1. 35E00100 Service Operations and Strategy #6 Fall 2015
Dynamic Lot Sizing
35E00100 Service Operations and Strategy
#6 Fall 2015

2. Topics Demand management Lot sizing policies Order management
Key points
Useful material:
Hopp, W. & Spearman, M. (2000), Factory Physics, Chapter and 3.1.6
Nahmias, S. (2002) “Alternative Lot Sizing Schemes” Ch 7.2 in Production and Operations Analysis
Vollmann, T., W. Berry & C. Whybark (1997) “McLaren’s Order Moment” in Manufacturing Planning and Control Systems

3. Demand management is a part of the MPC system!
MPC boundary
Resource
planning
Production
planning
Demand
management
Marketplace
(customers and
other demand sources)
Master
production
scheduling
Front end
Engine
Back end
Vollmann et al. 1997, 313

4. Need for capacity management depends on the market situation
Sales forecasts
FGI and Backlog
Define production plan rates
Business plan
Orders
Master schedule rough cut
Approvals
Master schedule
Vollmann et al. 1997

5. Capacity and Demand Control Tools
Ways to manage capacity
“Stretch” production capacity
Speed up the process
Schedule downtime (e.g. maintenance) during periods of low demand
Squeeze more people in or rent / share extra facilities equipment
Workforce management
Employ part-timers, seasonal workers, flexible work force
Cross-train employees
Prepare intelligent schedules for both workers and equipment
Strategies for managing demand
Organize better
Avoid needless division of work (finance, customer service, transport planning, etc.)
Design rules and procedures for providing flexibility
Manage service levels
Adjust delivery promises continuously
Utilize different pricing methods
Communicate capabilities

6. Lot Sizing Schemes

7. Comparison of Lot Sizing Policies
Example 1
Comparison of Lot Sizing Policies
A component used in a manufacturing facility is ordered from an outside supplier. Because the component is used in a variety of end products, the demand is high.
Estimated demand (in thousands) over the next 10 weeks is:
Cost per component is 0.65.
The interest rate used to compute holding costs is 0.5 % per week.
The fixed ordering cost is estimated to be 200.
What ordering policy you recommend and why?
Which method would result in the lowest-cost policy for this problem?

8. Lot for Lot Ordering Basic principle of LFL
Production quantity = time-phased net requirements
No inventory carried from one period to another
Normal assumption in MRP examples
For convenience and ease of use
Rarely the optimal production rule
e.g. Hopp and Spearman 2000, 125

9. Economic Order Quantity (EOQ)
The principle
Production quantity = EOQ quantity
Information required
Fixed setup/ ordering cost A
Holding cost h
Demand rate D
Shortcomings are due to the assumptions of the modell
Instantaneous production
Immediate delivery
Deterministic and constant demand over time
Fixed setup cost
Products can be analyzed individually
e.g. Hopp and Spearman 2000, 49-56

10. Periodic Order Quantity (POQ)
The principle
Calculate the time between orders (TBO) using EOQ formula TBO = EOQ / D
TBO (rounded to closest integer) shows for how many periods products should be produced or ordered.
Fixed order period (FOP) is a similar method.
Periods with no demand are skipped.
e.g. Hopp and Spearman 2000,

11. Part Period Balancing (PPB)
The principle
Definition of a part-period
[# of parts in a lot] * [# of period they are carried in inventory]
Combines the procedure of Wagner-Whitin with the mechanics of the EOQ
Set the order horizon equal to the number of periods that most closely matches the total holding cost with the set-up cost over that period
Steps of the procedure
Calculate holding costs per different number of periods
Compare when holding cost is closest to set-up costs
Stop and repeat
e.g. Hopp and Spearman 2000,

12. McLaren’s Order Moment (MOM)
The principle
Evaluates the set-up cost for an integral number of future periods
Applies part period (=an unit of inventory carried for one period) accumulation principle directly
Lot size is determined by matching the number of accumulated part periods to the number that would be incurred if an order for an EOQ were placed under conditions of constant demand
Calculate order moment target (OMT)
Two tests are used
Tentatively order covers the requirements of periods (r) for which
Once accumulated parts reach or exceed the OMT, test if one more period should be included
T* = largest integer less than or equal to TBO
K = period currently under consideration
rj = requirement/demand for period j
e.g. Vollman et al. 1997,

