Supply Chain Management

1. Supply Chain Management One's work may be finished some day, but one's education never. – Alexandre Dumas

2. Inventory is the Lifeblood of Manufacturing • Plays a role in almost all operations decisions • shop floor control • scheduling • aggregate planning • capacity planning, … • Links to most other major strategic decisions • quality assurance • product design • facility design • marketing • organizational management, … • Managing inventory is close to managing the entire system…

3. Plan of Attack • Classification: • raw materials • work-in-process (WIP) • finished goods inventory (FGI) • spare parts • Justification: • Why is inventory being held? • benchmarking

4. Plan of Attack (cont.) • Structural Changes: • major reorganization (e.g., eliminate stockpoints, change purchasing contracts, alter product mix, focused factories, etc.) • reconsider objectives (e.g., make-to-stock vs. make-to-order, capacity strategy, time-based-competition, etc.) • Modeling: • What to model – identify key tradeoffs. • How to model – EOQ, (Q,r), optimization, simulation, etc.

5. Raw Materials • Reasons for Inventory: • batching (quantity discounts, purchasing capacity, … ) • safety stock (buffer against randomness in supply/production) • obsolescence (changes in demand or design, also called obsolete inventory) • Improvement Policies: • ABC classification (stratify parts management) • JIT deliveries (expensive and/or bulky items) • vendor monitoring/management

6. Raw Materials (cont.) • Models: • EOQ • power-of-two • service constrained optimization model

7. ABCAnalysis (1) • A Parts —— The first 5% to 10% of the parts, accounting for 75% to 80% of the total annual cost • B Parts —— The next 10% to 15% of the parts, accounting for 10% to 15% of the total annual cost • C Parts —— The bottom 80% or so of the parts, accounting for only 10% of the total annual cost

8. ABCAnalysis (2) • Basic Idea：classify the parts according to their values per year • Conclusion: we should differentiate the parts in inventory and use different inventory control strategies for different parts. Value per year (%) Percentage to the total inventory Class AParts 75%-80% 5%-10% 10%-15% 10%~15% BParts 80% Cparts 10%

9. Part Number Percentage Annual Value($) Ratio Classes 90,000 77,000 26,350 15,001 12,500 8,250 1200 850 504 150 1 2 3 4 5 6 7 8 9 10 72% A 20% 23% B 30% C 5% 50% ABCAnalysis (3) • Example：A semiconductor manufacturer

10. ABCAnalysis (4)

11. Multiproduct EOQ Models • Notation: N = total number of distinct part numbers in the system Di = demand rate (units per year) for part i ci = unit production cost of part i Ai = fixed cost to place an order for part i hi = cost to hold one unit of part i for one year Qi = the size of the order or lot size for part i (decision variable)

12. Multiproduct EOQ Models (cont.) • Cost-Based EOQ Model: For part i, • Frequency Constrained EOQ Model: min Inventory holding cost subject to: Average order frequency F

13. Multiproduct EOQ Solution Approach • Constraint Formulation: • Cost Formulation:

14. Multiproduct EOQ Solution Approach (cont.) • Cost Solution: Differentiate Y(Q) with respect to Qi, set equal to zero, and solve: • Constraint Solution: For a given A we can find Qi(A) using the above formula. The resulting average order frequency is: If F(A) < F then penalty on order frequency is too high and should be decreased. If F(A) > F then penalty is too low and needs to be increased. No surprise - regular EOQ formula

15. Multiproduct EOQ Procedure – Constrained Case • Step (0) Establish a tolerance for satisfying the constraint (i.e., a sufficiently small number that represents “close enough” for the order frequency) and guess a value for A. • Step (1) Use A in previous formula to compute Qi(A) for i = 1, … , N. • Step (2) Compute the resulting order frequency: If |F(A)-F| < e, STOP; Qi* = Qi(A), i = 1, … , N. ELSE, If F(A) < F, decrease A If F(A) > F, increase A Go to Step (1). • Note: The increases and decreases in A can be made by trial and error, or some more sophisticated search technique, such as interval bisection.

16. Multiproduct EOQ Example • Input Data: Target F value: F = 12

17. Multiproduct EOQ Example (cont.) • Calculations:

18. Powers-of-Two Adjustment • Rounding Order Intervals: T1* = Q1*/D1 = 36.09/1000 = 0.03609 yrs = 13.17  16 days T2* = Q2*/D2 = 114.14/1000 = 0.11414 yrs = 41.66  32 days T3* = Q3*/D3 = 11.41/100 = 0.11414 yrs = 41.66  32 days T4* = Q4*/D4 = 36.09/100 = 0.3609 yrs = 131.73  128 days • Rounded Order Quantities: Q1' = D1T1'/365 = 1000  16/365 = 43.84 Q2' = D2T2' /365 = 1000  32/365 = 87.67 Q3' = D3T3' /365 = 100  32/365 = 8.77 Q4' = D4T4' /365 = 100  128/365 = 35.07

19. Powers-of-Two Adjustment (cont.) • Resulting Inventory and Order Frequency: Optimal inventory investment is $3,126.53 and order frequency is 12. After rounding to nearest powers-of-two, we get:

20. Questions – Raw Materials • Do you track vendor performance (i.e., as to variability)? • Do you have a vendor certification program? • Do your vendor contracts have provisions (防备) for varying quantities? • Are purchasing procedures different for different part categories? • Do you make use of JIT deliveries? • Do you have excessive “wait to match” inventory? (May need more safety stock of inexpensive parts.) • Do you have too many vendors? • Is current order frequency rationalized?

