Question

Consider the model in which an order is fulfilled by both an in-store shopper and a full-service shopper (this is the model II in Figure 2 of the case). We will assume that all orders are fulfilled in this way. In-store shoppers: Suppose that they operate as in Question 1 (i.e., they will check out one order at a time, instead of batching up two orders). On average, it takes 25 minutes on average for a shopper to pick all items on the list, and 15 minutes to check out the items and move them to the staging area. Full-service shoppers: Suppose that full-service shoppers focus on delivery of orders (they don't do any in-store shopping at the local grocery store). There is a relatively large pool of full-service shoppers who delivers for many grocers in the city. If the local grocery store keeps requesting full-service drivers to pick up order from the staging area, the maximum frequency of those shoppers arrive at the store is 3 visits/hour. Suppose that they will pick up one order in each visit. The collaboration by the two types of shoppers is demonstrated in the following diagram. For simplicity, assume that there is only one in-store shopper. What is the service capacity of this model that involves both types of shoppers?

Answer 1

The service capacity of the model with in-store and full-service shoppers is 1.5 orders per hour, as the in-store shopper rate limits the overall capacity.

Step-by-step explanation:

Service Capacity Calculation

The service capacity of the model involving both in-store shoppers and full-service shoppers is determined by the limitations of each type of shopper. The in-store shopper takes on average 25 minutes to pick items and 15 minutes to checkout and move them to the staging area, totaling 40 minutes per order. Full-service shoppers are available for a maximum frequency of 3 visits per hour (every 20 minutes). Since one in-store shopper is working, this shopper's rate of order preparation (60 minutes / 40 minutes per order = 1.5 orders per hour) limits the service capacity. However, the full-service shoppers can handle up to 3 orders per hour. Therefore, the bottleneck is the in-store shopper, making the service capacity of the model 1.5 orders per hour.