Inventory control at a food pantry

To combat hunger, food pantries serve individuals in need of food assistance (referred to as clients), with a balanced and healthy selection of food items that they source from food donors. However, food pantries are often very low-tech, operationally speaking. For example, below are two pictures of the back-room of the food pantry where my daughter and I volunteer every Monday morning. In this room, the pantry stores products with long shelf-lifes such as canned goods, pasta, beans, etc. They do not store produce or dairy-type items in this room (it is also not temperature controlled).

Food is sorted by category (canned fruit, soup, etc.) and there is a line of boxes for each category.

In a given category, such as canned vegetables, there will be different types of food (corn, green beans, etc.) but inventory is not managed at that level of granularity. For each category, the number of boxes in the corresponding line gives a rough estimate of the amount of inventory in a category. However, rarely are the boxes full, and some boxes may be empty. In addition, for different categories, the number of actual items that fit in a box can be different (e.g. you can fit 24 cans of soup in a box, but you can fit 50 boxes of Macaroni & Cheese in a box). Every morning a food pantry volunteer goes into this back room and does a quick count of the number of boxes for each category. Todays inventory is as follows:

Table 1: Category inventories

Category	# boxes	Typical % full	Items per box
Beans	8	50%	24
Vegetables	10	75%	24
Meat (chicken, tuna)	8	75%	24
Macaroni & Cheese	12	75%	50

In terms of demand, the food pantry provides a bag of food items to 50 clients each week. Every day from Monday to Friday, 10 different clients show up to receive their bag of food. There are two types of clients: vegetarian (20% of the clients) and non-vegetarian (80% of the clients). Each type of client gets 16 food items from the back-room when they visit. The number of food items of each category that goes into each type of bag is as follows:

Table 2: Client needs in number of items per category

Category	Beans	Vegetables	Meat	Mac & Cheese
Vegetarian	6	6	0	4
Non-vegetarian	4	4	4	4

The food the pantry provides to its clients primarily comes from donations. When food is donated to the pantry, a volunteer at the pantry has to check the expiration date to ensure the food is still safe to eat, and then sort each donated item into a box in the line for its category.

Due to COVID, the food pantry has to let donations sit for three days before they can be checked and sorted, because it is believed that the virus can live on surfaces such as packaging for at most three days. The past experiences of the managers at the pantry suggest that the current set of unsorted donations will likely replenish each categories inventory to what is listed in Table 1.

The following questions focus on whether and how the food pantry can meet its client needs for the next three days with the inventory levels provided in Table 1. For the last two questions, you can ignore the chance of having to give meat to a vegetarian. There is enough spare inventory that the food pantry can prevent that from happening.

5. Given the economic impact of COVID, the food pantry is receiving requests from more and more clients for food assistance. If the food pantry decides to ignore individual food categories, and instead just give each client 16 items of food, how many additional clients per day can the pantry serve?