A Stochastic Programming Approach to Managing Email Overload

1. A Stochastic Programming Approach to Managing Email Overload

2. Email Overload • Inability to respond to all email • Inability to respond to all email in a timely manner • The knowledge worker must not only take into consideration the current email that is in need of processing and the timeliness of this email, but he or she must also consider what future email demands may be on the horizon.

3. Stochastic Programming • Stochastic Programming (SP) is an optimization tool that allows for the consideration of stochastic parameters. • SP allows the user to find an optimal solution while taking into consideration all possible future scenarios.

4. Email Overload / SP • The purpose of this paper is to explore the potential use of Stochastic Programming as a tool for finding the optimal processing sequence of email.

5. Efforts Aimed at Reducing Email Overload • Filtering (Sharda, et. al., 1999) • Ifile (Rennie, 2000) • Sieve (Marsan, 2000) • SurfControl (Surfcontrol, 2002) • Bifrost Inbox Organizer (Balter, 2000)

6. Efforts Aimed at Reducing Email Overload • EchoMail (Goldschmidt, 2001 & EchoMail, 2002) • Losee (1989) • The PRIORITIES system (Horvitz, Jacobs, and Hovel (1999)

7. SP vs. Previous Efforts • Stochastic Programming takes possible FUTURE scenarios into consideration • All other efforts consider only the present state

8. An Illustrative Example: Optimizing Email Processing • With respect to email processing, the optimization involves maximizing the utility or value of the email that are processed. • The optimal solution must take into consideration that the utility of a processed email may decrease with time. • The optimal solution must also consider the potential arrival of different types of email in the future. • The decision variables correspond to whether or not to process an email in a given stage (time frame). • The stochastic parameters include the potential arrival of various types of emails.

9. An Illustrative Example: Optimizing Email Processing • Beginning Inbox (i = type, j = age)

10. An Illustrative Example: Optimizing Email Processing • Utility of email processed (i = type, j = age)

11. An Illustrative Example: Optimizing Email Processing • Arrival scenarios (number of type i email arriving)

12. An Illustrative Example: Optimizing Email Processing • Time needed to process email (days)

13. Formulations • LP – Single-period • LP – Multi-period • SP – Perfect Information • SP – Here and Now

14. Formulation Sets and Indices • T is the set of the different days under consideration • I is the set of possible types of email messages • J is the set of possible ages of an email message in days • Q is the set of possible arrival scenarios • t = 1..4 denotes the day under consideration • i = 1..2 denotes the type of email message • j = 1..5 denotes the age of an email message • q = 1..64 denotes the arrival scenario

15. LP – Single-Period Formulation Parameters • Ni,j This represents the number of email of type i that are j days old. This represents the inbox • Ui,j This represents the utility or value of an email of type i, having an age of j. • Di This represents the time needed, in days, to process an email of type i. Variables • Xi,j This represents the number of email that are processed of type i having an age of j.

16. LP – Single-Period Formulation (cont.) Objective Function • Max ΣiΣj Xi,jUi,j Constraints • Xi,j <= Ni,j i = 1..2, j = 1..4 • Xi,j = Ni,j i = 1..2, j = 5 • ΣiΣj Xi,jDi <= 1 i = 1..2, j = 1..5

17. LP – Multi-Period Formulation Parameters • Nt=1,ij This represents the number of email of type i that are j days old during day 1. This represents the beginning inbox. • Ui,j This represents the utility or value of an email of type i, having an age of j. • Di This represents the time needed, in days, to process an email of type i. • At,i This represents the expected number of arriving email of type i during day t. Variables • Xt,i,j This represents the number of email that are processed of type i having an age of j. • Nt,i,j This represents the number of email of type i that are j days old during day t.

