I work at a manufacturing company and we have some lumpy cash flows (both going in and coming out). What are the best forecasting methods?

This is a very common problem that has two general schools of thought:

First, we could take a probabalistic approach and assign some likelihood of receiving (or making) a payment at any given point in time. For example, if I'm 50% confident that I'll receive a particular payment for, say, $10 next week then I'll include 0.5*$10 = $5 as part of my expectation for next week's receipts. Similarly, if there is a 25% likelihood I'll receive the payment next week and a 25% likelihood I'll receive the payment two weeks from now then my expected cash inflow for those two weeks is adjusted by 0.25*$10 = $2.5. My forecast for this $10 payment over the next three weeks is $5, $2.5 and $2.5, respectively. We could even use Monte Carlo methods to blend these lumpy expectations with our traditional "non-lumpy" cash forecast.

The second approach takes the conservative route and focuses on risk. Here we might assume the worst case scenario for each cash flow and manage liquidiy accordingly. In other words, if I can't make an accurate assessment of the likelihood of receiving a lumpy payment in a particular period I might simply assume that I won't get it and make sure I have enough liquidity on hand to cover that scenario.

I would also consider the two following points:

Inflows:

If those lumpy cashflows are originating from a business that is lumpy but regular (e.h. monthly payments from car-manufacturing companies to suppliers) you should analyze the historical payment behaviour and apply the results to your short term forecast (for items already billed) and to your long-term forecast based on your predicted inflows.
If those lumpy cashflows are originating from the progress achieved in a project-oriented business, you need to make sure, that you are in contact with the people in charge of the projects. They are the only ones who can give the information, when which part of the project is finished and can therefore be billed. On that information you can again apply historic payment behaviour of the customers. For the medium and long term planning for those flows your best guess is the project plan, which hopefully, gets revised during the course of the project.

Given your lumpy cashflows I assume that you are not in a serial business, which should be pretty straightforward to predict based in historical data and planned turnover.

Outflows: Hard to say without any further information about your kind of business.

In any case, there is not "one-for-all" solution in forecasting, as it not only depends on your business but also on the setup of your ERP-system (how often are payment runs done, how long does it take to actually generate a bill) and the incentives to local management. Very often, they are not even aware which impact their behaviour can have on cash. So also keep in mind that analysing their situation and educating them could also have a huge impact on forecasting quality.

Also, if you do forecasting analyse the quality and feed this information back to the local people in charge of forecasting. If they keep on missing the actual values on a regular basis by a wide margin you again need to put your heads down with them and work on the process of forecasting.

Difficult to make sound suggestions since more information is needed about your business. Before I design/suggest a cash flow forecasting system I would need to ask the following questions so as not to waste time and effort on a forecasting systeming to mask possible poor business practices/processes.
What is causing the inconsistence cash flow and is it a common occurance in your industry? Is this a new problem, supported my your historical trends in the past, compare DSO? Do you have access to a line of credit? Is your credit terms in line with your industry and how are you inforcing it? Do you enforce late charges? Is operations causing the products to be shipped late or with problems that would cause you customers to withhold payments? Are you experiencing a process delay in invoicing and are the invoices going to the right person and address?