SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Additional Information (Details) $ in Thousands	12 Months Ended
	Jul. 27, 2019 USD ($) store segment	Jul. 28, 2018 USD ($)	Jun. 24, 2019 store
Accounting Policies [Abstract]
Number of operating segments | segment	1
Business Acquisition [Line Items]
Number of stores | store	30
Cash and Cash Equivalents [Abstract]
Credit and debit card receivables	$ 8,061	$ 8,227
Inventory Disclosure [Abstract]
Percentage of LIFO inventory	64.00%
LIFO reserve inventory	$ 14,512	14,234
Leases [Abstract]
Deferred rent obligation	13,102	13,259
Marketing and Advertising Expense [Abstract]
Advertising expense	11,705	11,514
Gourmet Garage Specialty Markets
Business Acquisition [Line Items]
Number of stores | store			3
Wakefern
Related Party Transaction [Line Items]
Demand deposits invested at related party Wakefern	$ 73,879	63,413
Buildings
Property, Plant and Equipment [Line Items]
Useful life	30 years
Store fixtures and equipment
Property, Plant and Equipment [Line Items]
Useful life	10 years
Vehicles
Property, Plant and Equipment [Line Items]
Useful life	3 years
Operating Expense
Business Acquisition [Line Items]
Prior period reclassification adjustment		4,027
Cost of Sales
Business Acquisition [Line Items]
Prior period reclassification adjustment		$ 997