# Comet Cupboard

The Comet Cupboard is a free to use UT Dallas food pantry initiative dedicated to helping students in need. Its primary mission is to provide necessary food and personal care items to members of the school community.

Since the facility is located  [locationnext door to my office in library, I always wondered how they managed their inventory being a not profit organization, and run by undergraduate students. Classical inventory management assumes cost minimizing or profit maximizing participants and very less research has been dedicated to not for profit management.

### Key Features:

1. Not for profit - objective is to maximize social surplus,
2. Accepts donations of non-perishable, unexpired food items only (durable goods) such as canned soups, ramen, dried fruits etc. - unused inventory is carried over,
3. Accepts monetary donations, therefore has a budget to buy items not received via donations,

### A Naïve Problem Formulation:

 $\inline \dpi{300} \large \noindent \mbox{Demand:} ~(d_1,\dots,d_N),\\ \noindent \mbox{Inventory at hand including gifts:} ~(x_1^0,\dots,x_N^0),\\ \noindent \mbox{Price of each unit of product 1,\dots,N:} ~(p_1,\dots,p_N),\\ \noindent \mbox{Inventory ordered:}~(x_1,\dots,x_N), ~x_i \geq 0~,\\ \noindent \mbox{Demand Satisfaction Constraint:}~ d_i \leq x_i+x^0_i ~\mbox{for}~ i \in \{1,\dots,N\},\\ \noindent \mbox{Budget Constraint:}~ \sum_{i=1}^Np_i x_i \leq \mathboldb{B} ~\mbox{for}~ i \in \{1,\dots,N\},\\ \noindent \mbox{Objective:}~ \min_{(x_1,\dots,x_N)}\sum_{i=1}^N (d_i-x_i-x^0_i)^+.\\$ Problem Formulation
This is a very simple formulation, where we assume there are N items managed by comet cupboard, and demand for each items is known in advance given by di's. They know exact inventories at hand x0's , the money received B as donation, and the prices pi. With this the decision is to order i.e. xi's.

The key is the objective function as this focuses on demand satisfying and procuring as much so that budget constraint is usually tight (assuming high levels of demand). In such a situation, demand forecasting is very crucial and they did a good job by identifying high demand items (they can do better though by high medium low demands). Moreover, because of large assortment size, the problem becomes more complicated.

### Recommendations:

1. Track inventories, to estimate demands,
2. Surveys to see what students 'prefer' in terms of products,
3. This model does not assume substitutability among products, a better model will include this and it is a good idea to save money by providing cheaper substitutes,
4. We can make this model richer by adding constraint on individuals (which is right now implemented): each student is allowed to  take up to 4 items.
Feel free to share comments and thoughts on this.

1. I did not understand the demand satisfactions constraint. would you care to explain

2. This means demand for each product is less than the total inventory after order is placed. This is a simplifying assumption.

3. They also tried to implement some kind of "optimal diet": you can take 5 items, and one of them should be "protein", another -- "grains" and the third one -- "fruits".

4. Taking balanced diet into account is good, as I was thinking most of the stuff is processed food and how can school promote consumption of ramen, tinned soups. This makes the modeling richer, and forecasting of demand and hence their inventory management problem deeper.