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. . og s cs an s r u on ys ems

Dynamic Economic Lot Sizing Model

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Outline{ The Need for DELS

{ DELS without capacity constraints:z

po cy;

z Shortest path algorithm.{ DELS with capacity constraints:

z apac y cons ra ne pro uc on sequences;z Shortest path algorithm.

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Strategic Sourcing Inputs

Transportationcosts, rules forshipping out of

territory overflowSupplier

WH cost, capacity,safety stock targets,and current on hand

territory overflowfacilities

constraints, costs,fixed orders, etc

and current on-handposition

Mfg constraints, costs, runrules, fixed production

schedules set ups tooling etc

Current demandforecast by forecast

Product info and

BOM

3

schedules, set-ups, tooling, etc.by time period

y

location by time periodBOM

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Key Drivers in Sourcing Decisions

Freight costs forexisting andotential lanes

Availability at differenttimes of the year

Frei ht Production

Raw Materials

Duties for different

customer countries

& Duties Capabilities

LocationsMfg

SourcingDecisions

Suppliers Plants Warehouses Customers

Products Demand

Demand by productby customer

Product attributes

Purchase prices

What can be made

where, tooling, etc.g spee s

capacities

Setups, batches, yieldloss, etc.

Production costs

variable overheads

Economies of scale

Special rules and Monthly or weeklyforecasts

constraints

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Strategic Sourcing Outputs

Total volume andcost on each lanein each time periodAmount purchased

from each supplier

Throughput by WH byproduct by time period,

ending inventory byfrom each supplier,where and when itshould be shipped

ending inventory byperiod, costs by period

What products should bemade where, made when,

Total landed cost bytime period by

Strategic sourcing minimizesStrategic sourcing minimizestotal supply chain coststotal supply chain costs

5

, ,

and shipped to where

p y

customer/productsubject to all constraintssubject to all constraints

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ICI LOCATIONSDase Study: Strategic Sourcing

PR

6

Gulf of Mexico

Atlantic OceanPacific

Ocean

0

0

800 km

500 km

CA 2

CA 1

TX 2

TX 1

GA

OH

PA

PR

Mexico

Canada

Image by MIT OpenCourseWare.

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Background

Sold product throughout US to variety of customersz Through their own storesz Through retailers

Wide variety of productz 4,000 different SKUsz 1500 different base products (could be labeled differently)z

Many low-volume products

Batch Manufacturingz anu ac ur ng one n a c , so ere s gn can econom es o sca e a

single product is made in one location

z Each plant had many different processesz Many plants can produce the same problem

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Business Problems

Are products being made in the right location? Should plants produce a lot of products to serve the local

minimize production costs?

Should we close the high cost plant? ow s ou we manage a t e ow vo ume s

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Key Driver - Data Collection

Raw Material CostsInvoice cost

Variable Mfg. CostsVariable Mfg costs by process/by siteInvoice cost

Freight cost% shrinkageDifficulty - Medium

Variable Mfg. costs by process/by siteDifficulty - High

Technical Capability Manufacturing Capabil ity

Key Drivers

p yProduct FamilyDifficulty - High

Manufacturing Capabil ity

Demonstrated CapacityDifficulty - High

Interplant Freight CostsYield Loss Interplant Freight CostsAverage run rates in from site to siteDifficulty - Low

Yield Loss% of lost volume per 100 unitsSite SpecificDifficulty - Low

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Process Change

Existing Process New Process

Sourcing decisions currently made in isolation Decisions are made for small groups of

products

Sourcing decisions made in context of entire supplychain

Decisions are made considering the entiresupply chain

Excel is the primary decision tool Many drawbacks Excel does not capture the many different

trade-offs that exist in the supply chain E l l l l t th t f i

supply chain

Sourcing decisions are made using Master Planning Optimization model provides global

optimization capability Excel can only calculate the costs for a given

decision; it cannot make decisions

No formal data collection process Data not collected systematically across the

Model automatically updates for on-going decisionmaking Developed process for automatically updating

and maintaining the model so the decisions Data not collected systematically across thesupply chain to make these decisions

and maintaining the model so the decisionscan be made on an on-going basis

Built 2 Models1. Model for all the base products2 Model for low volume SKUs

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2. Model for low volume SKU s

