The classic work on logistics is Martin van Creveld's Supplying War: Logistics from Wallenstein to Patton which, as its subtitle implies, approaches the subject very broadly. As is common with such sweeping histories, van Creveld sometimes loses some nuance and made some errors in interpretation and judgement, but the book is still quite important for this topic. Critiques of van Creveld, and much more, are in the anthology Feeding Mars: Logistics In Western Warfare From The Middle Ages To The Present edited by John Lynn. Based on a conference on the history of logistics convened in 1990, the contributors broach a number of topics such as the wider historiography of logistics or the logistical systems of the Crusades. Finally, although it is not about logistics per se, John Brewer's The Sinews of Power: War, Money and the English State, 1688-1783 is a landmark text about the creation of the fiscal-military state in the eighteenth century. In short, Brewer examines how economic resources could translate into military power, which, as the example of Habsburg Spain sometimes demonstrates, was not the easiest of accomplishments. Despite focusing on one state, The Sinews of Power is important in regards to the historiography of logistics because it examines how civil state structures are vital for the sustaining military force.

Well, you said that broader coverage works too, so here's something from Japan - Karl Friday's Samurai, Warfare and the State in Early Medieval Japan, which deals quite well with the development of logistics throughout Japanese history. I've never found a single book dedicated to the development of military logistics, although Friday's book seems to cover quite a bit, dedicating entire sections to the development of Japanese logistics throughout the different periods and markers (e.g. the Genpei war). If you like, I could throw you some small excerpts if you'd like first.