18. LP – Multi-Period Formulation Objective Function • Max ΣtΣiΣj Xt,i,jUi,j Constraints • Nt,i,j = Nt-1,i,j-1 – Xt-1,i,j-1 t > 1, i = 1..2, j > 1 • Nt,i,j = At,I t > 1, i = 1..2, j = 1 • Xt,i,j <= Nt,i,j t = 1..4, i = 1..2, j = 1..4 • Xt,i,j = Nt,i,j t = 1..4, i = 1..2, j = 5 • ΣiΣj Xt,i,jDi <= 1 t = 1..4, i = 1..2, j = 1..5

19. SP Formulation (Perfect Information) Parameters • Nt= 1,i,j,qThisrepresents the number of email of type i that are j days old on day one. This represents the beginning inbox. • At,i,qThis represents the number of arriving email of type i, given scenario q • Ui,jThis represents the utility or value of an email of type i, having an age of j. • PqThis represents the probability of scenario q. • DiThis represents the time needed, in days, to process an email of type i.

20. SP Formulation (cont.) (Perfect Information) Variables • Xt,i,j,q This represents the number ofemail that are processed on day t, that are of type i and have an age of j, given scenario q. • Nt>1,i,j,qThis represents the number of email of type i that are j days old on day t, given scenario q. Objective Function • Max ΣqΣiΣj Pq Xt,i,j,q Ui,j

21. SP Formulation (cont.) (Perfect Information) Constraints • Nt,i,j,q = Nt-1,i,j-1,q – Xt-1,i,j-1,q t > 1, i = 1..2, j > 1, q = 1..64 • Nt,i,j,q = At,i,q t > 1, I – 1..2, j = 1, q = 1..64 • Xt,i,j,q <= Nt,i,j,q t = 1..4, i = 1..2, j < 5, q = 1..64 • Xt,i,j,q = Nt,i,j,q t = 1..4, i = 1..2, j = 5, q = 1..64 • Σi Σj Xt,i,j,q Di <= 1 t = 1..4, i = 1..2, j = 1..5, q = 1..64

22. SP Formulation(Here and Now) Parameters • Nt= 1,i,j,qThis represents the number of email of type i that are j days old on day one. This represents the beginning inbox. • At,i,qThis represents the number of arriving email of type i, given scenario q. • Ui,jThis represents the utility or value of an email of type i, having an age of j. • PqThis represents the probability of scenario q. • DiThis represents the time needed, in days, to process an email of type i.

23. SP Formulation (cont.)(Here and Now) Variables • Xt,i,j,q This represents the number ofemail that are processed on day t, that are of type i and have an age of j, given scenario q. • Nt>1,i,j,qThis represents the number of email of type i that are j days old on day t, given scenario q. Objective Function • Max ΣqΣiΣj Pq Xt,i,j,q Ui,j

24. SP Formulation (cont.)(Here and Now) Constraints • Xt,i,j,q = Xt,i,j,q+1 t = 1, i = 1..2, j = 1..5, q < 63 • Xt,i,j,q = Xt,i,j,q+1 t = 2, i = 1..2, j = 1..5, q < 63 • Xt,i,j,q = Xt,i,j,q+1 t = 3, i = 1..2, j = 1..5, q < 63 • Xt,i,j,q = Xt,i,j,q+1 t = 4, i = 1..2, j = 1..5, q < 63 • Nt,i,j,q = Nt-1,i,j-1,q – Xt-1,i,j-1,q t > 1, i = 1..2, j > 1, q = 1..64 • Nt,i,j,q = At,i,q t > 1, I – 1..2, j = 1, q = 1..64 • Xt,i,j,q <= Nt,i,j,q t = 1..4, i = 1..2, j < 5, q = 1..64 • Xt,i,j,q = Nt,i,j,q t = 1..4, i = 1..2, j = 5, q = 1..64 • Σi Σj Xt,i,j,q Di <= 1 t = 1..4, i = 1..2, j = 1..5, q = 1..64

25. Results

26. Conclusions • Potential exists for Email Processing Decision Support. • SP outperforms LP and FCFS. • Possible future states need to be considered.