June 2020 -

Jan 2021


Industrial Engineer Fellowship



Stochastic Optimization

Data Analysis



Seyed Iravani

Maximizing Probability: Shift Assignment

The goal is to develop an algorithm that can maximize the probability that a nurse accepts a shift, once matched, based on their preference, location, qualifications, and payment.

As labor cost makes up a large share of healthcare facilities costs, it is crucial to create an adequate staffing and scheduling system for nurses to help drive the operating costs down.


The U.S. is projected to experience a shortage of Registered Nurses that is expected to intensify as Baby Boomers age and the need for health care grows. With the projected shortage in nurses, there is an increase in the workload and working hours for nurses which are affecting the quality of healthcare in the hospitals.


Problem Analysis

I Identified other healthcare facilities that face similar problems and industry solutions to address them

Mathematical Formulation

Designed a stochastic optimizing model in at-Risk to increase the probability that nurses fill all shifts with 55% improvement from the original rate


  • First, I needed to design a nurse-shift matching model based on the nurses' degrees, certifications, work experience, and years of experience.

    • The matching model would reduce the number of vacant shifts on the platform through the available set of nurses.

  • Second, it is not a guarantee that nurses will accept to work in a matched shift.

    • ​The stochastic algorithms can help predict the probability that the shifts are filled with different match combinations and identify the best match combination to show nurses the shifts. ​

Model Design

The model focuses on two keys aspects, matching nurses to a shift and maximizing the probability that nurses accept a shift through controlling the shift content that nurses see. 

  • Sets:

    • 𝑖 𝜖 𝐼 {1,...,10}: (Nurses)

    • 𝑗 𝜖 𝐽 {1,...,3}:   (Hospitals)

    • 𝑘 𝜖 𝐾 {1,...,3}: (Shifts)

    • 𝑟 𝜖 𝑅 {1,...,5}:  (Certifications) 

    • 𝑡 𝜖 𝑇 {1,...,3}:  (Vaccines) 

  • Parameters:

    • 𝑃𝑖𝑗𝑘: The preference value for nurse i to work at hospital j at shift k; 0 otherwise

    • 𝐷𝑖𝑝: 1 if nurse i works at department p; 0 otherwise

    • 𝐶𝑖𝑟: 1 if nurse i has certification r; 0 otherwise

    • 𝑉𝑖𝑡: 1 if nurse i has vaccine t; 0 otherwise

    • 𝑌𝑖𝑠𝑝: Nurse i has s years of experience department p​; 0 otherwise

  • Decision Variable:

    • 𝑋𝑖𝑗𝑘: 1 𝑖𝑓 𝑛𝑢𝑟𝑠𝑒 𝒊 𝑔𝑒𝑡𝑠 𝑎𝑠𝑠𝑖𝑔𝑛𝑒𝑑 𝑎𝑡 ℎ𝑜𝑠𝑝𝑖𝑡𝑎𝑙 𝒋 𝑡𝑜 𝑤𝑜𝑟𝑘 𝑠ℎ𝑖𝑓𝑡 𝒌; 0 otherwise

  • Objective Function:

    • Maximize sum {i in I} {j in J} 𝑋𝑖𝑗𝑘 × 𝑃𝑖𝑗𝑘

Three nurses availability are to work in three shifts are in the table​

Three nurses availability are to work in three shifts are in the table​

I multiplied the number of nurses by the number of shifts to account for all scenario possibilities 

Through comparing the Stochastic Optimization to PARA's algorithm, it is noticeable that for fulfilling all three shifts. The probability is twice as high in the new algorithm compared to the traditional method that PARA uses.


  • Stochastic Algorithm offers a new approach to redesign the nurse-shift assignment by taking into account the nurse's probabilities of accepting and rejecting shifts. 

  • Analysis of nurses' working schedules can enhance the performance of the algorithm

My Ventures


Analyzing banks S&P 500 companies recommendations.  Surprisingly, there were no trackers following the performance of analyst picks over the long term and I decided to build one.


Stroke Code

Redesigning the CODE stroke activation process to reduce the Door-in-door out time for stroke patients