dynamic lot sizing 35e00100 service operations and strategy #6 fall 2015

Dynamic Lot Sizing

35E00100 Service Operations and Strategy#6 Fall 2015

35E00100 Service Operations and Strategy #6 Aalto/BIZ Logistics2

Topics

Demand management Lot sizing policies Order management Key points

Useful material: Hopp, W. & Spearman, M. (2000), Factory Physics, Chapter 2.1-2.4 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


Demand management is a part of the MPC system!

Productionplanning

Demandmanagement

Resourceplanning

Masterproductionscheduling

Front end

Marketplace (customers and

other demand sources)

Vollmann et al. 1997, 313

MPC boundary

EngineBack end


Need for capacity management depends on the market situation

Define production plan rates

Business plan

Sales forecasts

Orders

FGI and Backlog

Master schedule rough cut

Approvals

Master schedule

Vollmann et al. 1997


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


Lot Sizing Schemes


Week 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30

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?

Example 1


e.g. Hopp and Spearman 2000, 125

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


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

* 2ADQ

h


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.


* 2AT

hD


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



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

* 1

1

T

j

OMT D j TBO T T

T* = largest integer less than or equal to TBO

K = period currently under considerationrj = requirement/demand for period j

e.g. Vollman et al. 1997, 445-446

1

1T

jj

j r OMT

( 1) jh j r A


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

.

.

1

)1(r

AC

21

2)2(rr

hrAC

j

j

rrr

hrjhrhrAjC

...

)1(...2)(

21

32

e.g. Nahmias 2001, 369-370


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

AC )1(

2)2( 2

hrAC

3

2)3( 32

hrhrAC

j

hrjhrhrAjC j

)1(...2)( 32

e.g. Nahmias 2001, 368-369


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 43 5



Week 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30

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?

Example 1


1 2 3 4 5 6 7 8 9 10Requirements 22 34 32 12 8 44 54 16 76 30 Cost

22 34 32 12 8 44 54 16 76 30 2 00064 0 64 0 0 64 64 0 64 64 2 30556 0 44 0 52 0 70 0 106 0 1 44256 0 52 0 0 98 0 92 0 30 1 62456 0 52 0 0 98 0 16 106 0 1 47556 0 44 0 106 0 0 92 0 30 1 89156 0 52 0 0 114 0 0 106 0 1 37956 0 52 0 0 44 70 0 106 0 1 352

Week

EOQLFL

W-W

POQPPBMOMLUCS-M

Costs of the Different Lot Sizing Policies Compared

Example 1


Ranking of the Policies

1. Wagner-Whitin (W-W) 1352

2. Silver-Meal (S-M) 1379

3. Periodic Order Quantity (POQ) 1442

4. McLaren's Order Moment (MOM) 1475

5. Part Period Balancing (PPB) 1624

6. Least Unit Cost (LUC) 1891

7. Lot-for-Lot (LFL) 2000

8. Economic Order Quantity (EOQ) 2305

Example 1


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


Elements of Marketing Planning

Capacity

CustomersOrders

Sche

dulin

g

Forecasting

Account Selection


Manufacturing-Marketing Collaboration

Problem area Marketing complaints Manufacturing complaints

Capacity planning and long-range sales forecasting

Insufficient capacity Lack of accurate long-range sales forecasts

Production scheduling and short-range sales forecasting

Excessive lead times Unrealistic customer commitments and mercurial short-range sales-forecasts

Delivery and physical distribution Insufficient inventory Excessive inventory requirements

Quality assurance Insufficient quality at excessive cost Too many options offered with insufficient customer interest

Breadth of product line Insufficient product variety to satisfy customer demand

Excessive product variety necessitating short, uneconomical production runs

Cost control Excessive costs which hamper competitiveness

Unrealistic requirements on quality, delivery time, product variety and response to change

New product introduction New products are important Unnecessary design changes are expensive

Adjunct services e.g. spare parts inventory support, installation and repair.

Field service costs are excessive Products should not be used in ways for which they were not designed

Shapiro 1977, 105


Why Orders Fall through the Cracks?

Shapiro et al. 1992, 105


Key Points

Lot sizing policies 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


Abbreviations Used

EOQ = economic order quantity FOP = fixed order periodLUC = least unit costMOM = McLaren’s order momentMRP = material requirements planningOMT = order moment targetPPB = part period balancingPOQ = periodic order quantity S-M = Silver-Meal heuristicTBO = time between ordersW-W = Wagner-Whitin heuristic

dynamic lot sizing 35e00100 service operations and strategy #6 fall 2015

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