Operations Management

Final Review

EOQ

Buying a couple of beer kegs or a six pack? Depends on Demand (D)Space in the refrigerator / cost of a new refrigerator (H)Distance to the nearest seller (S)

Therefore the relationship SQRT(2 * D * S / H) = EOQ

Time

Quantity

Q system

Q

Safety Stock

Reorder Point

Q

SS + Q

Q

L

Q 14 Total Inventory

Time

??

4500

6000

SS + Q

R = 4500 = Red + Safety stock

Red = Mu * L = 800 * 5 = 4000

Safety stock = 4500-4000 =500

PLUS

Cyclical stock = Q = 6000

So, AVG cyclical stock = (6000 + 0)/2

= 3000

= 3000+500 = 3500

PLUS

L

Q 14 continued

days

Assembly

800

BY Little’s law

I = 800 *4 = 3200

SO

total=3500+3200= 6700

P-system

Time

Quantity

Target Q

L

Period P

Order placement date Next order placement date

A combination of P and Q

• Every Saturday I top up my gas at Costco (P)• Maximum gas my tank can take = target qty T• But during the week if I see an empty tank warning light (re-order

point) I top it up again

• Note: I reach the gas station and the tank is filled up in 4 minutes. So is my lead time 4 min?– NO The lead time here is the time it takes for me to reach

Costco.

MRP

Explanations: a) The lead time for next item need not be same as final assembly time so

what’s the logic behind making the final assembly start be the trigger for ordering?

b) All items have safety stock

c) Definitely wrong, in fact just the opposite

1) The underlying logic for level-by-level (or “backward explosion”) processing in an MRP system is: a) Starting final assembly signals an order release for the next item.

b) Items without safety stock quantities must be processed before items that have safety stocks greater than zero.

c) Items must be processed in order of increasing lead time.

d) All parents (subassemblies or inputs) of an item must be processed before that item is processed.

Q 2

Explanations: b) Cant be, then how would companies adopt MRP?

c) No way, in fact just the opposite.

d) Again, just the opposite.

2) Which one of the following statements is an advantage of using an MRP system instead of a reorder point system? a) MRP provides forward visibility for planning purposes.

b) MRP assumes a uniform demand rate.

c) MRP assumes independence among the inventory items.

d) MRP does not need bills of materials as an input.

Q 3

Explanation: b) Can’t be Q because many items are non standard so how can you order a

large qtty and just wait for it to be consumed?

c) Can’t be Newsvendor because this company cant afford to work on the ‘probability’ that there will be an understockage, besides there’s no marginal profit from overstocking

d) Its made to order so the inventory has non standard items with a one time demand so a target order quantity makes no sense

3) Consider the following scenario. A company produces products to customer order but has plenty of lead time to get the job done. Some components are standard, but many are designed or purchased for the particular customer order. The number of levels in the bills of material is variable, but tends to be large. Lot sizes must be large in some cases because of lengthy setup times or bottleneck operations. Based on this information, the production inventory system most likely to succeed would be: a) Materials requirements planningb) Q-systemc) Newsvendord) P-system

MRP - So what is it?

• http://en.wikipedia.org/wiki/Material_resource_planning

• Explodes the Master Production Schedule (MPS) to give you a start date for each antecedent process.

• A project plan with the end date in sight, (sort of)

MRP - So what?

• SO if it’s so cool, why is everybody not using it? I’ve never heard of MRP before.

• They are using it!• Functionality got added to address capacity, non

manufacturing activities, services, suppliers etc.• So MRP => MRP II + SRP + DRP +bells and whistles =

ERP, which every one has heard of!

MRP Thanksgiving MRP

9:30processturkey

01

10:00Turkey In oven

2:00Turkey

out of oven

12:00start mashed potatoes

2:05prep yams

01

2:15yams in

1:15 – 1:30prep dressing

01

2:00dressingin oven

2:20green beans

11:45start rolls rising

02

2:45rolls cook

3:00pm

Dinner01 – Turkey

– Taters01 – Dressing02 – Rolls

rise: 38, cook: 1201 – Yams ½ hr

– green beans– gravy

News Vendor Model

• You have to place an order Q in an environment where demand is unknown.

• So rationally you’d decide such that the profit of having the qth item > the loss incurred by having the qth item.

• What are we really doing?– Marginal Profit (qth item) > Marginal Loss (qth item)– Prob of profit = p and prob of loss = 1-p– So p x Profit > (1-p) x Loss– So p > Loss/ (profit + loss) = Co/(Co + Cu)=> Pr (p) = Pr (D>Q) = Co/(Co + Cu)

Q 15 sample final

• Customer cost of late flight = opportunity cost

• Opportunity cost = money that could have been made if there was one more quantity available

• This money = cost of under stocking

Q 16 sample final

55 69

0 zZ = (69 – 55) / 6 = 2.33

Corresponding to 2.33 from the table we get 99% HOW?

666

= 1 – .99 = .01 = 1%

Q 17 sample final

• Pr (D>Q) = Co / (Co + Cu) = .217355

0

0.2173

• Because .2173 is on the left

of the mean and most tables

give the right of the mean,

calculate the are of the green

blob and look that up on the

table. Which is 1- .2173

= .7827 so from the table the

Z that gives a value of .7827

= .785

So converting Z to the un-normalised value

Q = Z * 6 + 55 = 59.71 = 60

.785

.7827

Product Cycling

• HW#2 q9, see archived TA session.

• The M&M problem is nothing new. – Demand = throughput – But easier way

• From lecture slides: insights for Product Cycling– < Tmin? Cant be done because MINIMUM time required to

meet demand– > Tmin? Idle time, Tmin is all that’s required.

SCM

• Learnings from the beer game– Information transparency or else suffer the Bullwhip!– Single point inventory quantity decision– Decide qtty based on historic info not forecast.

More on Bullwhip

• Real Life: i2 a leading SCM product vendor removed a demand forecast module from their suite after some remarkable failures (e.g. NIKE)

• Why it happens?– Guesstimates– Local maximisation (transport dept reduces cost by dispatching

only full trucks – order batching)– Price promo – induces variability. But can be countered by

information transparency– Shortage Gaming

• Vendor-Managed Inventory

JIT

• We looked at Q, lead time, total cost, where

use the adjective

“Right”

= JIT

• PULL system

• No bullwhip