Gantt plotter for industry in an online game

I am looking for a Gantt-like plotter with specific functionality.

I want to visualise the timelines of my manufacturing activities in EVE Online, an MMO game with an industrial part implemented not unlike an online strategy. Each manufacturing activity is a task for the game that is launched by you for a specified number of cycles (amounting to hours or days in real time) that then run in background until completion. The challenging part is that any real manufacturing (e.g. advanced ship building) is a multi-step process that involves manufacturing tens of items, then transforming and combining them into higher-tier items.

I would like to find an application that can take in each manufacturing task, represent it on a timeline (with up to a minute precision), and keep track of the items that I get when manufacturing ends (e.g. I get 2000 x Fusion Thrusters on July 23rd, 11:05). Bonus points if the application can support tasks that require these items as prerequisites (e.g. 1 x ‘Crusader’ Interceptor takes 1d, 9h and 20m to build and requires, among dozens of other things, 45 x Fusion Thrusters), and visualise them as arrows.

I’ve tried ProjectLibre, but it was a mismatch by several points. First, working hours make no sense for an online game where manufacturing continues even when you’re logged off. Second, there is no ‘workers’ in the game (unless you’re mining everything yourself, which does involve active participation), only tasks, manufacturing centers, and input resources.

Is there a tool like that?

I am familiar with Windows 7 and Ubuntu Linux. If it’s a web application package, I’m not a total stranger to a LAMP pack. Preferably freeware, because I’m not willing to spend more than a monthly subscription costs – and my regional equivalent is ~$14.