Operations Management - II Post Graduate Program Session 7. Vinay Kumar Kalakbandi Assistant Professor Operations & Systems Area

Transcription

1 Operations Management - II Post Graduate Program Session 7 Vinay Kumar Kalakbandi Assistant Professor Operations & Systems Area 2/2/2016 Vinay Kalakbandi 1 Agenda Course updates Recap Inventory Management Uncertainty 2/2/2016 Vinay Kalakbandi 2 1

2 Demand uncertainty!!! 2/2/2016 Vinay Kalakbandi 3 If life were predictable it would cease to be life, and be without flavor. Eleanor Roosevelt 2/2/2016 Vinay Kalakbandi 4 2

3 Lets keep it simple first! Single period, perishable product Uncertain demand Examples? Fire crackers Apparel seasonal time horizon Airline seat class perishable service Electronic goods with upgrade cycles How do you represent uncertainty? 2/2/2016 Vinay Kalakbandi 5 Demand characteristics Based on historic data demand follows a discrete probability distribution D P[D=d] How much would you order? 2/2/2016 Vinay Kalakbandi 6 3

4 Managing the average will make you an average manager! A quote by 2/2/2016 Vinay Kalakbandi 7 Understanding Service level What if demand follows a normal distribution NORM(5,2) What area of the demand distribution would you cover? Extending the idea to multiple periods 2/2/2016 Vinay Kalakbandi 8 4

5 Inventory Level Inventory Level Certain Demand Q Inventory Position Physical Inventory ROP Mean Demand during LT L Time Uncertain Demand Inventory Position Physical Inventory ROP Mean Demand during LT Safety Stock L Time 5

6 Impact of demand uncertainty 2/2/2016 Vinay Kalakbandi 11 Computing safety stock Let the demand during lead time follow a Normal distribution Mean demand during lead-time = (L) Standard deviation of demand during lead-time = Desired service level = ( 1 ) (L) The probability of a stock out = Standard normal variate corresponding to an area of ( 1 ) covered on the left side of the normal curve = Z Safety stock (SS) is given by SS = Z * ( L), 6

7 Inventory Level Relationship between Service Level and Safety Stock 2/2/2016 Vinay Kalakbandi 13 Continuous Review (Q) System Q Inventory Position Physical Inventory ROP SS Mean Demand during LT Safety Stock L Time 7

8 Inventory Level Continuous review policy 2/2/2016 Vinay Kalakbandi 15 Periodic Review (P) System Inventory Position Physical Inventory S Q R Q 2R Q 3R Order Up to Level SS Safety Stock R 2R 3R L Time 8

9 Periodic Review policy 2/2/2016 Vinay Kalakbandi 17 Periodic & Continuous Review Systems Criterion How much to order When to order Continuous Review (Q) System Fixed order qty: Q ROP = μ (L) + Z α σ (L) Periodic Review (P) System S = μ (L+R) + Z α σ (L+R) Q R = S I R Every R periods Safety stock SS = Z α σ (L) SS = Z α σ (L+R) Salient aspects Implemented using two bin system Suited for medium and low value items Kardex system Transaction processing system More safety stock More responsive to demand Ease of implementation 9

10 Inventory Planning Models Mean of weekly demand : 200 Standard deviation of weekly demand : 40 Unit cost of the raw material : Rs. 300/- Ordering cost : Rs. 460/- per order Carrying cost percentage : 20% per annum Lead time for procurement : 2 weeks EOQ Model Weekly demand = 200 Number of weeks per year = 52 Annual demand, D = 200*52 = 10,400 Carrying cost, C c = Rs per unit per year Economic Order Quantity = Time between orders = DS H * 460*10, weeks Inventory Planning Models Q System Q System Standard deviation of weekly demand = 40 Lead time, L = 2 weeks Mean demand during L, (L) = 2* 200 = 400 Standard deviation of demand during L, (L) = 2 * For a service level of 95%, SS = Z * ( L) = 1.645*56.57 = ROP = (L) + Z * ( L) = = 493 Using EOQ as the fixed order quantity, Q system can be designed as follows: As the inventory level in the system reaches 493, place an order for 400 units. This will ensure in the long run a service level of 95%. 10

11 Inventory Planning Models P - system P System Using the time between orders derived from the EOQ model as the basis for review period Review period, R = 2 weeks Mean demand during (L + R), ( L R) = 200*(2 + 2) = 800 Standard deviation of demand during (L + R), ( L R) = For a service level of 95%, SS = Z * ( L R) = 1.645*80 = Order up to level, S = ( L R) + Z * ( L R) = = *40 80 The P system can be designed as follows: The inventory level in the system is reviewed every two weeks and an order is placed to restore the inventory level back to 932 units. This will ensure a service level of 95%. Hybrid Inventory Policies (s,s) policy Optional replenishment system Periodic review with a order upto level Ensures minimum ordering level Eliminates continuous review Base stock system Order as much as you sell Base stock level = expected demand during lead time + safety stock Usually orders are accumulated periodically 2/2/2016 Vinay Kalakbandi 22 11

12 2/2/2016 Vinay Kalakbandi 23 What is the Optimal service level? Happiness is a mysterious thing, to be found somewhere between too little and too much Ruskin Bond 12

13 Newsvendor model Inventory decision under uncertainty The too much/too little problem : Order too much and inventory is left over at the end of the season Order too little and sales are lost. Notation Demand D is a random variable Cumulative distribution function F(D) Wholesale price W Selling price R Salvage value S (<W) How much should the retailer order? 13

14 Too much and too little costs C o = overage cost The cost of ordering one more unit than what you would have ordered had you known demand. Increase in profit you would have enjoyed had you ordered one unit lesser. C o = Cost Salvage value = W S = C u = underage cost The cost of ordering one fewer unit than what you would have ordered had you known demand. Increase in profit you would have enjoyed had you ordered one unit more. C u = Price Cost = R W = 27 Balancing the risks and benefits Risk : Ordering one more unit increases the chance of overage Expected loss on the Q th unit = C o x F(Q), where F(Q) = Prob{Demand <= Q) Benefit: Ordering one more unit decreases the chance of underage: Expected benefit on the Q th unit = C u x (1-F(Q)) 14

15 Expected profit maximizing order quantity To minimize the expected total cost of underage and overage, order Q units so that the expected marginal cost with the Q th unit equals the expected marginal benefit with the Q th unit: C F( Q) C 1 F o Q Rearrange terms in the above equation -> u Cu F( Q) C C The ratio C u / (C o + C u ) is called the critical ratio. In other terms, (R-W)/(R-S). R and S are determined by the market. o u 29 What is the Optimal service level? Let C o = Cost of over stocking per unit C u = Cost of under stocking per unit Q = Number of units to be stocked d = Single period demand P( d Q) = The probability of the single period demand being at most Q units P( d Q) Cu C C u o = Service Level 15