This is a pretty tough question I think. Here it is in full and I'll give what I've worked out so far at the bottom.

I just need people to tell me what the letters mean and how I would describe how I formulated everything.

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A large engineering firm, Heavy Automation Logistics (HAL), is changing its focus to become a services firm, and seeks an efficient way to do this. HAL has identified three categories of customer-facing staff: Engineers, IT Consultants and Business Consultants. It is embarked on a workforce repositioning effort, wherein it wishes to decrease the number of engineers and increase the numbers of business consultants and IT consultants. Its approach to achieving this will be a combination of hiring, firing and training (new skills development). Coupled with this workforce repositioning, the current economic climate is expected to mean a short term reduction
in the total number of staff required. Table 4 gives the expected number
of staff of each category required over the next three years.

Engineer IT Consultant Business Consultant
Current 3000 500 1000
Required 2010- 2000 600 1100
Required 2011- 1200 1200 1900
Required 2012- 500 2000 2500
Table 4. Current and expected required staff levels by category, up to 2012

HAL wishes to identify its policy to achieve these numbers, in terms of (a) hiring,
(b) firing and (c) training.
A complicating factor is that there is a normal turnover of staff (that is, staff leaving HAL). HAL’s experience is that staff are more likely to leave during their first year. Taking into account that turnover is expected to be lower during an economic downturn, HAL have forecast the staff turnover percentage rates as in Table 5.

Engineer IT Consultant Business Consultant
≤ 1 year service- 12% 15% 10%
> 1 year service- 7% 10% 5%
Table 5. Expected staff turnover rates, by category

Currently, all staff have been working for HAL for more than one year.
The information to hand regarding possibilities of hiring, firing and training is
as follows.
Hiring: It is possible to recruit from outside a limited number of people with
the appropriate skill sets for HAL. It is expected that in each of the years from now to 2012, the availabilities of the three categories will be as in Table 6:

Engineer IT Consultant Business Consultant
Number available 400 900 800
Table 6. Expected staff availability for hiring, by category

Firing: The costs of making staff redundant are as in Table 7:

Engineer IT Consultant Business Consultant
Redundancy cost 100 120 140
Table 7. Cost in thousands of euro of making staff redundant, by category

Training: Certain categories of staff may be retrained to other categories, as given below. However, it is considered too expensive to retrain Engineers to be Business Consultants, or vice versa, since their skillsets are so different.

• Up to 400 Engineers may be retrained to be IT Consultants each year,
at a cost of e 5000 each, by sending them on external courses.
• IT Consultants may be retrained to be Business Consultants, at a cost
of e 7000 each; however, some of this training is done on the job by existing
HAL Business Consultants, which means that the number trained
in this way each year is limited to one third of that year’s Business Consultant
population.
• Up to 300 Business Consultants may be retrained to be IT Consultants
each year, at a cost of e 6000 each, again by sending them on external
courses.
• Up to 200 IT Consultants may be retrained to be Engineers each year,
at a cost of e 4000 each, also by sending them on external courses.
For simplicity, it is assumed that all the events, namely, hiring, firing, training and staff turnover, occur once each year, on the first day of the year.

Part A - HAL’s objective is to meet these staffing requirements while minimising the
amount of staff redundancy (firing) required.
Formulate this problem as an LP and solve.

Part B - If their objective were changed to minimising costs, how much extra money could they save? Modify your LP to answer this revised question.
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Ok here is what I've formulated so far using the programme LINGO.....
Part A:
MIN = EAF + EBF + ECF + ITAF + ITBF + ITCF + BAF + BBF + BCF;

EA - 0.07*EA + EAH + XA - YA - EAF = EB;
EB + EBH + XB - YB - EBF - 0.12*EAH - 0.07*(EB - EAH) = EC;
EC + ECH + XC - YC - ECF - 0.12*EBH - 0.07*(EC - EBH) = ED;

ITA - 0.1*ITA + ITAH + YA - XA + ZA - WA - ITAF = ITB;
ITB + ITBH + YB - XB + ZB - WB - ITBF - 0.15*ITAH - 0.1*(ITB - ITAH) = ITC;
ITC + ITCH + YC - XC + ZB - WC - ITCF - 0.15*ITBH - 0.1*(ITC - ITBH) = ITD;

BA - 0.05*BA + BAH + WA - ZA - BAF = BB;
BB + BBH + WB - ZB - BBF - 0.10*BAH - 0.05*(BB - BAH) = BC;
BC + BCH + WC - ZC - BCF - 0.10*BCH - 0.05*(BC - BCH) = BD;

WA - 1/3*BA <= 0;
WB - 1/3*BB <= 0;
WC - 1/3*BC <= 0;

