Write the GAMS code of the mathematical model given below for an assembly line balancing problem. $($There are $41$ work elements, $19$ stations, $19$ workers, $8$ equipment. Cycle time is $16\mathrm{.}64)$

Indices;

i$,$ j Indices for job element numbers

w Index of worker numbers

s Index for workatation numbers

r Index of the numbers of gets of work elements that must be done together, $r=1,$dots,rmax

parameters

n Total number of work staff $0-1$ matrix showing whether worker

BWI w can do work element i Pi is the duration of work element i

FG is a $0-1$ matrix indicating whether work element i can be done at workstation s due to the relevant equipment

required to perform work element $i$

Dw $0-1$ matrix ghowing whether worker w comes to work or not $kl{z}_{7}k2$ Objective function coefficients, $kl>>k2$

decision variables

Xswi $1$ if worker w performs work element xswi at workstation s; otherwise $0$

Ysw $1$ if worker w is assigned to workstation s; otherwise $0$

Zsi $1$ if work element $i$ is assigned to workstation s; otherwise $0$

C cycle time

clusters

I Set of work elements, $i,$jinI

E Set of work elements requiring equipment, EsubeI

W Set of workers, winW

S Station cluster, $sinS$

A Set of precedence relations, $(i,j)inA,$ where job element $i$ is the neighboring predecessor of job element $j$

L Set of work elements that must be individually agsigned to the workstation

Tr that must be assigned together to the same workstation.

M Set of work element pairs $(i,j)$ that cannot be assigned to the same workstation

Minz$=k_1**C+k_2**{\displaystyle \underset{sin5}{\overset{?}{}}}{\displaystyle \underset{\text{w}\text{i}\text{n}\text{W}}{\overset{?}{}}}{y}_{sw}$

${\displaystyle \underset{sinS}{\overset{?}{}}}{\displaystyle \underset{\text{w}\text{i}\text{n}\text{W}}{\overset{?}{}}}{x}_{\text{s}\text{w}\text{i}}=1,$AAiinI

$x_{\text{s}\text{w}\text{i}}{B}_{wi},$AAsinS,AAwinW,AAiinI

${\displaystyle \underset{\text{w}\text{i}\text{n}\text{W}}{\overset{?}{}}}{x}_{\text{s}\text{w}\text{i}}=F{G}_{is},$AAiinE,AAsinS