Fundamentals of Industrial Plants Prof. Andrea Sianesi academical year 2008/2009

1. Fundamentals of Industrial Plants Prof. Andrea Sianesiacademical year 2008/2009 Inventory Management & Pull techniques

2. Plan make plan source make deliver • Problem: specification of “what”, “how much” and “when” to order at any stage of the production process • Two approaches can be identified: • “PULL”, also called “INVENTORY” management • “PUSH” also called “ON DEMAND” management

3. Approaches to plan make PUSH Systems Traditional PULL Systems JustInTime

4. Approaches to plan manke MANUFAC. MANUFAC. ASSEMBLY COMPON. SUBASS.Y FINISHED P. PULL SYSTEM MANUFAC. MANUFAC. ASSEMBLY COMPON. SUBASS.Y FINISHED P. PUSH SYSTEM

5. Why to hold inventory ? • To absorb demand uncertainty • Safety stock (stock of flexibility); • Seasonal stock (stock of capacity). • To decouple different operations phases • To keep stock is a way to allow source, make and delivery systems to work with different rate, as it allows the different phases to be “asynchronous” and it absorbs upstream variations. • Speculative stocks • Total cost minimization • Setup costs reduction • Order emission cost reduction

6. Stock “performances” • Effectiveness: service level guaranteed to downstreams phases: • Quantity and duration of stock-outs in case of safety stocks and decoupling stocks; • Efficiency • Amount of fixed costs and/or of workforce saved in case of seasonal stocks; • Amount of setup costs saved due to the application of lot policies; • Amount of purchasing costs saved in case of speculative stocks.

7. What should be decided • Replenishment policy, i.e. how much and when to order. • Impact on: • Stock holding costs; • Setup/order emission costs; • Stock out / downstream service costs; • Constraints: • Production capacity and flexibility of upstream productive level; • Physical space limit of warehouses. • Control level, i.e. the detail and the frequency of control of the stock level of each item. • Impact on: • Cost of control • Constraints : • Availability of resources to perform the controls (people, computers, ...).

8. “Stock management” Suppliers Suppliers WKG RM FP MTG SFP Clients • The moment and the quantity to order are decided only based on the actual level of stock. • Stock management approach is basically to simply react to demand. • For this reasin this tecnique is called "Pull", i.e. pulled by downstream consumption.

9. “Stock management” • Stock management approach should therefore be used when: • Demand is constant (uniform demand) in time, or: • It is impossible to foresee demand with enough accuracy, or: • Upstream phase is highly flexible.

10. “Stock management” objectives • The main objective of stock management is to minimize the related costs and to maximize the service level for the downstream phases. • This objective can be expresses as the minimization of a total cost function composed by: • Stock holding costs; • Execution costs (order / setup); • Costs of control; • Costs of low service level at downstream phases (stock out costs).

11. Classification profiles • According to the type of control • Continuous control; • Discrete control: time intervals • According to the order issue interval • Fixed interval; • Variable interval. • According to the ordered quantity • Fixed quantity; • Variable quantity. • According to the type of re-order • Independent entries: each item is re-ordered independently from the others; • Joint entries: orders for the different items are coordinated.

12. Classification profiles Discrete control Combined entries reorder Continuous control Independent entries reorder Interval of order issue Fixed Variable Quantity ordered Fixed EOQ-OP Model Variable IE Model Switch Models

13. The EOQ model • Characteristics • Variable interval of orders issuing • Fixed quantity ordered • Continuous control • Independent entries reorder • Objectives • Identifying the quantity Q [pieces] to re-order that minimizes the total cost, sum of the:ordering cost, purchasing/production cost stock holding cost, • and the conditions that determine the orders issuing

14. The EOQ model • Hypothesis • Constant consumption over time D [units/year] • Constant setup/ordering cost S [€] • Constant variable cost/price per unit C [€/unit] • Constant ownership rate i [€/€*year] • Annual cost for keeping a unit in stock H = i C • Constant lead time L [days] • Pre-defined working days GG [days/year] • Average daily consumption d = D / GG • Infinite stock replenishment rate r [unit/day] • Infinite capacity of warehouse • Shipment costs negligible (or included in the re-ordering cost)

15. The EOQ-ROP model Inventory level AVAILABILITY Economic Order Quantity Q INVENTORY Re-order Point R Time Re-order Point = demand in the LT= R = d x L Lead Time L Order emission Material arrival

16. The EOQ-ROP model Stock Q (= Lot) Time Average stock = Lot / 2 Number of orders issued= annula demand / Lot

17. The EOQ-ROP model • Cost of stock holding [€/year] • Under the stated hypothesis, the average inventory level is equal to q/2. So, the annual stock holding cost is linear in q. • Cost of order issuing Cs (or setup cost) [€/year] • The number of orders issued in a year is equal to D/q. So the cost of order issuing Cs and q are inversely proportional. • Cost of purchasing Ca (or cost of production) [€/year] • The total cost of purchasing (or cost of production) Ca is indipendent from q.

