Integrated Forecasting, Markdown & Replenishment Framework

An Integrated Framework for Forecasting,
Markdown and Replenishment Optimization
Presented by Dr. Ulas Cakmak at the annual
INFORMS conference
October 9, 2013

1

©2013. Predictix. All Rights Reserved.

Background on this content
!   This content was first presented in October 2013 by Dr. Ulas
Cakmak, senior scientist at Predictix, at the annual conference of
The Institute for Operations Research and the Management
Sciences (INFORMS), which is the largest society in the world for
professionals in operations research, management science, and
business analytics.
!   Ron Menich, EVP and chief scientist at Predictix, said: “We're proud
of the work Ulas is presenting, which represents the efforts of many
members of the Predictix science team and our strategic partner
LogicBlox. This innovative retail physics modeling—designed by
optimization expert Mokhtar Bazaraa and developed by Emir Pasalic
and Zografoula Vagena—helps ensure that Predictix incorporates
the latest scientific breakthroughs into our retail solution offerings."

2


Agenda
■ 
■ 
■ 
■ 

Problem Overview
Integrated Framework & Benefits
Forecasting
Markdown Optimization (MDO)
»  Problem Description
»  Optimization Model
»  Illustrative Example

■  Replenishment Optimization
»  Post Optimization Processes

3


■ 
■ 
■ 
■ 

Problem Overview
Forecasting


4


Problem Overview

!   Project for a retailer selling furniture and home goods
»  Forecasting; for procurement and as input to other decision
processes
»  Markdown optimization; for merchandising department and also
input to replenishment process
»  Replenishment optimization; end-to-end supply chain
optimization (flow of goods from vendor to store)

!   In many companies these functions are performed within
isolated departments; these groups may even use their
own forecasts
!   Our client wanted a unified and integrated solution

5


Problem Overview

!   Dimensions of the business
»  Online Sales and Physical Stores (about 120, mostly in the
USA), Franchise and Outlet stores
»  More than 140k SKUs grouped into 130 Classes
»  Only 8-10k active SKUs; high number of new and discontinued
products
»  3 main DCs and several specialized mini-DCs
»  More than 100 vendors

!   Considered as a whole the problem size is large, we
separate the problem into reasonable size sub-problems
and utilize parallelization

6


■ 
■ 
■ 
■ 

Problem Overview
Forecasting


7


Integrated Framework

Forecas(ng

Engine

Replenishment

Engine

Markdown

Engine

Data
Staging

Client

8


Benefits

!   Forecasting accuracy improved by more than 5% for
Stores, more than 10% for Online Sales

!   Markdown solution that properly exhausts all possible
actions and picks the optimal one, and updates the plan
dynamically

!   Replenishment solution promises significant reductions
in inventory and provides various auxiliary information
for other business units

9


■ 
■ 
■ 
■ 

Problem Overview
Forecasting


10


Forecasting Process

3
Years
of
Sales
&

Promo
History

Classiﬁca9on

Forecast
Type

Mul9-‐level

Regression

Compute
Trend

and
Level

(Smoothing)

Forecasts

11


Compute

Forecasts

Promo
and
Seasonality

Coeﬃcients

Base
Sales
Level
and

Trend

Forecasting Extensions

!   For Markdown Optimization
»  Compute markdown discount elasticity estimates
»  Produce a separate set of baseline forecasts

!   For Replenishment Optimization
»  Compute daily forecasts
»  Compute safety stock requirements at store and DC level (this
task includes calculating forecast error at different aggregation
levels)

12


■ 
■ 
■ 
■ 

Problem Overview
Forecasting


13


Markdown Optimization Problem Description

!   Client provides
»  Product and Store groupings; SKU-Store combinations that
should share a Markdown plan
»  Applicable discount percentages (can be different per SKU and
Store groupings)
»  Earliest start date and projected out date
»  Store-DC pairing per SKU
»  Starting Inventory at DCs and Stores per SKU
»  Regular price and salvage value

!   Forecasting Engine provides
»  Baseline forecasts
»  Markdown discount elasticity estimates

14



!   A markdown plan is a selection of non-decreasing
discounts to be applied at specific time periods over the
planning horizon

!   Decision variables are:
»  Binary indicator for a percentage of discount applied at time t for
SKU group p at Store group l
»  Inventory and sales at SKU-Store-Week level

!   The objective is to select the optimal allocation from the
DCs to all locations and to determine the markdown plan
that maximizes revenue

15


Weeks

16

6

DC
1

2

3

4

5

6

DC
2

2

3

4

5

6

DC
3

1

2

3

4

5

6

Store
1

1

2

3

4

5

6

Store
2

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

Store
m

2

3

4

5

6

7

8

9

Outlet
1

1

2

3

4

5

6

7

8

9

Outlet
2

.

