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I have got a job scheduling problem. We are given start time, time to complete the order, deadline.

It is given that start time + time to complete <= deadline.

I have also been given the loss that will occur if I am not able to complete the job before the deadline. I have to design an algorithm to minimize the loss.

I have tried changing the standard algorithm of dynamic programming for maximizing the profit in job scheduling but to no success.

What algorithm can I use to solve the question?

user1
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user3649611
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3 Answers3

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Dynamic Programming isn't the right approach based on what you're aiming to optimize. You can find the optimized schedule by using a greedy approach.

Here's a thorough guide with sample code for your desire language (C++), in the guide it assumes each jobs takes only 1 unit of time, which you can easily modify by using time_to_complete instead.

Ling Zhong
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  • I guess it wont work if we have different times for completion for each job – user3649611 Oct 17 '15 at 08:03
  • you just need to do one extra calculation in addition to what's in the guide. you will need to check the feasibility by `current_time < end_time - time_to_complete` – Ling Zhong Oct 17 '15 at 08:05
  • I guess many, for example there are two jobs, the deadline for the first job is overlaps with the starting time of the second job. In that case, the solution will take only one of them. But what if (deadline2 - time to complete 2nd) > deadline1. I dont think it will work there, correct if I am wrong. And then if there are three jobs then, starting of third job may cause a problem – user3649611 Oct 17 '15 at 08:09
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Your problem is similar to the knapsack one. Using a greedy approach is convenient if you aren't actually looking for the best possible solution, but just a "good enough" one.

The big pro of the greedy approach is that the cost is rather lower than other "more thorough" approaches but, if you need the best solution to your problem, I would say that backtracking is the way to go.

Flavio Giobergia
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Since the deadline can be violated, the problems looks like a Total Weighted Tardiness Scheduling Problem. There are many flavors of it, but most problems under this umbrella are computationally hard, therefore Dynamic Programming (DP) would not be my first choice. In my experience, DP also poses difficulties during modeling and implementation. Same comment for mathematical programming "as-is". Some approaches that can be implemented more quickly are:

  1. constraint programming: very small learning curve, and there are many libraries out there, included very good open source ones (most have C++ API). Bonus: constraint programming can demonstrate optimality.
  2. ad hoc heuristics: (1) start with a constructive algorithm (like the greedy approach suggested by Ling Zhong and Flavio Giobergia), then (2) use some local search approach to improve if and finally (3) embed the approach into a metaheuristic scheme. This way you can build on top of the previous step, and learn a lot about the problem. Note: in general, heuristics cannot demonstrate optimality
  3. special mention: local solver, a hybrid approach between the two above: it lets you model the problem using a formalism similar to constraint programming and then it solves it using heuristics. It is very easy to learn, it usually lets you get started quickly and, in my tests, it provides remarkably good results.
kr1zz
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