Mathematical Models for Supporting Available to Promise (ATP)

1. Mathematical Models for Supporting Available to Promise (ATP) Michael Ball R. H. Smith School of Business & Institute for Systems Research University of Maryland based on joint work with C.Y. Chen & Z.Y. Zhao

2. Outline • Introduction and Overview of Model • Research Topics • Experience from Toshiba Prototype

3. Outline • Introduction and Overview of Model • Research Topics • Experience from Toshiba Prototype

4. Available to Promise (ATP) &Assemble to Order (ATO) The Available to Promise (ATP) Function provides a response to a customer order with a quantity and delivery date commitment. In an assemble-to-order (ATO) production environment, final product assembly is not carried out until a customer order is received; also consider make-to-order (MTO), configure-to-order (CTO). Why ATO, MTO, CTO?? • Provide customers with greater product variety • Reduce inventory

5. Push and Pull Production Systems PUSH VS PULL Forecast demand customer order Order raw materials Order raw materials transport & storage transport & storage Produce product Produce product transport & storage transport & storage Deliver product to customer/retailer Deliver product to customer/retailer customer order

6. Push-Pull Systems product models suppliers Manufacturing incl final assembly generic products and components inventory Push-pull boundary Assembly to order Manufacturing forecast driven order driven

7. The Role of Advanced ATP in Production Planning and Control Push-based planning Sales & Market Pull-based promising Order Management Order placement Sales forecast Customer Due date promise Production Planning (MPS,MRP) Confirmed orders Pseudo orders Promised quantity & due dates Optimization-based ATP Order Delivery Matl Planning Dmd Prod. Ctl Procurement Order (PO) Committed orders Production status Supplier Production Execution Warehouse Material Delivery Product Delivery Manufacturing & Logistics

8. Conventional ATP (make-to-stock environment) immediate delivery delivery in 2 days delivery in 1 week delivery in 2 weeks When can you deliver order for 6 units?? local inventory inventory in warehouse this week’s planned production next week’s planned production

9. ATP in ATO/CTO/MTO Environment customer orders • Resources: • raw material • and component • availability • production • capacity ATP in assemble-to-order environment: match available resources to customer orders Decisions: accept/reject/split order; order quantities and delivery dates Considerations: order profitability; customer priority; customer satisfaction (reducing response/delivery time); production efficiency

10. Classes of Products • Discrete parts electronics product production • Specific cases considered (all in B2B setting): • Maxtor hard disk drive • Toshiba Notebook PC • Toshiba Point-of-Sale terminal

11. Real-Time vs Batch ATP Real-time ATP: response and order commitment given for each order immediately after receipt of order Batch ATP: orders collected over time interval, e.g. one hour, one 8-hour shift, one day, etc.; response and order commitments generated for batch of orders at end of each time period Model described here solves batch ATP problem It should be noted that there are very few true real-time ATP systems operating today; most systems that give an immediate response (including most web-based retail sites) produce an initial “soft” promise, run a batch ATP module later and then produce a “hard” promise.

12. Mixed Integer Programming Model : indicates if order i is accepted, (1 if accepted; 0 otherwise), : the commitment level for order i, : the material requirement from the kth supplier for the jth type of material for the ith order during time period t (here i consists of both new and old orders). MAJOR DEC VARIABLES ATP vs Production Planning & inventory mgmt: short time horizon; fixed resources; front end/back end integration MODEL SUMMARY Objective Function Maximize: (net revenue) – (production cost) – (material cost) – (inventory cost) – (order denial penalty) – (capacity under-utilization penalty) – (order lateness penalty) Constraints • Order commitment constraints • Material requirement constraints • Production capacity constraints • Production smoothness constraints • Inventory constraints

13. Product Structure in ATO/MTO/CTO Environments suppliers raw materials e.g. disk drive, LCD, etc products, e.g. pc model w. options customers S11 C1 S12 M1 P1 C2 M2 P2 constraints S21 C3 S31 Mk Pr Smn Cq constraints (material compatibility, customer preference, production capacity, etc.)

14. Customer Preference and Material Compatibility Constraints S11 S12 C1 M1 S1m1 material incompatibilities C2 S21 M2 customer-supplier preferences Sn1 Mn customers Snmn materials suppliers

15. Dynamic Use of ATP Model order commitments promise dates, quantities new orders ATP Decision Model (period t) production schedule for period t+1 order commitments for periods t+2, t+3, …

16. Production Flexibility batching interval production plan and resource allocation flexible (subject to quantity and delivery date commitment) production plan and resource allocation fixed batching interval

17. Outline • Introduction and Overview of Model • Research Topics • Experience from Toshiba Prototype

18. Research Topics • Model Simplification/Aggregation & Polyhedral Projection • Real Time vs Batch ATP: Applying Techniques from Analysis of Heuristics • Modeling Stochastic and Dynamic Problem Aspects

19. 1. Model Simplification/ Aggregation and Polyhedral Projection P = {(x,y) : A1x + A2y = b, x,y  0} The projection of P onto x is the polyhedron: P’ = {x : there exists a y s.t. (x,y)P} Min cx s.t. (x,y) P Min cx s.t. xP’ Examples: x = material allocation variables & y = product configuration variables. x = weekly resource allocation variables & y = daily resource allocation variables.