13. Least Unit Cost (LUC) The principle
Choose order horizon that minimizes the cost per unit of demand
Define C(T) as the average holding and set-up cost per unit if the current order spans the next T periods
Let (r1,…,rj) be the requirements over the j-period horizon .
e.g. Nahmias 2001,

14. Silver-Meal Heuristic (S-M)
The principle
Minimize average cost per period over T-period order horizon
Define C(T) as the average holding and set-up cost per period if the current order spans the next T periods
If we place an order in period 1, for…
r1:
r2:
r3:
In general rn:
Once Cj > Cj-1 stop, and set Q1 = r1 + r2 +…+ rj-1 and begin process again starting at period j
e.g. Nahmias 2001,

15. Wagner-Whitin Heuristic
The principle (one-way network, path enumeration)
Every path through the network = a specific exact requirement policy
Assign a value to each arc in the network
Determine minimum cost production schedule = shortest path through the network
Heuristic that determines the optimal lot size
Based on dynamic programming and two lemmas
Lemma 1: “Exact requirement policy”
An optimal policy has the property that each value of order quantities (Q) is exactly a sum of a set of future demands
Lemma 2: If optimal to produce something during period t, then it-1< rt
No production / ordering during period t, if enough inventory to satisfy the demand 1 2 4 3 5
e.g. Hopp and Spearman 2000, 59-64

16. Comparison of Lot Sizing Policies
Example 1
Comparison of Lot Sizing Policies
A component used in a manufacturing facility is ordered from an outside supplier. Because the component is used in a variety of end products, the demand is high.
Estimated demand (in thousands) over the next 10 weeks is:
Cost per component is 0.65.
The interest rate used to compute holding costs is 0.5 % per week.
The fixed ordering cost is estimated to be 200.
What ordering policy you recommend and why?
Which method would result in the lowest-cost policy for this problem?

17. Costs of the Different Lot Sizing Policies Compared
Example 1
Costs of the Different Lot Sizing Policies Compared

18. Ranking of the Policies
Example 1
Ranking of the Policies
Wagner-Whitin (W-W) 1352
Silver-Meal (S-M) 1379
Periodic Order Quantity (POQ) 1442
McLaren's Order Moment (MOM)
Part Period Balancing (PPB)
Least Unit Cost (LUC) 1891
Lot-for-Lot (LFL) 2000
Economic Order Quantity (EOQ) 2305

19. Differences in Lot Sizing Policies
Lot-for-lot
Cost estimation or calculation is not required
Least likely to result in capacity problems
Likely to cause high changeover costs (produced / ordered every period)
EOQ
A simple calculation technique
Likely to produce cost-wise inefficient solutions if demand is not stable
Wagner-Whitin
Gives the optimal solution for static problems at one level of the product structure
Under some other conditions the optimality is lost
Relatively much calculations required
S-M, LUC, PPB, MOM
Similar methods that give a reasonable compromise between the simple LFL scheduling and the W-W heuristic
PPB is easiest in terms of calculations
S-M seems to provide the most cost effective solutions on average, and it involves less work than the W-W heuristic

20. Elements of Marketing Planning
Capacity
Scheduling
Account Selection
Orders
Customers
Forecasting

21. Manufacturing-Marketing Collaboration
Shapiro 1977, 105

22. Why Orders Fall through the Cracks?
Shapiro et al. 1992, 105

23. Key Points Lot sizing policies Order management
Consider the trade-off between holding inventory and changeover
By adjusting setup costs, the planner can trade inventory for capacity
Simple methods are popular in practice
People prefer to understand the solution
Heuristics are good because those are relatively robust and intuitive
Costs versus responsiveness
Order management
Information sharing and incentive alignment important
Separate orders from customers

24. Abbreviations Used EOQ = economic order quantity
FOP = fixed order period
LUC = least unit cost
MOM = McLaren’s order moment
MRP = material requirements planning
OMT = order moment target
PPB = part period balancing
POQ = periodic order quantity
S-M = Silver-Meal heuristic
TBO = time between orders
W-W = Wagner-Whitin heuristic