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204 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

CASE PROBLEM 4 Workforce Scheduling

he Emergency Department at the local hospital provides emergency health care on an as-needed basis
T for people involved in accidents, having injuries, etc. Understandably, it is difficult to predict how busy the
Department will be at any one time and, accordingly, it is also difficult to plan and schedule its workforce
requirements, particularly for nurses qualified and experienced in working in such a department. Recently the
hospital has started using WorkForce Unlimited, a company that specializes in providing temporary nursing
staff to the health care sector. WorkForce Unlimited offered to provide temporary nurses under three contract
options that differ in terms of the length of employment and the cost. The three options are summarized:

Option Length of Employment Cost

1 One month E2 000
2 Two months E4 800
3 Three months E7 500

The longer contract periods are more expensive because WorkForce Unlimited experiences greater difficulty
finding temporary nursing staff who are willing to commit to longer work assignments.
Over the next six months, the hospital projects the following needs for additional nurses in the Emergency
Department.

Month January February March April May June
Nurses Needed 10 23 19 26 20 14

Each month, the hospital can hire as many temporary nurses as needed under each of the three options.
For instance, if the hospital hires five nurses in January under Option 2, WorkForce Unlimited will supply
the hospital with five temporary nurses who will work two months: January and February. For these
nurses, the hospital will have to pay 5(E4800) ¼ E24,000. Because of some negotiations under way, the
hospital does not want to commit to any contractual obligations for temporary nurses that extend beyond
June.
The hospital’s health and safety programme requires each temporary nurse to receive training at the time of
hire. The training programme is required even if the person worked for the hospital in the past. The hospital
estimates that the cost of training is E875 each time a temporary nurse is hired. Thus, if a temporary nurse is
hired for one month, the hospital will incur a training cost of E875, but will incur no additional training cost if the
employee is on a two- or three-month contract.

Managerial Report
Develop a model that can be used to determine the number of temporary nurses the hospital should hire each
month under each contract plan in order to meet the projected needs at a minimum total cost. Include the
following items in your report:
1 A schedule that shows the number of temporary nurses that the hospital should hire each month for each
contract option.
2 A summary table that shows the number of temporary nurses that the hospital should hire under each
contract option, the associated contract cost for each option, and the associated training cost for each
option. Provide summary totals showing the total number of temporary nurses hired, total contract costs
and total training costs.
3 If the cost to train each temporary nurse could be reduced to E700 per month, what effect would
this change have on the hiring plan? Explain. Discuss the implications that this effect on the hiring
plan has for identifying methods for reducing training costs. How much of a reduction in training

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