20. Material Compatibility Constraints The direct approach to modeling material compatibility would be to include explicit product configuration variables (in general there could be a very large number of such variables) Consider the following special case (from Maxtor): Bplate components can be arranged into levels; incompatibility constraints only exist between adjacent levels; PCB HDA Product specification is path that avoids all incompatible edges extension to multiple levels

21. Material Compatibility Constraints X11 X12 X13 X14 X15 5 instances (e.g. suppliers) of generic component 1 incompatibilities 5 instances (e.g. suppliers) of generic component 2 X21 X22 X23 X24 X25 A product using component (1,1) or (1,4) must also use (2,2), (2,3) or (2,4)  X22 + X23 + X24  X11 + X14 Must be satisfied by all compatible material assignments, i.e. necessary condition. All such constraints provide necessary and sufficient conditions for “level incompatibility systems” Based on results on projection of perfectly matchable sub-graph polytope (Balas and Pulleyblank)

22. 2. Real-Time vs Batch ATP and Size of Batching Interval • Real-Time ATP: as each order comes in make decision based on customer response (accept or not, time/quantity) and production resource allocation  equivalent to “greedy” algorithm • Batch ATP: collect all orders that arrive in batching interval; optimize customer response and resource allocation over this set. • Real-Time vs Batch ATP  greedy heuristic vs optimization. • Variants of Batch ATP based on size of batching interval

23. Profitability -- Customer Service Tradeoff Two key customer service criteria: Time to commit: Time to delivery: time delivery order commit production depends on length of batching interval • As response times decrease, customer service improves • Longer response times provide more production flexibility leading to higher revenues and/or lower costs

24. Missed Orders vs Batching Interval Size: Maxtor Scenario

25. Tangible Profit vs Batching Interval Size: Maxtor Scenario

26. Tangible Profit vs Batching Interval Size: Toshiba Notebook Scenario

27. 3. Stochastic and Dynamic Problem Aspects: Material Reservation Policy: It is sometimes useful to reserve material from one time period in anticipation (forecast) of more profitable or higher priority orders that might arise in a later time period. Material reservation policy: • For each raw material: • Material reserve level • Per unit shortfall penalty (material “price”) • Orders that violate material shortfall penalty are not accepted unless they remain profitable when charged the shortfall penalty Basis for Formal Analysis: Stochastic Dynamic Programming

28. Effect of Material Reservation Policy: Toshiba Notebook Scenario

29. Other Research Issues • What is nature of customer service/production efficiency tradeoff? • key issue: what is value of reducing time to order commitment and/or time to ship date • Model support for real-time ATP • Multiple sales channel strategies • Coupling ATP models to supply chain infrastructures (ERP and SCM systems) • Scalability issues • B2B vs B2C strategies • ATP as a strategic weapon

30. Outline • Introduction and Overview of Model • Research Topics • Experience from Toshiba Prototype

31. Variation in Fixed Resources over Time Customer orders Order Commitment Resources t Inventory W W+1 W+2 W+3 W+4 W+5 W+6 W+7 -> Fixed Production Schedule Fixed material availability and production capacity Fixed production capacity

32. Flexibility in Adjusting Material Availability 2 weeks expedite 1 week de-expedite W+4, 100 {A, B, C} A C B W+1 W+2 W+3 W+4 W+5 W+6 Inventory holding cost Extra Cost Expedite cost De-expedite cost Inventory cost savings

33. Scenario comparing current approach and optimization-based approach #1 #2 #1 #2 #1 #1 t Inv MO PC1 PC2 PC3 PC Expedite Due date violation #2 #2 #1 #1 #1 #2 #1 #2 Re-commit C-ATP A-ATP

34. Two level (approximate) model used to allow for solution of real (large) problem instances • Customer orders • Weekly resource availability Aggregation Daily resource availability Committed week, qty Weekly ATP Daily ATPs Daily ATP Daily ATP Weekly production & inventory plan • Committed date, qty • Daily resource allocation Weekly resource allocation

35. Inventory weight increase Due date weight increase Trade-off Analysis of Multiple Objectives Due date only Inventory only

36. Supply Chain ATP Model (preliminary implementation completed): Commitment Production Transportation Orders Finished goods Sales Factory MO, PC Warehouse MO, PC MO, PC