OSU Walk-in Health Clinic Staffing

Complaints of excessive waiting times have led the OSU Walk-In Health Clinic (OSUWIHC) to study its staffing. You have been asked to create an aggregate daily staffing plan based upon the following guidelines.

The facility is open from 9 am to \(6 \mathrm{pm}\). Staffing requirements are given on an hour by hour basis (see table below). You are to come up with a least cost way to staff the facility meeting these staffing requirements (and other relevant constraints). Your solution will be the number of people of the different medical staffs to work specific shifts throughout the day.

Two types of medical professionals are used on a part time basis at the OSUWIHC. Physician Assistants (PA) are used, as are LPN's.

PA's work 4 consecutive hours, and, except for those who start at 9 am or \(2 \mathrm{pm}\) (the last shift), are paid $\$ 160$. The shifts that start at 9 am and \(2 \mathrm{pm}\) are paid $\$ 170$. LPN's work a total of three hours -2 hours 'on', one hour 'off', then a final hour 'on'. Their pay depends on which hours they work (also see table). For instance, an LPN that works a shift starting at 9am will 'cost' \(20+22+23=65\) dollars (the 9 am LPN shift would work from \(9 \mathrm{am}-11 \mathrm{am}\), then \(12 \mathrm{pm}-1 \mathrm{pm}\) ).

All possible shift combinations should be considered. Remember, shifts are different than hours. Also, only viable shifts should be considered - for instance, there can be no PA shift starting at 4pm.

To level out staffing requirements, no one shift can have a solution value of more than 4 people. Also, each hour can have no more than 3 'extra' total staff members present.

Find the optimal aggregate daily staffing plan.

PA Requirements, Total Requirements, LPN cost per hour shown below per hour.

Mr. GoodMeal

A recent article identified 7 best fast food meal under 350 calories. The 'best meals' are found at seven different fast food restaurants. The article gives information such as calories, grams of fat, grams of saturated fat, and sodium content. One meal is a 'breakfast' meal (Dunkin' Donuts). Three of the meals have 'beef' (counting ham in this category) - three have chicken, one (breakfast) has nothing in these categories.

Being the adventuresome soul that you are, you set out to create an aggregate plan (not a daily plan) for a one week diet that uses these 7 proposed meals to account for at least 14 and no more than 20 of your weekly meals.

You are constrained by a budget of $\$ 70$ for food (we are not worried about transportation cost now - maybe we'll see this problem again!). You have collected some data about approximate cost for each meal, and that is shown below in the table along with your own personal preferences on the favorability of each meal (higher is more preferential on a scale of 1 to 50 ). In creating your aggregate plan, your objective is to maximize this weighted preference value (number of times using that meal multiplied by the preference measure).

You also need to add constraints that reflect some health related parameters - Your aggregate meal plan cannot 'provide' more than 5400 calories, \(150 \mathrm{~g}\) of fat, \(50 \mathrm{~g}\) of saturated fat, and \(22000 \mathrm{mg}\) of sodium. Note that this aggregate plan is providing an unknown number of meals (subject to the limitations stated above) and thus there will be some additional food allowed in the course of the week.

Your aggregate plan must provide at least 2 breakfast meals during the course of the week. And, for the sake of variety, your plan must limit the number of visits to each individual location (meal) to no more than \(25 \%\) of the total number of meals found in the aggregate plan. So, as an example, if your aggregate plan accounts for 8 total meals, that means that you can visit each location at most 2 times ( \(25 \%\) of the total).

Create an appropriate mathematical programming model that determines the aggregate meal plan which maximizes 'preference' subject to the constraints outlined above. And yes, the number of visits must be whole numbers.

Tequila

Tequila is made from the blue agave plant, a member of the lily family. It takes up to \(8-12\) years for a blue agave plant to mature. They grow only in the Guadalajara region of Mexico. Most tequila producers contract with area farmers and buy agaves locally.

There are laws that dictate the composition of tequila, including the percentage of sugars coming from the fermented blue agave and the alcohol content of the final product.

You are to plan tequila production for the next period for the Simply Perfect distillery. SP buys agaves that are already processed (by the barrel) by 4 local companies - Baja, Guad J, Mexicali, and Jose. The processed agaves are differentiated by PROOF (amount of alcohol on a 1 to 200 scale) and quality (a 1 to 100 scale).

SP wishes to blend together processed agave (and 'filler') to make three kinds of tequila for the next production period - white, yellow and gold. They can ultimately sell a barrel of white tequila for $\$ 60$ barrel, yellow tequila for $80 /barrel and gold for $195/ barrel. They can produce as much white tequila as profitable, but MUST produce NO MORE than 100 barrels of yellow tequila and 50 barrels of gold tequila (they can produce less if it is not profitable enough).

All three tequila types are required to be at least 78 proof (that is, the average of the agave and filler mixed together should be at least 78 proof for each tequila). When blending the processed agaves (and the filler) from the source companies, the barrels of white tequila produced must average at least " 80 " on the quality scale, the yellow tequila average at least "85" in quality, and the gold, at least "95".

The table below identifies cost, quality and proof of purchasing processed agave (or filter) from the five aforementioned companies based on historical records and known facts.

We must purchase at least $1 / 2$ of the max available processed agave from each farm, and we must also purchase a minimum amount (in $$$ ) from each of the first four farms listed. This minimum dollar amount is \(20 \%\) of the total $$$ spent purchasing processed agave from the 4 farms.

A couple of other compositional constraints are necessary. To ensure that the tequila has a 'blended' flavor, one farm cannot compose more than \(50 \%\) of the total amount of white and yellow tequila produced. THIS IS 50% for EACH of WHITE and YELLOW - separately. So if there is 10 barrels of white tequila produced, at most 5 barrels can come from any one of the four farms. Also, for BOTH WHITE AND YELLOW individually, each farm must consist of at least \(10 \%\) of the total volume of each product.

Find the most profitable way to mix together the agave and fillers from the 4 farms to produce the three types of tequila for the next production period. Do NOT worry about whole numbers of barrels.

Price: $23.52

Solution: The downloadable solution consists of 11 pages, 1252 words and 3 charts.
Deliverable: Word Document