A hospital's emergency ward provides emergency care as needed. Of course, it is difficult to predict the occupation rate of the service and, therefore, it is also difficult to predict labor requirements, particularly for qualified and experienced nurses. Recently, the hospital began using the services of WorkForce Medical, an agency specializing in the hiringof temporary nursing staff. WorkForce Medical has offered to provideinterim nurses under three contracts that differ in terms of length of employment and cost. The three contracts are summarized in the table:

 

Contract	length of employment	Cost ($)
C1	1 month	2000
C2	2 months	4800
C3	3 months	7500

 

Month                                   January	February	March	April	May	June
Need for additional                         10	23	19	26	20	14

 

 

Longer contracts are more expensive because it is more difficult for WorkForceMedical to find temporary nurses willing to commit for longer periods of time. Over the next six months, the hospital anticipates the following needs for additional nurses in the emergency ward.

 

 

Month	January	February	March	April	May	June
Need for additional  nurses	10	23	19	26	20	14

 

Each month, the hospital may hire as many temporary nurses as necessaryunder each of the three contracts. For example, if the hospital hires five nurses in January under the C2 contract, WorkForce Medical will provide the hospital with five temporary nurses who will work for two months: January and February. For these nurses, the hospital will have to pay 5 × (4800 $) = $24 000.

Due to some ongoing negotiations, the hospital does not want to commit to interim contracts that exceed June.

Hospital regulations require that each temporary nurse receive training at the time of hiring. The training program is required even if the person has previously worked for the hospital. The hospital estimates that the cost of training is $875 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 $875. On the other hand, if the nurse has a contract of several months, the cost of the training will only be incurred once, at the beginning of the first month.

 

 

1- Work to do

Develop a linear programming model that can be used to determine the number of temporary nurses that the hospital should hire each month under each contract to meet anticipated needs at a minimum total cost. Use this model to answer the following questions:

 

          a.    What is the optimal hiring plan (i.e. how many temporary workers should be hired on what dates and under what contract to minimize the total cost of recruitment and employment? what are the associated costs (contract cost, training cost, total cost)?
 

         b.   If the hospital can hire permanentnurses for a total monthlysalary cost of €2500, what effect would this have on total labour and training costs over the six-month period compared to the recruitment of temporary nurses (assuming that the workload required for an interim nurse is the same as that of a permanent nurse)? Would you recommend that the hospital hire permanent nurses? How many? (You may need to modify your model to answer this question).