Royster13 has a good point.
Purpose is primary. 3 P’s in decision making: People, Purpose, Profit. Can you take care of the people (customers and staff) achieve your primary purpose in the community and do so with a profit? If your goal is to create a business which creates plenty of cash for the purpose of selling in the future and retiring early… that may change your purpose.
Since a pizza restaurant serves its local community, you can easily create marketing material (both offline and online) that will keep the customers informed. If you are looking for balance, I have seen plenty of small businesses do fine with six days. (caution: pizza + football + sports needs to be a consideration for which day you might close) The owners are happy and paying the bills (and do not look at the missing sales as a negative since they gain so much on the seventh day)
I have a simple breakeven spreadsheet you can download in my library and take a look at the different scenarios (sales with 6 days, 5 days or 7 days).
http://rejuvenateyourrestaurant.com It’s free… help yourself.
Also, if you use tech for those who call on a closed day, you can offer a special offer for the next time the call. Each week leave a code on an answering machine, a “secret” website page, something special foir the next time they visit. Also, with such things as VoIp you can track the calls … and with caller ID you can track who called and return the call the next day with a special invitation… thereby maintaining good relationships. Don’t forget: your website can offer support should your customers need more information on the day you close.
Being open for lunch is usually a different market than the dinner. Different group of people with different habits. You need a new separate marketing strategy for lunch. Many start with dinner… and then as business grows, add lunch. This depends on your time / team / finances.
Hope the spreadsheet helps.