While conservative Christian scholars have relied heavily on the book of Acts in the reconstruction of Paul's journeys, other academics have rejected the historicity/reliability of Acts, and preferred to rely upon Paul's letters alone. The problem with the second approach is that there is very little in Paul's letters to establish dates with, or even to put them in order.
A Chronology based on Acts
A basic modern approach using Acts is given by Gerd Luedemann in "A Chronology of Paul", Colloquy on NT Studies, Ed. Bruce Corley, SBTS (Mercer U., 1983) p. 289 fwd.
'The Conventional View:
'The conventional view...may be broadly described as ...ingenious combination of ...Acts with info in [Paul's] letters. ...One proceeds on the basis of the sole absolute datum ...the Gallio inscription. Since Gallio held office in A.D. 51-52, Acts 18:12 is taken as a sure indication that Paul stood trial before Gallio in this year. Further confirmation is then derived from 18:2, which mentions the arrival of Priscilla and Aquilla from Rome after the expulsion of the Jews (the year is assumed, on the basis of Orosius, to be A.D. 49). Since these two dates confirm one another, it is held that Luke's report of Paul's 1st Cor. Mission in Acts 18 is historically accurate. With the date of the mission on European soil relatively set, other dates are reckoned both before and after this period.After the stay in Corinth Paul traveled to Ephesus, then on to Palestine, and then back to Ephesus (Acts 18:18ff.). There Paul wrote the Corinthian letters and later traveled back to Jerusalem (by way of Macedonia) to deliver the [money] collection. In Jerusalem, Paul was arrested and was eventually taken to rome to meet his death as a martyr.Before the stay in Corinth, Paul had worked as a missionary in Philippi, Thessalonica, and Athens (and agreement of 1st Thess. with Acts 17ff.). Prior to this mission, Paul had traveled as a delegate of the Antioch congregation, to Jerusalem for the conference (Acts 15:2ff.). One determines this date of the conference, 14 - 17 years after Paul's conversion, on the basis of Gal 1ff. Confirmation of this view is then found in the reference to the ensuing conflict between Paul and Barnabas in both Acts and Gal. 2:13.For 11 - 14 years prior to the Jerusalem conference, Paul had worked, as a missionary of the Antioch congregation, in Syria and Cilicia (a combin. of Gal 1:21 and Acts 13ff.).
I wish to emphasize at this point that if this veiw were correct, then all of Paul's letters would have been composed within about 5 years of one another. They would all have been written by a man who had already been a Christian for about 19 years and who was a veteran missionary. Accordingly, one should expect the letters to be quite homogeneous; little room would be left for any theory regarding a development in Paul's thought reflected in the letters. The historian's exposition could rather proceed from the old theological principle, "scriptura ipsius interpres". (i.e., "Scripture is [self]-explanatory")Luedemann goes on in his article to develop a "non-conventional view" (i.e., a chronology that rejects the historicity and usefulness of Acts. But that does not concern us here. We remain grateful for Luedemann's concise description of the 'conventional view'.