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STOCKHOLDERS' EQUITY (Details 2) (USD $)
 0 Months Ended 12 Months Ended
Mar. 20, 2014
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Stockholders' Equity        
Cash distributions declared per share of common stock (in dollars per share)   $ 1.50us-gaap_CommonStockDividendsPerShareDeclared $ 1.42us-gaap_CommonStockDividendsPerShareDeclared $ 1.34us-gaap_CommonStockDividendsPerShareDeclared
Common shares issued under the Distribution Reinvestment Plan   227,000us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan 210,000us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan 215,000us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan
Maximum aggregate sales price of shares to be sold under an Equity Offering Sales Agreement (in dollars) $ 38,360,000olp_MaximumAggregateSalesPriceOfSharesToBeSoldUnderEquityOfferingProgram      
Number of shares sold   179,051us-gaap_StockIssuedDuringPeriodSharesNewIssues 363,463us-gaap_StockIssuedDuringPeriodSharesNewIssues  
Proceeds from sale of shares, net of commission and before offering costs   3,889,700olp_StockIssuedDuringPeriodValueNewIssuesNetProceedBeforeOfferingCosts 9,227,800olp_StockIssuedDuringPeriodValueNewIssuesNetProceedBeforeOfferingCosts  
Payment of commissions on sale of shares   39,000olp_PaymentOfCommissionsOnSaleOfShares 93,000olp_PaymentOfCommissionsOnSaleOfShares  
Payment of offering costs on sale of shares   $ 122,000olp_PaymentOfOfferingCostsOnSaleOfShares $ 63,000olp_PaymentOfOfferingCostsOnSaleOfShares  
Maximum        
Stockholders' Equity        
Discount rate (as a percent)   5.00%olp_PercentageOfDiscountOnCommonStockPurchasedThroughDividendReinvestmentPlan
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