An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 7

Assume that a third grocery store, Quick Stop Groceries, enters the market share and customer loyalty situation described in Section 16.1. Quick Stop Groceries is smaller than either Murphy's Foodliner or Ashley's Supermarket. However, Quick Stop's convenience with faster service and gasoline for automobiles can be expected to attract some customers who currently make weekly shopping visits to either Murphy's or Ashely's. Assume that the transition probabilities are as follows:
a. Compute the steady-state probabilities for this three-state Markov process.
b. What market share will Quick Stop obtain?
c. With 1000 customers, the original two-state Markov process in Section 16.1 projected 667 weekly customer trips to Murphy's Foodliner and customer trips to Ashley's Supermarket. What impact will Quick Stop have on the customer visits at Murphy's and Ashley's? Explain.