Page 1 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 Discussion of Marty Reiman’s Markov Lecture A Stochastic Programming Based Approach to ATO Inventory Systems Alan Scheller-Wolf Tepper School of Business or New Frontiers in ATO or The Continuing Evolution of a Great Idea

Page 2 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 Background for My Talk Like Amy, and probably most of you, I have been familiar with Marty’s asymptotic analysis of queueing networks for some time –This is work I admired, but it was outside my primary stream of research Within the past few years, led by student interest, I have begun to work on ATO systems –And whose work should I find dead center in in my research stream? Marty’s!

Page 3 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 ATO: So what’s the Problem? n Components m Products Inventory replenishmentAnd allocation! Highly dependent Highly multi-dimensional And non-linear!

Page 4 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 Selected Literature (I) Structural Results: –Special product architectures Markovian systems: Benjafaar and ElHafsi (‘06); ElHafsi (‘08); Nadar et al. (‘12) SP Analysis: DRW (‘10); Lu et al. (‘12); RW (‘12) Heavy Traffic: Plambeck and Ward (‘07, ‘08); RW (‘13) –No-Holdback: Song and Zhao (‘2009), Lu et al. (‘2010) General results still lacking

Page 5 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 Selected Literature (II) Optimization Results: –Approximations: Zhang (‘97); Song (‘98); Song and Yao (‘02); Cheng et al. (‘02); Kapucinski et al. (‘04); Lu and Song (‘05); van Jaarsveld et al. (‘11) –SP Formulations: Swaminathan and Tayur (’98); Akcay and Xu (’04); Huang and de Kok (‘11), van Jaarsveld and S-W (‘13) Limited problem size. No guarantees*

Page 6 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 “New” Ideas are Needed The “New” Idea: –Heavy Traffic Approach – “same hammer, new nail.” The New Idea: –Stochastic programming lower bound using full recourse Both ideas continue to evolve…

Page 7 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 DRW ’10 (I) Formulate ATO problem as two-stage SP, like NV Network –Assume identical LT’s Formulate second, Lower Bound SP by: –Giving controller complete freedom to reallocate inventory over the leadtime demand –Giving controller complete freedom to select initial backlog level

Page 8 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 DRW ’10 (II) – So What!? New LB: –Obliterates dependence of ordering policy on the past, as controller has complete freedom to reallocate decisions Makes base-stock ordering optimal –Forms universal lower bound over all policies –Provides guidance for “good” (maybe optimal) policies for original problem Follow LB policy when possible A great idea

Page 9 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 But… New LB: –Limited to identical lead times –Translating SP solution into actionable allocation policy can be difficult

Page 10 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 RW ’12 See evolution of LB: –Extended to non-identical leadtimes Creates (K+1) stage SP –Verification Lemma: Provide sufficient conditions for when can track SP optimal policy Now can determine quality of solutions in some cases

Page 11 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 RW ’13 Show sol of SP optimal under diffusion scaling Further evolution (reformulation) of LB: –Finite parameters at optimality –Actionable Backlog Targeting Heuristic Now can more easily implement policy implied by SP So what’s next?

Page 12 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 The Next Stages in Evolution? Extend asymptotic results to unequal LT’s and/or non-base stock replenishment Extend to industrial-sized problems –Make applicable in practice

Page 13 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 What About Practice? (I) Companies use a variety of simplifying assumptions: –Ignoring simultaneous stock outs (ISS): Wait time for product n is sum of wait time for components –Simpler allocation rules: First come first served (FCFS); First Ready First Served (FRFS)

Page 14 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 What About Practice? (II) Van Jaarsveld and SW (‘13) provide two-stage SP algorithm for larger problems –Tagged Job approach for waiting time –Novel formulation of second-stage SAA High-quality asymptotic lower bound –Limited to base stock + selected allocation rules Can DRW methodology be extended to practical- sized problems?

Page 15 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 Extending DRW to Larger Problems Requires workable solution to SP with unequal lead times –(K+1) stages may be too many Requires efficient way to solve allocation problem for optimal backlog targets This appears very promising

Page 16 Alan Scheller-Wolf INFORMS Minneapolis October 6, 2013 Conclusion ATO is classically difficult problem –Requires new solution approaches Marty and co-authors continue to provide these As ideas evolve, new results become possible It is exciting to follow evolution and see where this leads… Stay Tuned!