Manpower planning

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### PARAMETERS

tsk0 = 1000   ! skilled in previous year
tss0 = 1500   ! semi-skilled in previous year
tus0 = 2000   ! unskilled in previous year

! requirements 
RSK = 1000    ! total skilled required
RSS = 1400    ! total semi-skilled required
RUS = 1000    ! total uskilled required

### END PARAMETERS

### COMPONENTS

! Strength of labour force
tsk1 ! number of skilled men employed in year i
tss1 ! number of semi-skilled men employed in year i
tus1 ! number of unskilled men employed in year i
tsk2
tss2
tus2
tsk3
tss3
tus3

! Recruitment
usk1 ! number of skilled men recruited in year i
uss1 ! number of semi-skilled men recruited in year i
uus1 ! number of unskilled men recruited in year i
usk2
uss2
uus2
usk3
uss3
uus3

! Retaining
vusss1 ! number of unskilled retained to semi-skilled in year i
vsssk1 ! number of semi-skilled retained to skilled in year i
vusss2
vsssk2
vusss3
vsssk3


! Downgrading
vskss1 ! number of skilled downgraded to semi-skilled in year i
vskus1 ! number of skilled downgraded to unskilled in year i
vssus1 ! number of semi-skilled downgraded to unskilled in year i
vskss2
vskus2
vssus2
vskss3
vskus3
vssus3

! Redundancy
wsk1  ! number of skilled men made redundant in year i
wss1  ! number of semi-skilled men made redundant in year i
wus1  ! number of unskilled men made redundant in year i
wsk2
wss2
wus2
wsk3
wss3
wus3

! Short-time working
xsk1  ! number of skilled men on short-time working in year i
xss1  ! number of semi-skilled men on short-time working in year i
xus1  ! number of unskilled men on short-time working in year i
xsk2
xss2
xus2
xsk3
xss3
xus3

! Overmanning
ysk1  ! number of superfluous skilled men employed in year i
yss1  ! number of superfluous semi-skilled men employed in year i
yus1  ! number of superfluous unskilled men employed in year i
ysk2
yss2
yus2
ysk3
yss3
yus3

### END COMPONENTS

## EQUALITY

! Continuity
tsk1 = 0.95*tsk0 + 0.9*usk1 + 0.95*vsssk1 -vskss1 -vskus1 -wsk1
tss1 = 0.95*tss0 + 0.8*uss1 + 0.95*vusss1 -vsssk1 +0.5*vskss1 -vssus1 -wss1
tus1 = 0.9*tus0 + 0.75*uus1 -vusss1 +0.5*vskus1 +0.5*vssus1 -wus1

tsk2 = 0.95*tsk1 + 0.9*usk2 + 0.95*vsssk2 -vskss2 -vskus2 -wsk2 
tss2 = 0.95*tss1 + 0.8*uss2 + 0.95*vusss2 -vsssk2 +0.5*vskss2 -vssus2 -wss2
tus2 = 0.9*tus1 + 0.75*uus2 -vusss2 +0.5*vskus2 +0.5*vssus2 -wus2

tsk3 = 0.95*tsk2 + 0.9*usk3 + 0.95*vsssk3 -vskss3 -vskus3 -wsk3 
tss3 = 0.95*tss2 + 0.8*uss3 + 0.95*vusss3 -vsssk3 +0.5*vskss3 -vssus3 -wss3
tus3 = 0.9*tus2 + 0.75*uus3 -vusss3 +0.5*vskus3 +0.5*vssus3 -wus3


! requirements
tsk1-ysk1-0.5*xsk1 = RSK
tss1-yss1-0.5*xss1 = RSS
tus1-yus1-0.5*xus1 = RUS
tsk2-ysk2-0.5*xsk2 = RSK
tss2-yss2-0.5*xss2 = RSS
tus2-yus2-0.5*xus2 = RUS
tsk3-ysk3-0.5*xsk3 = RSK
tss3-yss3-0.5*xss3 = RSS
tus3-yus3-0.5*xus3 = RUS

## END EQUALITY

## INEQUALITY

! Retaining semi-skilled men
vsssk1 - 0.25*tsk1 <0
vsssk2 - 0.25*tsk2 <0
vsssk3 - 0.25*tsk3 <0

! overmanning
ysk1 + yss1 +yus1 < 150
ysk2 + yss2 +yus2 < 150
ysk3 + yss3 +yus3 < 150


! Upper bounds
usk1 < 500
uss1 < 800
uus1 < 500
xsk1 < 50
xss1 < 50
xus1 < 50
vusss1 < 200

usk2 < 500
uss2 < 800
uus2 < 500
xsk2 < 50
xss2 < 50
xus2 < 50
vusss2 < 200

usk3 < 500
uss3 < 800
uus3 < 500
xsk3 < 50
xss3 < 50
xus3 < 50
vusss3 < 200

## END INEQUALITY

## COST

400*vusss1+500*vsssk1+200*wus1+500*wss1+500*wsk1    &
+500*xus1+400*xss1+400*xsk1+1500*yus1+2000*yss1     &
+3000*ysk1                                          &
+400*vusss2+500*vsssk2+200*wus2+500*wss2+500*wsk2   &
+500*xus2+400*xss2+400*xsk2+1500*yus2+2000*yss2     &
+3000*ysk2                                          &
+400*vusss3+500*vsssk3+200*wus3+500*wss3+500*wsk3   &
+500*xus3+400*xss3+400*xsk3+1500*yus3+2000*yss3     &
+3000*ysk3                                          

## END COST

