Module 4

1
Operations Management Performance Modeling

• 1 Operations Strategy
• 2 Process Analysis
• 3 Lean Operations
• 4 Supply Chain Management
• Class 5a Inventories Economies of Scale
• Class 5b Dealing with Uncertainty role of
  Centralization
• The impact of uncertainty safety stocks
• Centralization pooling benefits
• 5 Capacity Management in Services
• 6 Total Quality Management
• 7 Business Process Reengineering

2
South Face warehousesService levels inventory
management

• The South Face has 4 warehouses which experience
  a demand that is not steady from one week to the
  next. Weekly demand is in fact normally
  distributed with a mean of 5,000 and a standard
  deviation of 1,500. SFs order lead time is two
  weeks. Fixed order costs are 2,000/order and it
  costs 50 to hold one jacket in inventory during
  one year.
• If SF uses the ordering policy discussed last
  class, what will the probability of running out
  of stock in a given cycle be?
• SF would like this probability to be no higher
  than 5 for customer satisfaction. What ordering
  policy would you recommend for SF?

3
Safety Stocks
Inventory on hand I(t)
Q
Q
order
order
order
ROP
mean demand during supply lead time m R L
ss
safety stock ss
0
Time t
L
4
Hedge against demand uncertainty with safety
stocks

• L Supply lead time,
• DN(R, sR) Demand per unit time is normally
  distributed
• with mean R and standard deviation sR ,
• Cycle service level P(no stock out)
• P(demand during lead time lt ROP)
• P(N(0,1) lt z (ROP- m)/sLTD)
• F(z) use tables to find z
• Safety stock ss z sLTD
• Reorder point ROP RL ss

5
The standard normal distribution F(z)

• Transform X N(m,s) to z N(0,1)
• z (X - m) / s.
• F(z) Prob( N(0,1) lt z)
• Transform back, knowing z
• X m zs.

6
Determining the required Safety Stock at each
warehouse of the South Face

• DATA
• R 5,000 jackets/ week sR 1,500 jackets/
  week
• H 50 / jacket, year
• S 2,000 / order L 2 weeks
• QUESTION What should safety stock be to insure a
  desired cycle service level of 95?
• ANSWER
• 1. Determine s lead time demand
• 2. Required of standard deviations z
• 3. Answer Safety stock

7
Comprehensive Financial EvaluationWarehouse
Inventory Costs of the South Face

• 1. Cycle Stock (Economies of Scale)
• 1.1 Optimal order quantity
• 1.2 of orders/year
• 1.3 Annual ordering cost per warehouse
  114,017.
• 1.4 Annual cycle stock holding cost/w.h.
  114,017.
• 2. Safety Stock (Uncertainty hedge)
• 2.1 Safety stock per warehouse 3,500
• 2.2 Annual safety stock holding cost/w.h.
  174,982.
• 3. Total Costs for 4 warehouses 4 (114,017
  114,017 174,982)
• 1,612,069.

8
Learning Objectives safety stocks

• Safety stock increases (decreases) with an
  increase (decrease) in
• demand variability or forecast error,
• delivery lead time for the same level of service,
• delivery lead time variability for the same level
  of service.

9
The Effect of Centralization

• Weekly demand per warehouse 5,000 jackets/
  week
• with standard deviation 1,500 / week
• H 50 / jacket, year
• S 20,000 / order
• Supply lead time L 2 weeks
• Desired cycle service level F(z) 95.
• The South Face decides to merge all of its
  warehouses.
• m
• s

10
The Effect of Pooling pairs of warehouses

• R 10,000 widgets/week s Sqrt(2) 4,000
  5,657 widgets/week
• Optimal order quantity Q per 2-warehouse
  20,396 widgets/order.
• Annual ordering cost per 2-warehouse 50,990.
• s lead time demand 6,928 widgets.
• Safety stock per 2-warehouse 11,432 widgets.
• Reorder point 26,432 widgets.
• Average inventory 2-warehouse 21,630
  widgets.
• Average cycle time 2.16 weeks.
• Annual holding cost per 2-warehouse 108,150.
• Total average inventory across two 2-warehouses
  43,260 widgets.
• Total annual cost across two 2-warehouses
  318,280.

11
Comprehensive Financial Evaluation of
centralizing Four Warehouses into One

• R 20,000 jackets/week sR Sqrt(4) 1,500
  3,000 jackets/week
• 1. Cycle Stock
• Optimal order quantity Q consolidated warehouse
  9,121 jackets/order.
• Annual ordering cost 228,035.
• 2. Safety Stock
• s lead time demand 4,242 jackets.
• Safety stock consolidated warehouse 7,000
  jackets.
• Reorder point 47,000 jackets.
• Average inventory consolidated warehouse
  11,560 jackets.
• Average flow time 0.578 weeks.
• Annual holding cost 578,000.
• Total annual cost consolidated warehouse
  806,034.

12
Supply Chain of IBM PC Europe

• Build to Plan (BTP) vs.
• Late Customization (LC) vs.
• Build to Order (BTO) vs.
• Exploiting component commonality(FLEX)
• Physical Pooling of transhipment points

Source Feigin, An, Connors and Crawford, ORMS
Today April 96
13
Learning Objectives centralization/pooling

• Different methods to achieve pooling
  efficiencies
• Physical centralization
• Information centralization
• Specialization
• Raw material commonality (postponement/late
  customization)
• Cost savings are sqrt( of locations pooled).

14
Postponement Commonality HP Laserjet
15
MidTerm Results
Median 85, Stdev 10, Max 99
25
20
15
Frequency
10
5
0
60
69
79
89
99