ABC Enterprises, Inc. Basic Decision Scenario

ABC needs a rolling-horizon planning model for determining the optimal numbers of temporary personnel to hire to minimize cost over Months 3 thru 5 (though also, because of hiring arrangements, there are implied costs in Months 6 and 7, but these implied costs are treated as irrelevant to determining an optimal hiring plan).

There are two types of temps hired 1-month [1M] and 3-month [3M]. Those hired of either type require up-front training (at a cost to ABC of $500 per person); their monthly pay is as follows:

1M - $7500 3M - $6300

ABC has known staffing complements/commitments for the three types of personnel (long-term [LT], 1M, and 3M) for 1Ms and 3Ms, for both a current month [month 1] and the following month [month 2], and for LTs, over an entire five month span and needs to make optimal decisions for the 1M and 3M hires in Months 3, 4, and 5 to meet the known staffing requirements [stated in units of staff-month].

An illustration of the known staffing situation for a hypothetical month 1 is as follows:

Month: 1 (This) 2 (Next) 3 4 5

LT 6 3 3 4 5

1M 7 7 # to hire? # to hire? # to hire?

3M 2 2 1+# to hire? # to hire? # to hire?

Known Staff-Month

Need: 15 12 14 15 12

(NOTE: All the specific values shown are part of the illustration. Actual month-to-month use of the model will involve entry of such values as ABC plan in rolling time horizon style.)

Unlimited numbers of 1M and 3M applicants exist; with respect to timing of hiring, there are limits on the number of hired 3Ms as follows:

Month: 3 4 5

Limit: (no limit) 3 2

Beyond Month 5 i.e., for Months 6 & 7 there needs to be at least one 3M but not more than three. Costs in Months 6 & 7 are not considered relevant to the optimization.

To achieve a smoother pattern of required personnel possibly lowering overall cost there is the possibility of shifting required staff-months of work between months 4 & 5. The limit in such shifting of work is that only up to four staff-months of work can be shifted either way. The cost of making shifts is as follows:

From Month 4 to Month 5: $3,000/staff-month

From Month 5 to Month 4: $5,000/staff-month

The cost related to shifting work, if incurred, is considered relevant to the optimization.

The company needs to make optimal decisions for the 1M and 3M hires in Months 3, 4, and 5 to meet the known staffing requirements.

1. Develop the algebraic formulations (which includes, decision variables, objective function, all the constraints.

2. And the optimal solution via excel solver