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"Linear Programming Case Study: Cost Minimization in Hospital Resource Allocation"

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This document presents a detailed linear programming case study in the service sector, specifically focused on hospital resource planning by Dr. Naseema Malik. It defines four types of hospital beds—Normal, ICU, OT, and Day Care—each with unique equipment requirements and associated costs. Using hypothetical but realistic data, the case aims to minimize the total cost of hospital bed allocation under eight well-defined constraints involving limited medical resources like IV stands, oxygen cylinders, and ventilators. The document includes a clear word problem, mathematical model, and the optimal solution, making it ideal for students and professionals studying operations research, healthcare management, or linear programming applications in real-world service settings.

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Linearprogramming
ServiceSectorAssignment

DrNaseemaMalikisplanningtobuildahospitalwhichrequireaNormalBed,BedofIntens
iveCarepatients,BedforthePatientsrequiredaoperationtheatre(OT)andbedindaycarec
enter.NormalBedrequires1IvStand,1Bench,0.2oxygencylinderand1BPchecker.Bedo
fIntensivecarepatientsrequires2IVstand,2benches,1.2Cylinder,1Hotlermachineand1
Bpchecker.BedforthePatientsrequiredaoperationtheatre(OT)requires2IVStands,2Be
nches,1.5Cylinder,4HotlerMachineand1SurgicalIv.bedindaycarecenterrequires1IVs
tands,2cylindersand1BpChecker.wehaveboughtatleast160IvStands,165benches,60
Cylinders,50Hotlermachine,12surgcalIV,16ventilatorand120bpcheckers.CostofNor
malbedperdayisRs5000,BedofIntensiveCarepatientsisRs50000,BedforthePatientsre
quiredaoperationtheatre(OT)isRs75000andbedindaycarecenterisRs10000
.Developacaseonlinearprogrammingyourcasemustbeadheredtothefollowingconditio
ns.
i:Objectiveofthefirmshouldbeminimizationand
ii;Caseshouldbeonservicessector
iii:Modelmusthaveatleastfourvariablesandeightconstraints.
iv:Firmandvariablesmustbewelldefined.
v:Allvariablesandinformationmustbelocalized
vi:Numbersmaybehypotheticalbuttheymustbeclosedtoreality.
i. Therequirementsoftheassignmentareasfollows:
Acompletewordproblem
ii. Amathematicalmodel
Solution(Optimalvaluesofallvariablesandtheobjectivefunction)
Determinetheoptimalsolutionifobjectiveiscostminimization.




Ward ICU OT DayCare
Resource
X1 X2 X3 X4
IVStand 1 2 2 1 >= 160
Bench 1 2 2 0 >= 165

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Uploaded on
August 2, 2025
Number of pages
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Written in
2025/2026
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