A service system with perishable products where customers are either fastidious or strategic

Many service systems in the fast food industry consist of two types of customers: fastidious and strategic. A fastidious customer will always join the queue and wait for a fresh product, while a strategic customer, depending on queue length and on stock availability, may either join the queue for fresh products, purchase an inventoried pre-prepared (perishable) product, or balk. When the system is empty, the server produces pre-prepared items up to a pre-determined capacity level. The server may assign different prices to pre-prepared items and to fresh products in order to maximize expected profit, while taking into account revenue from selling food, sojourn and balking costs, capacity costs, and costs associated with food deterioration. We formulate and analyze this stochastic queueing-inventory system and derive its steady-state probabilities using matrix geometric methods. Our economic analysis, which follows a Stackelberg game and Nash equilibrium, shows that the presence of strategic customers is always beneficial for non-strategic customers, and can also be beneficial for the operating server. Moreover, in some cases, the server benefits from charging a higher price for less-fresh (pre-prepared) products than for fresh items, and even when pre-prepared items are offered at a discount, the discount may have a stronger positive effect on non-strategic customers' utility than on strategic customers' utility. Notably, in some cases, the percentage increase in the customers' utility (as compared with the case in which pre-prepared food is not offered) may be even higher than the percentage increase in the server's expected profit, even though the server is the one who controls the decision variables.