Solve the ILP model to determine an optimal weekly phlebotomist schedule template for

the phlebotomists currently available in the hospital laboratory.

$(3)$ Using the ILP model developed in Part $($a$),$ determine the minimum number of

phlebotomists needed in this the hospital laboratory in order to handle all blood

collections in time.

The ILP model to determine phlebotomist shift schedule :

Sets :

Set of all phlebotomists $($

to

$)$

Set of all shifts $($

to

$)$

Set of all days $($

to

$)$

Set of all hours $($

to

$)$

Set of order types $("$STAT$"$ and "regular"$)$

Parameters :

Number of working days per week $(5)$

Working hours per day $(8)$

Number of phlebotomists required in shift j on day k

Average number of orders of type o received in hour t

Time $($in minutes$)$ to collect blood for one order

Decision Variables :

Binary variable.

if phlebotomist i is assigned to shift j on day k$,$

otherwise.

Objective Function :

Minimize :

$($Maximize workload balance$)$

Constraints :

Shift Requirement :

This ensures required number of phlebotomists are assigned to each shift on each day.

Phlebotomist Workload :

Limits number of shifts phlebotomist can be assigned per week.

Night Shift Constraint :

Prevents assigning phlebotomist to morning shift day after working night shift.

Order Fulfillment :

Ensures enough phlebotomists are assigned to each day and hour to handle expected number of orders of both types within time limit$.$

Binary Variables :