21. Work-in-Process • Despite the JIT goal of zero inventories, we can never operate a manufacturing system with zero WIP, since zero WIP implies zero throughput. • WIP Inventory will be in one of 5 states: • queueing (if it is waiting for a resource) • processing (if it is being worked on by a resource) • waiting to move (if it has to wait for other jobs to arrive in order to form a batch) • moving (if it is actually being transported between resources) • waiting to match (synchronization)

22. Work-in-Process (Improvement Policies) • pull systems (will achieve the same level of throughput with a lower average WIP – reduce ququeing and wait-for-match) • synchronization schemes (– reduce wait-for-match) • lot splitting (process lots and move lots do not have to be the same – reduce wait-for-batch) • flow-oriented layout (more frequent moves can be facilitated by the plant layout – reduce wait-for-batch) • floating work (cross-trained workers can increase the effective capacity of the production line – reduce ququeing)

23. Work-in-Process (Improvement Policies) • setup reduction (reducing setups increases effective capacity and more frequent setups will decrease effective variability at machines – reduce ququeing) • reliability/maintainability upgrades (reduce effective variability at machines – reduce ququeing) • focused factories (Not all WIP need be treated equally: low-volume parts could be produced in a job shop environment; high-volume parts could be assigned to lines with few setups and steady flow by using high efficient pull system – reduce ququeing) • improved yield/rework (enhanced quality– reduce ququeing) • better finite-capacity scheduling (– reduce ququeing)

24. Work-in-Process (cont.) • Benchmarks: • WIP below 10 times critical WIP (smallest WIP level required by a line to achieve full throughput under the best conditions) • relative benchmarks depend on position in supply chain • Models: • queueing models • simulation

25. Science Behind WIP Reduction • Cycle Time (can be approximated as): • WIP (by Little’s Law): • Conclusion:CT and WIP can be reduced by reducing utilization, variability, or both. te: mean processing time; ce: coefficient of variation of processing time; ca: coefficient of variation of arrivals; u: utilization rate

26. Questions – WIP • Are you using production leveling and due date negotiation to smooth releases? • Do you have long, infrequent outages (储运损耗) on machines? • Do you have long setup times on highly utilized machines? • Do you move product infrequently in large batches? • Do some machines have utilizations in excess of 95%? • Do you have significant yield/rework problems? • Do you have significant waiting inventory at assembly stations (i.e., synchronization problems)?

27. Finished Goods Inventory • Reasons for Inventory: • respond to variable customer demand • absorb variability in cycle times • build for seasonality • forecast errors • Improvement Policies: • dynamic lead time quoting (instead of fixed lead time) • cycle time reduction • cycle time variability reduction (more variability in cycle times, the more safety stock we must build) • late customization (Semi-finished inventory is more flexible, if can be used to produce more than one finished product, which makes it possible to carry less total inventory) • balancing labor, capacity and inventory (product is produced during low-demand periods and held as FGI to meet demand during peak periods) • improved forecasting

28. Finished Goods Inventory (cont.) • Benchmarks: • seasonal products • make-to-order products • make-to-stock products • Models: • reorder point models • queueing models • simulation

29. Questions – FGI • All the WIP questions apply here as well. • Are lead times negotiated dynamically? • Have you exploited opportunities for late customization (e.g., product standardization, etc.)? • Have you adequately considered variable labor (seasonal hiring, cross-trained workers, overtime)? • Have you evaluated your forecasting procedures against past performance?

30. Spare Parts Inventory • Reasons for Inventory: • customer service • purchasing/production lead times • batch replenishment • Improvement Policies: • separate scheduled/unscheduled repairing demand • increase order frequency • eliminate unnecessary safety stock • differentiate parts with respect to fill rate/order frequency • forecast life cycle effects on demand • balance hierarchical inventories

31. Spare Parts Inventory (cont.) • 2 distinct types of spare parts • Scheduled preventive maintenance • Unscheduled emergency repairs • Scheduled maintenance represents a predictable demand source • This demand is much more stable than customer demand • MRP logic is applicable to these parts • Unscheduled emergency repairs are unpredictable • (Q, r) model can be used

32. Spare Parts Inventory (cont.) • Benchmarks: • scheduled demand parts • unscheduled demand parts • Models: • (Q,r) • distribution requirements planning (DRP) • multi-echelon models