EA = 3000; EB = 2000; EC = 1200; ED = 500;
ITA = 500; ITB = 600; ITC = 1200; ITD = 2000;
BA = 1000; BB = 1100; BC = 1900; BD = 2500;

EAH <= 400; EBH <= 400; ECH <= 400;
ITAH <= 900; ITBH <= 900; ITCH <= 900;
BAH <= 800; BBH <= 800; BCH <= 800;

XA <= 200; XB <= 200; XC <= 200;
YA <= 400; YB <= 400; YC <= 400;
ZA <= 300; ZB <= 300; ZC <= 300;

@GIN (EA); @GIN (EB); @GIN (EC); @GIN (ITA); @GIN (ITB); @GIN (ITC); @GIN (BA); @GIN (BB); @GIN (BC);
@GIN (EAH); @GIN (EBH); @GIN (ECH); @GIN (ITAH); @GIN (ITBH); @GIN (ITCH); @GIN (BAH); @GIN (BBH); @GIN (BCH);
@GIN (WA); @GIN (WB); @GIN (WC); @GIN (XA); @GIN (XB); @GIN (XC); @GIN (YA); @GIN (YB); @GIN (YC); @GIN (ZA); @GIN (ZB); @GIN (ZC);
@GIN (EAF); @GIN (EBF); @GIN (ECF); @GIN (ITAF); @GIN (ITBF); @GIN (ITCF); @GIN (BAF); @GIN (BBF); @GIN (BCF);
-----------------------------

and part b:

MIN = 100*EAF + 100*EBF + 100*ECF + 120*ITAF + 120*ITBF + 120*ITCF + 140*BAF + 140*BBF + 140*BCF + 4*XA + 4*XB + 4*XC + 5*YA + 5*YB + 5*YC + 6*ZA + 6*ZB + 6*ZC + 7*WA + 7*WB + 7*WC;

EA - 0.07*EA + EAH + XA - YA - EAF = EB;
EB + EBH + XB - YB - EBF - 0.12*EAH - 0.07*(EB - EAH) = EC;
EC + ECH + XC - YC - ECF - 0.12*EBH - 0.07*(EC - EBH) = ED;

ITA - 0.10*ITA + ITAH + YA - XA + ZA - WA - ITAF = ITB;
ITB + ITBH + YB - XB + ZB - WB - ITBF - 0.15*ITAH - 0.10*(ITB - ITAH) = ITC;
ITC + ITCH + YC - XC + ZB - WC - ITCF - 0.15*ITBH - 0.10*(ITC - ITBH) = ITD;

BA - 0.05*BA + BAH + WA - ZA - BAF = BB;
BB + BBH + WB - ZB - BBF - 0.10*BAH - 0.05*(BB - BAH) = BC;
BC + BCH + WC - ZC - BCF - 0.10*BCH - 0.05*(BC - BCH) = BD;

WA - 1/3*BA <= 0;
WB - 1/3*BB <= 0;
WC - 1/3*BC <= 0;

EA = 3000; EB = 2000; EC = 1200; ED = 500;
ITA = 500; ITB = 600; ITC = 1200; ITD = 2000;
BA = 1000; BB = 1100; BC = 1900; BD = 2500;

EAH <= 400; EBH <= 400; ECH <= 400;
ITAH <= 900; ITBH <= 900; ITCH <= 900;
BAH <= 800; BBH <= 800; BCH <= 800;

XA <= 200; XB <= 200; XC <= 200;
YA <= 400; YB <= 400; YC <= 400;
ZA <= 300; ZB <= 300; ZC <= 300;

@GIN (EA); @GIN (EB); @GIN (EC); @GIN (ITA); @GIN (ITB); @GIN (ITC); @GIN (BA); @GIN (BB); @GIN (BC);
@GIN (EAH); @GIN (EBH); @GIN (ECH); @GIN (ITAH); @GIN (ITBH); @GIN (ITCH); @GIN (BAH); @GIN (BBH); @GIN (BCH);
@GIN (WA); @GIN (WB); @GIN (WC); @GIN (XA); @GIN (XB); @GIN (XC); @GIN (YA); @GIN (YB); @GIN (YC); @GIN (ZA); @GIN (ZB); @GIN (ZC);
@GIN (EAF); @GIN (EBF); @GIN (ECF); @GIN (ITAF); @GIN (ITBF); @GIN (ITCF); @GIN (BAF); @GIN (BBF); @GIN (BCF);
-------------------------------------------------

Do people agree how I've formulated this question?
The letters in the formulation are
E=engineer
B=business consultant
IT= it consultant
H=hiring
F=firing
W,x,y,z = training


How would I describe my formulation for this?


Thanks.