The　acquisition　of　used　products　(cores)　is　essential　for　leveraging　the　advantages　of　remanufacturing.　Due　to　limited　historical　information　about　cores,　it　is　difficult　for　the　remanufacturers　to　accurately　assess　the　quality　of　cores　before　disassembly　and　inspection.　In　this　article,　we　investigate　the　joint　acquisition　and　remanufacturing　problem　with　a　discrete　empirical　distribution.　Under　both　deterministic　and　stochastic　demands,　two　integer　programming　models　are　developed　to　obtain　operational　rules　for　making　optimal　decisions.　Since　the　discrete　empirical　distribution　is　assumed　to　be　the　nominal　distribution　or　asymptotic　distribution　of　the　true　quality,　the　error　caused　by　the　difference　between　the　estimated　discrete　empirical　distribution　and　the　true　distribution　cannot　be　neglected.　Thus,　we　evaluate　the　error　using　the　Phi-divergence　measure,　and　the　corresponding　effects　of　this　difference　on　the　resultant　acquisition　and　remanufacturing　rules　are　analyzed.　Through　numerical　examples,　we　observe　that　optimal　acquisition　and　remanufacturing　decisions　are　negatively　affected　by　the　difference　between　the　estimated　distribution　and　the　true　distribution,　even　if　the　estimated　distribution　can　pass　a　hypothesis　test.　Furthermore,　to　overcome　suboptimal　outcomes,　a　multisource　information　fusion　approach　is　proposed,　which　can　utilize　quality　information　collected　from　multiple　sources　to　make　accurate　acquisition　and　remanufacturing　decisions.