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z

Results

Savingsz en e mme a e ow vo ume movesz Identified $4-$10M in savings for moving base productsz

Identified negotiation opportunities for raw materials

Detailsz Moved 20% more volume into the hi h cost lantz 80% of savings were from 10% of the production moves

z Implementation done in phases, starting with the easiest and highestvalue changes first

- , -implement

z Expect to adjust plans as you go forward

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More Volume to High Cost Plant

Baselinez ro uc : o e vo ume, o e var a e cosz Product B: 80% of the volume, 55% of the variable cost

p m za onz Product A: 5% of the volume, 15% of the variable costz Product B: 95% of the volume, 85% of the variable cost

Net change was an increase in total volume

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Case Study 3: Optimizing S&OP at PBG

M k S ll D li S iMake Sell Deliver Service

PBG Operates57 Plants in theU.S. and 103Plants Worldwide

Over 125 Million8 oz. Servingsare Enjoyed byPepsi Customers

240,000 Miles areLogged Every Day toMeet the Needs ofOur Customers

StrongCustomer ServiceCulture Identifiedas Customerp

Each Day!Our Customers

Connect

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PBG Structure - The PBG Territory

{PBG accounts for 58% of the domestic Pepsi Volumethe other 42% is

{ enerated throu h a network of 96 Bottlers

{Each BUs act independently and meet local needs

Southeast

Atlantic

Central

Great West

WestAK

CA

NV

OR

WA

ID

MT ND

SD

MN

WI

IL

MI

IN

KY

TN

ALGA

ME

NH

VT

NY

PA

VA

NC

WV

OH

SC

CT

MA

RI

NJ

DE

MD

FL

MS

IA

MO

AR

LA

NE

KS

OK

TX

WY

UT

AZ NM

CO

Central

Atlantic

Southeast

Great West

West


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Challenges and Objective

Problem: How should the firm source its products to

Ob ective: Determine where roducts should be roducedto reduce overall supply chain costs and meet all relevantbusiness constraints

15

Copyright 2008 D.-

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Optimization Basics

Tradeoffs associated with optimizing a network

Copyright 2008 D.Simchi-Levi

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Would like to maximize thenumber of products produced at alocation to minimize transportation

costs

Hi h tHigh costplants may be

close to keymarkets

Would like to minimize the number ofproducts produced at a location tomaximize product run size

CapacityConstraints


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Optimization Scenario

Optimized Central BU model:

Total Cost

Category Baseline Optimized Difference % savingsMFG Cost 2,610,361.00$ 2,596,039.00$ 14,322.00$ 0.6%Trans Cost 934,920.00$ 857,829.00$ 77,091.00$ 9.0%Total Cost 3 545 281 00$ 3 453 868 00$ 91 413 00$ 2 6%Total Cost 3,545,281.00$ 3,453,868.00$ 91,413.00$ 2.6%

Production Breakdown

Plant Baseline Optimized % changeBurnsville 2 444 277 00 2 457 688 00 1%

Units Produced

Burnsville 2,444,277.00 2,457,688.00 1%Howell 3,509,708.00 3,828,727.50 8%Detroit 2,637,253.00 2,304,822.50 -14%

Copyright 2008 D. Simchi-Levi 17

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Multi Stage Approach

Stage 1-2: 2005-6POCPOC 6 months

2 Business Units

Stage 3: 2007 AnnualOperating Plan (AOP)

Model USA Full year model

St 4 Q1 Q4 2007 Stage 4: Q1 Q4 2007 Quarter based model Package / Category

Copyright 2008 D. Simchi-Levi 18


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- -

Impact

Creation of regular meetings bringing together Supplychain, Transport, Finance, Sales and Manufacturingfunctions to discuss sourcing and pre-build strategies

Reduction in raw material and supplies inventory from $201 A 2 percentage point decline in in growth of transport miles An additional 12.3 million cases available to be sold due to

reduction in warehouse out-of-stock levels

- -,

effectively added one and a half production lines worth of capacity to the firms

supply chain without any capital expenditure.

