They are considering two main approaches: improve physical plant capacity (beds, surgery resources) or expand work schedule (they currently operate from Sunday to Friday with Saturday off). Our goal for this assignment is to consider these options for expansion using an LP model. Specifically:
1. Formulate a linear program model to maximize the number of patients to be admitted each week, i.e. find the optimal admissions schedule. Shouldice currently operates with a capacity of 33 surgeries (operating capacity) per day, 89 beds, and works 6 days a week (Sun-Fri). You may consider formulating a problem around setting a weekly admittance schedule and assume unlimited demand (Shouldice is popular but can’t respond to the demand).
2. Identify different capacity options that are captured by your formulation based on bed capacity or work week. For example, what would be the effect of increasing operating capacity by 5, 10 or 15 surgeries per day? Or, how about increasing bed capacity to 100, or 150? How about expanding operations to Saturday? In addition to these options, you can explore different configurations on your own and make assumptions as you see fit.
3. For each option:
• Calculate the optimal schedule
• What is the annual throughput (# patients) that can be treated)?
• What is the capacity utilization?
• What is the annual cost?
• What is the annual profit?
Each admitted patients brings in about $2,100 in revenues. Total annual cost of the hospital is currently around $12m ($8.5 for hospital operations and $3.5 for clinic operations). We know that a 50% expansion in bed capacity by adding a new plant is about $4m. Feel free to make assumptions about the costs of your proposed expansion options (and clearly annotate them and briefly argue for their validity).
4. Write a brief report of your findings (max of 2 pages, not counting tables or figures). This two page report, in addition to briefly presenting the results of your LP analysis, should include practical considerations. I want you to worry about side effects of your proposed expansion options. For example, even though your LP analysis may favor one option over another, you are free to recommend another good enough option because it may enable Shouldice to maintain its quality levels. Feel free to also discuss (or even better, analyze using your LP model) other capacity expansion opportunities you may identify in addition to the ones I suggest above even if you cannot directly evaluate them in your LP models.

 

Day 1 Day 2 Day 3 Day 4 Day 5 What Happens admit, exam, test, orientation, dinner surgery, anesthesia, recovery recovery, exercise, meals recovery, exercise, meals discharge When pm all day am Resources Used bed, ... surgery, bed bed bed