time cost of AGV \(k\) going from machine \(i\) to machine \(h\) is \(\Delta T_{iik}^{A}\). The waiting time of the job \(j\) on machine \(i\) after processing is \(\Delta T_{ij}^{WA}\). Next, the job \(j\) is processed on the machine \(h\). The starting time of operation \((h,j)\) is \(y_{hj}\). The processing time of operation \((h,j)\) is \(p_{hj}\). The completion time of operation \((h,j)\) is \(C_{hj}\). The completion time of the job \(j\) is \(C_{j}\).