Theproblem

A hospital's emergency ward provides emergency care as needed. Of course, it is difficult to predict theoccupation rate of the service and, therefore, it is also difficult to predict labor requirements, particularly forqualified and experienced nurses. Recently, the hospital began using the services of WorkForce Medical, anagencyspecializinginthehiringoftemporarynursing staff.WorkForceMedicalhas offeredtoprovideinterimnurses under three contracts that differ in terms of length of employment and cost. The three contracts aresummarizedinthetable:

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

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

Longercontractsaremoreexpensive becauseitismoredifficultforWorkForceMedicaltofindtemporarynurses willingtocommit forlongerperiods oftime.Overthenextsixmonths, thehospitalanticipatesthefollowingneeds for additional nurses intheemergency ward.

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

Eachmonth, thehospitalmayhireasmanytemporarynursesasnecessaryundereachofthethreecontracts.For example, if the hospital hires five nurses in January under the C2 contract, WorkForce Medicalwillprovide the hospital with five temporary nurses who will work for two months: January and February. Forthese nurses,thehospitalwill havetopay5 (4800$) =$24000.

Duetosomeongoing negotiations,thehospital doesnotwanttocommit tointerimcontractsthatexceedJune.

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 thatthe cost of training is $875 each time a temporary nurse is hired. Thus, if a temporary nurse is hired for onemonth,thehospitalwillincuratrainingcostof$875.Ontheotherhand,ifthenursehasacontract ofseveralmonths, thecostofthetraining willonlybeincurredonce,atthe beginningofthe firstmonth.

1- Worktodo

Develop a linear programming model that can be used to determine the number of temporary nurses thatthehospital shouldhireeachmonthundereachcontract tomeetanticipatedneedsataminimumtotalcost.Usethis modeltoanswer thefollowingquestions:

a. What is the optimal hiring plan (i.e. how many temporary workers should be hired on what dates andunderwhatcontract tominimizethetotalcostofrecruitmentandemployment?whataretheassociatedcosts (contract cost,trainingcost,total cost)?

b. Ifthehospitalcanhirepermanentnursesforatotalmonthlysalarycostof2500,whateffectwouldthishave on total labour and training costs over the six-month period compared to the recruitment oftemporary nurses (assuming that the workload required for an interim nurse is the same as that of apermanent nurse)? Would you recommend that the hospital hire permanent nurses? How many? (Youmay needtomodifyyourmodel toanswerthis question).