Table 11 The parameter values for test problems.

AGV speeds

Speed of AGVs used for material handling

\(\sim U\left[\text{1,5}\right]\)

meter/minute

\({\widetilde{Pr}}_{jmsl}\)

Fuzzy triangular processing time

\(\sim\)(\(U\left[\text{1,5}\right],U\left[\text{6,9}\right],U\left[\text{10,15}\right]\))

minute

\({D}_{ms{m}{\prime}(s+1)}\)

Travel distance

\(\sim U\left[\text{5,50}\right]\)

meter

\({Se}_{jims}\)

Sequence-dependent setup time

\(\sim U\left[\text{0.25,5}\right]\)

minute

\({\widetilde{a}}_{jim}\)

Fuzzy learning coefficient

\(\sim U\left[-5,-1\right]\)

dimensionless

\({PEC}_{msl}\)

Processing energy consumption cost

\(\sim U\left[\text{10,1000}\right]\)

dollar

\({SEC}_{ms}\)

Setup energy consumption cost

\(\sim U\left[\text{10,200}\right]\)

dollar

\({IEC}_{ms}\)

Idle energy consumption cost

\(\sim U\left[\text{10,80}\right]\)

dollar

\({LEC}_{jsu}\)

Loaded AGV energy consumption cost

\(\sim U\left[\text{10,500}\right]\)

dollar

\({UEC}_{su}\)

Un-loaded AGV energy consumption cost

\(\sim U\left[\text{10,200}\right]\)

dollar