33. Multi-Product (Q,r) Systems • Many inventory systems (including most spare parts systems) involve multiple products (parts) • Products are not always separable because: • average service is a function of all products • cost of holding inventory is different for different products • Different formulations are possible, including: • constraint formulation (usually more intuitive) • cost formulation (easier to model, can be equivalent to constraint approach)

34. Model Inputs and Outputs Costs Order (A) Backorder (b) or Stockout (k) Holding (h) Stocking Parameters (by part) Order Quantity (Q) Reorder Point (r) Inputs (by part) Cost (c) Mean LT demand (q) Std Dev of LT demand (s) MODEL Performance Measures (by part and for system) Order Frequency (F) Fill Rate (S) Backorder Level (B) Inventory Level (I)

35. Multi-Prod (Q,r) Systems – Constraint Formulations Backorder model min Inventory investment subject to: Average order frequency F Average backorder level B Fill rate model (or Stockout model) min Inventory investment subject to: Average order frequency F Average fill rate S Two different ways to represent customer service.

36. Multi Product (Q,r) Notation

37. Multi-Product (Q,r) Notation (cont.) • Decision Variables: • Performance Measures:

38. Backorder Constraint Formulation • Verbal Formulation: min Inventory investment subject to: Average order frequency  F Total backorder level  B • Mathematical Formulation: • “Coupling” of Q and r makes this hard to solve.

39. Backorder Cost Formulation • Verbal Formulation: min Ordering Cost + Backorder Cost + Holding Cost • Mathematical Formulation: • “Coupling” of Q and r makes this hard to solve.

40. Fill Rate Constraint Formulation • Verbal Formulation: min Inventory investment subject to: Average order frequency  F Average fill rate  S • Mathematical Formulation: • “Coupling” of Q and r makes this hard to solve.

41. Fill Rate Cost Formulation • Verbal Formulation: min Ordering Cost + Stockout Cost + Holding Cost • Mathematical Formulation: Note: a stockout cost penalizes each order not filled from stock by k regardless of the duration of the stockout • “Coupling” of Q and r makes this hard to solve.

42. Relationship Between Cost and Constraint Formulations • Method: 1) Use cost model to find Qi and ri, but keep track of average order frequency (F) and fill rate (S) using formulas from constraint model. 2) Vary order cost A until order frequency constraint is satisfied, then vary backorder cost b (stockout cost k) until backorder (fill rate) constraint is satisfied. • Problems: • Even with cost model, these are often a large-scale integer nonlinear optimization problems, which are hard. • Because Bi(Qi,ri),Si(Qi,ri), Ii(Qi,ri) depend on both Qiand ri, solution will be “coupled”, so step (2) above won’t work without iteration between A and b (or k).

43. Type I (Base Stock) Approximation for Backorder Model • Approximation: • replace Bi(Qi,ri) with base stock formula for average backorder level, B(ri) • Note that this “decouples” Qi from ri because Fi(Qi,ri) = Di/Qi depends only on Qi and not ri • Resulting Model:

44. Solution of Approximate Backorder Model • Taking derivative with respect to Qi and solving yields: • Taking derivative with respect to ri and solving yields: EOQ formula again base stock formula again if Gi is normal(i,i), where (zi)=b/(hi+b)

45. Using Approximate Cost Solution to Get a Solution to the Constraint Formulation • 1) Pick initial A, b values. • 2) Solve for Qi, riusing: • 3) Compute average order frequency and backorder level: • 4) Adjust A until Adjust b until Note: use exact formula for B(Qi,ri) not approx. Note: search can be automated with Solver in Excel.

46. Type I and II Approximation for Fill Rate (or Stockout) Model • Approximation: • Use EOQ to compute Qi as before • Replace Bi(Qi,ri) with B(ri) (Type I approx.) in inventory cost term. • Replace Si(Qi,ri) with 1-B(ri)/Qi (Type II approx.) in stockout term • Resulting Model: Note: we use this approximate cost function to compute ri only, not Qi

47. Solution of Approximate Fill Rate Model • EOQ formula for Qi yields: • Taking derivative with respect to ri and solving yields: Note: modified version of basestock formula, which involves Qi if Gi is normal(i,i), where (zi)=kDi/(kDi+hQi)

48. Using Approximate Cost Solution to Get a Solution to the Constraint Formulation • 1) Pick initial A, k values. • 2) Solve for Qi, riusing: • 3) Compute average order frequency and fill rate using: • 4) Adjust A until Adjust b until Note: use exact formula for S(Qi,ri) not approx. Note: search can be automated with Solver in Excel.

49. Multi-Product (Q,r) Example Cost and demand data

50. Multi-Product (Q,r) Example Results of multipart Stockout model (Q,r) calculations Step 1. Assume a target average order frequency of F=12. Step 2. Assume a target average fill rate of S=0.95. Too low!! Result: k = 7.213