Oaoa

(a). Formulate this model in AMPL, and solve the following instance. There are T = 13 periods, l = 8 production lines, and a maximum change of M = 3 crews per period. Theproducts are 18REG, 24REG, and 24PRO, with production rates r p of 1.194, 1.509 and 1.509 respectively. Crews work either a day shift with wages ws of $44,900, or a night shiftwith wages $123,100. Display the numbers of crews required on each shift. You will find many fractional numbers of crews; how would you convert this solution to an optimal onein whole numbers?

set SHIFT;

set PROD;



param L > 0;

param rate {PROD}>0;

param T > 0;

param hours {1..T}>=0;

param wages {SHIFT}>0;

param demand{PROD,1..T}>=0;

param M >= 0;



var x { i in PROD,j in 1..T} >= demand [i,j];

var y {i in SHIFT, j in 1..T} >=0, =0;

param inv0 {PROD} >= 0;

param invcost{PROD}>=0;

param wages {SHIFT}>0;

param demand {PROD,1..T}>=0;

param M >= 0;

var x { i in PROD,j in 1..T} >= demand [i,j];

var y {i in SHIFT, j in 1..T} >=0, =0;minimize Total_Cost:

sum{i in SHIFT, j in 1..T} wages[i] * y[i,j]+sum{p in PROD,j in 1..T} inv[p,j]*invcost[p];



subject to hores_totals {j in 1..T}:

sum{i in PROD} rate[i]*x[i,j] 0;

param hours {1..T}>=0;

param inv0 {PROD} >= 0;

param invcost {PROD}>=0;

param wages {SHIFT}>0;

param demand {PROD,1..T}>=0;param M >= 0;

param A>=0;



var x { i in PROD,j in 1..T} >= demand [i,j];



var y {i in SHIFT, j in 1..T} >=0, =0;



minimize Total_Cost:

sum{i in SHIFT, jin 1..T} wages[i] * y[i,j]+sum{p in PROD,j in 1..T, k in 1..A} inv[p,j,k]*invcost[p];



subject to hores_totals {j in 1..T}:



sum {i in PROD} rate[i]*x[i,j]