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{ DELS without capacity constraints:z po cy;z Shortest path algorithm.

{DELS with capacity constraints:z apac y cons ra ne pro uc on sequences;z Shortest path algorithm.

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Assumptions{ Finite horizon: T periods;

t, = ,,

{ Linear ordering cost: Kt(yt)+ctyt ;{ Linear holding cost: ht ;{ Inventor level at the end of eriod t I { No shortage;

{ Sequence of Events: Review, Place Order,r er rr ves, eman s ea ze

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Wagner-Whitin (W-W) Model

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Zero Inventory Ordering Policy (ZIO){ Any optimal policy is a ZIO policy, that is,

t-1 t= , = ,, .

{ Time independent costs: c, h.t, t.

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-

ZIO PolicyExtreme Point { Definition: Given a polyhedron P, A vectorx is

vectorsy,z in P, and a scalar,01, such that= - .

problem of minimizingcx over a polyhedron P,

- ,

there exists an extreme point which is optimal.

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Min-Cost Flow ProblemS

21 t TT-1

It-1

dTd1 dt

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Implication of ZIO{ Each order covers exactly the demands

.

{ Order times sufficient to decide on orderquantities.

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Network Representation

i1 T+1t

j1 j1 j1K+c d+ h d 1i

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Shortest Path Algorithm

{

{ Com lexit of the shortest ath al orithm: O T2 .{ With a sophisticated algorithm, O(T lnT).

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{ DELS without capacity constraints;z po cy;z Shortest path algorithm.

{DELS with capacity constraints;z apac y cons ra ne pro uc on sequences;z Shortest path algorithm.

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DELS with Capacity Constraints

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DELS model with capacity: description

21 t

y1C1 yT

TytCt

TT-1

d

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Feasibility of DELS with capacity

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Inventory Decomposition Property

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Structure of Optimal Policy

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Production Sequence Sij

yi+1

Ci+1 yt

Ct yj

j

i+2i+1 t jj-1

d -

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Network Representation

+

lij ?36

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Calculation of Link Costs { Time-dependent capacities: difficult;

{ Time-independent capacities: Ct=C.

{ Let m and f such that mC+f =di+1++jdt,,

define Yk =tk

=i+1yt, i

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00 0

C C

C+f

Calculation of Link CostsYi+1=yi+1 Yi+2=yi+1 +yi+2 Yj=yi+1 ++yj

0

C

C+f

mC+f38

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Complexity: equal capacity{ Computing link cost lij: shortest path algorithm:O((j-i)2).{ Determ n ng t e opt ma pro uct on sequence etween

all pairs of periods: O(T2)O(T2) = O(T4).{ Shortest path algorithm on the whole network : O(T2).{ omp ex y or n ng an op ma so u on or

model with equal capacity: O(T4) + O(T2) = O(T4).

{ With a sophisticated algorithm: O(T 3) .

Not applicable to problems with time-dependent capacity{

constraints, why? 39

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Tree-Search Method

yT+1=0

yT=0 yT= min{CT, dT}

yT-1=0 yT= min{CT-1, dT-1+dT} yT-1=0 yT= min{CT-1, dT-1+dT-yT}

- .{ Not ol nomial.

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ZICO Policy{ Theorem: Any optimal policy is a ZICO policy,

t-1 t- t t = , = ,, .

{Corollary: If (y1, y2, yT) represents an optimalsolution, and t= max{j:y >0}, then

yt = min{Ct, dt++dT}.

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ESD.273J / 1.270J Logistics and Supply Chain ManagementFall 2009

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MITESD_273JF09_lec04