Modeling remaining duration for prediction

Question

Suppose we're in the business of repairing broken specialty widgets and reselling them. At each point in time, we want to predict how much cash we'll make in the next 30 days on the existing inventory. All widgets are different although some may have similar characteristics.

The data we have: a list of all widgets repaired in the past 5 years, along with widget characteristics (numeric and categorical variables), dates of start and finish, original value, and resale value. We also have a list of all widgets that are currently being repaired, which contains the same info excluding finish date and resale value.

We have reason to believe that widget characteristics can help predict time to repair and resale value ratio.

My current idea is this: consider two models, one to predict the time until finish, and one to predict a "resale ratio", i.e. $\frac{\text{resale value}}{\text{original value}}$.

I'd like to focus on the first model.

One possibility is to take the finished repairs, and fit time to repair ~ characteristics via a gamma GLM. This is straightforward and can be cross validated. However, how would we handle cases when the predicted repair time is less than elapsed time?

Another possibility is to utilize techniques in survival analysis, but I'm not familiar with it and am not able to find existing case studies.

I'm sure similar problems have been solved in many fields, so I'd like feedback on best practices and whether I'm on the right track.

Answer 1

I will rename "original value" to "purchase cost" (PC) since I think that is the value you are referring to. I will call Resale Value (RV) - PC the Turn Value (TV). The time from start of valuation to floor I will call Turn Time (TT), this is the sum of valuation time (VT), queue time (QT), and repair time (RT). The costs of repair (RC) are the third metric you should calculate.

I assume this prediction model has the sole purpose of allowing you to determine whether a purchase will be lucrative, e.g. $TV>0$. As a caveat, there is a strong risk management aspect to this: you can wait for low-balling sales that require minimal work for maximum TV. You can specify $TV > c$, $c>0$ for a decision rule, but this will cost you when many nearly new (e.g. high RV, low TT low RC) have many units with TV - RC - PV < c, TT very low. Incorporating these into a single metric would be useful.

To assess the real impact of TT, you should calculate your fixed costs: parts, tools, hours, facility costs, and define a unit of FC/T (fixed value per time), then TT can be transformed to a cost (turn cost or TC) by calculating TC = FC/T*TT. This is like a tax that you pay to have unsalable goods sitting on the floor, waiting for parts or services, and depreciating.

So using valuation you can develop a prediction model for TC and TT as these are the sole determining factors of PC and TV. Predicting TT with a gamma GLM is reasonable. Parsing out RC makes the outcome of TT more justifiable than RT alone, since waiting to receive parts or for available labor (QT) costs you.

I would hazard against using the metric of resale to purchase value. It makes the assumption of scalability. You may come up with predictions from such equations that justify buying too much stock at once, and overexpend fixed costs and capacities such as available labor, storage, etc. (this creates a third time, queue time, in which parts sit on the floor, depreciating, waiting for available mechanics and supplies). As business people say, "cash is king" and using TV as an outcome gives units of dollars.