18. The EOQ-ROP model The costs I costi Order emis Immob. C. Total cost E.O.Q

19. The EOQ-ROP model 2 x D x S EOQ = H The EOQ formula D = consumption (demand) annual in quantity S = order issuing cost (setup cost) H = annual stock holding cost per unit

20. Production lot not received istantaneously 2 x D x S EOQ’ = H x (1-d/r) • If the time needed to produce a (production) lot is high (some days or weeks) the production flows into inventory not all at once. • In the meantime demand is consuming the stock. 200 150 100 50 0 1 2 3 4 where d = consumption rate r = production rate

21. Production lot not received istantaneously Downstream level consumption [unit/day] Inventory level -d Rate of production or delivery of upstream level [unit/day] Maximum stock quantity [unit] (less than Q) r Q’ = T * (r – d) = Q * (r – d) / r Time Time needed to produce or to delivera complete lot Q [days] T = Q / r As d<r, then EOQ’ > EOQ

22. Reorder point definition INVENTORY REORDER POINT TIME REORDERS PRODUCTION OR PURCHASING LT Reorderpoint = demandduring LT= R = d x L

23. Safety stock • Safety stocks are used to prevent from stock-out • The level of safety stocks depends on: • variation of downstream consumption (demand) with respect to forecast • desired service • lead time duration • lead time reliability

24. Safety stock Inventory level 1 2 3 AVAILABILITY Q Q Q Reorder point R STOCK LEVEL Safety stocks SS Time L L L In reality: Reorder point = demand during LT+ SS = R = d x L+ SS

25. Safety stock R d time Lead-time

26. Hypotesis: demand during lead time is a random variable normally distributed with mean equal to d and standard deviation equal to sL. By defining safety stock level, the probability of stock coverage is univocally defined. Safety stock Probability of stock coverage equal to : 84,1% 97,7% 99,8% d+ s d d+2s Quantity in stock d +3s

27. Safety stock Z k

28. Data: R reorder point in units d average daily demand L lead time expressed in days k number of standard deviations (the expected service) L std-dev of demand during lead time Safety stock

29. Given the average daily demand and the standard deviation of daily demand d, the standard deviation during lead time L can be calculated as follows (the standard deviation of a series of independent events is the square root of the sum of the variances) : Safety stock

30. Safety stock s s l 2 2 2 LT = × s × + s × SS k L d l LT k function of service level standard dev. of demand L lead-time standard dev. of lead time d demand If LT is varying too, it must be considered as well when dimensioning safety stock.

31. Fixed-time period model • Characteristics • Discontinuous control • Fixed-time between reviews IE • Variable ordered quantity • Independent or combined entries reorder • Objective • Identifying the quantity to re-order at each review that allows the availability of each product to achieve a pre-defined level, called objective level (OL) • Hypothesis • The same as EOQ-ROP model

32. Fixed-time period model availability order quantity LO physical stock SS IE LT we order here… what will arrive here

33. Fixed-time period model • At fixed time interval (IE) of T days inventory level is reviewed and availability is calculated. Availability is: • I = Physical inventory level + Orders issued but not arrived yet • An order q is issued, it is equal to the difference between objective level LO and availability: • q = LO - I [units] • The objective level LO is defined in order to cover the demand in the time fence T+L (where L is supplier’s LT): • [units]

34. Fixed-time period model • Safety stock is calculated in the same way as in the EOQ-ROP model. However, the component derived from demand variability must prevent from stockouts that can happen during the time fence T+L.

35. Comparison between the two models fixed quantity fixed time • - easy joint (combined entries) re-orders planning • easy control of availiability level (periodic control) • low average stock level (continuous control) • Minimization of relevant costs (OPTIMIZATION) - difficult joint (combined entries) re-orders planning - many replenishment orders (also to the same supplier) - “heavy” control of availiability level (continuous control) - higher average stock level (periodic control)

36. Magee Boodman Model • It is a model for PRODUCTION PLANNING derived from inventory management models • Suitable for situations: • multi-product • single-machine with stationary demand deterministically predictable

37. Applicability field • Objective: • determine the economic length of the production cycle, i.e. the ECONOMIC NUMBER no (optimal) of the production cycles of the products in one year • no is the number of CAMPAIGNS that are performed in the planning horizon • in every campaign all the products are produced

38. Legend • k product index • H working days in a year • r(k) production rhythm for product k • D(k) annual demand for product k • Cm stock holding ownership rate • p(k) variable production cost of k • a(k) setup cost of product k

39. Notes • The setup cost does NOT take into account nor the time of lost production and neither the production sequence, but it is a cost that every time is sustained for setting up the production of a product k • However, it is possible to pre-determine the optimal sequence and keep it fixed in all the campaigns.

40. Stock holding cost • The total stock holding cost is:

41. Setup cost • Under the hypothesis to pre-calculate the production sequence of all the products, the total setup cost is :

42. Optimal number of cycles • By summing up all the costs, deriving the sum with respect to no and equalizing the derivative to zero the following formula is obtained:

43. Order Quantity • So, for the generical product k the economic quantity to produce is:

44. Limitations of Magee Boodman model • “Degenerate” campaigns • Uncertainty of demand forecast • Setups dependent on the sequence • Capacity constraints • Setup times

45. Magee Boodman model • “Degenerate” campaigns: it is not always worthwhile to produce in every campaign the products that have limited demand and high setup costs: • Calculate the Economic Order Quantity (Q(k)) of each of these products considered separately • if Q(k) >> Q0(k) the possibility to produce by alternating or occasional campaigns is taken into account • the costs associated to the different alternatives are calculated and the solution with the lowest total cost is chosen

46. Magee Boodman model • Uncertainty in demand forecast: adequate safety stock are used • Setups are dependent on the sequence : because there is no constraint on the sequence due to the campaign, the optimal sequence is chosen before the application of the model, and then the optimised setup cost, that derives from this sequence, is used

47. Magee Boodman model • Capacity constraints / setup times • Production rythm is taken into account • Setups are reducing the time available for production Number of campaigns no admissible zone Total demand