.

.

.

Online
sales

5

Regular
stores

Ini9al
store
inventories


4

1

DC3

3

1

DC2

2

1

DC1

1

Outlets

Alloca9ons

from
DCs

Markdown Optimization Business Constraints

!   Markdown Optimization model supports the following
business constraints
»  Discounts must be non-decreasing and belong to the applicable
set
»  Number of different discount percentages utilized is limited
»  First discount selected cannot be more than a threshold
»  There are periods where there cannot be a change in discount
(blackout weeks)
»  A selected discount should be effective for at least a minimum
number of weeks
»  Outlet stores have a minimum discount threshold and cannot
start selling before other locations hit that threshold

17


Markdown Optimization Process

!   The data is split based on product groupings
!   MDO Engine preprocess the data to build demand
estimates for each markdown scenario

»  Baseline forecasts are multiplied with the corresponding discount
multiplier for each period
»  The forecasts are scaled to obtain integer demand values

!   Build and solve MIP
!   The results and recommended markdown plan is

presented to the user who has the option to approve or
modify the plan (only the first discount step, the rest is
re-optimized dynamically)
!   There is also an on-demand re-optimizer per SKU

18


Illustrative Results – Optimal DC stock allocation

Initial DC Inventory

323

17

DC1
306

153

11

DC2
142

299

15

DC3
284

19


Outlet store 1
Store group 1

Outlet store 2

Store group 2

Outlet store 3

Store group 3

Illustrative Results – Optimal Markdown Plan
Ini9al
regular
store

inventory
is
137

Store
Group
1

323

DC1

12/30

1/6

1/13
1/20
1/27

2/3

2/10
2/17
2/24

3/3

0.0

0.0

0.2

0.3

0.3

0.4

306

153

0.2

0.3

0.3

0.4

17

DC2
11

Ini9al
outlet
store

inventory
is
0

Outlet
stores

299

DC3

20


2/3

15

2/10
2/17
2/24
3/3

3/10

0.3

0.3

0.4

0.4

0.4

0.4

Illustrative Results – Optimal Solution at Store Level

2

12/30

0.0

1/6

14

0.0

1/13

13

0.2

1/20

12

0.2

1/27

11

0.3

2/3

9

0.3

7

0.3

2/24

2/17

2/10

5

0.3

3

0.4

13

1

$18.22

1

$18.22

1

$14.58

1

$14.58

Revenue
from
sales
=
$200.43

Revenue
from
salvage
products
=
$0.00

Total
revenue
=
$200.43

21


2

$25.51

2

$25.51

2

$25.51

2

$25.51

3

$32.80

Ini9al
store
inventory
=
2

Allocated
inventory
from
DC1
=
13

Total
star9ng
inventory
=
15

0

■ 
■ 
■ 
■ 

Problem Overview
Forecasting


22


Replenishment Optimization Problem Description

!   Client provides
»  Vendor-SKU-DC triplets, ordering DCs and servicing DCs
»  Review period, transportation lanes, capacities, lead-times,
processing times and costs for the triplets
»  Same information for DC-SKU-Store triplets
»  Inventory related costs, for both DC and Stores
»  Display quantities at Stores, franchise reserves at DCs
»  Initial conditions; actual inventory, placed orders, in-transit
inventory

!   Forecasting Engine provides
»  Daily forecasts for the next 66 weeks
»  Safety stock quantities for DCs and Stores

23


Supply Chain Network
Vendor
1

Vendor
2

Vendor
3

Ordering

DC
1

Ordering

DC
2

DC
1

Store
1

Store
4

Store
6

Store
2

Vendor
4

DC
2

Store
5

Store
7

Store
3

24


DC
3

Store
8

Replenishment Optimization Model

!   Vendors, DCs and Stores are represented as nodes at
given time points (days)

!   Arcs with appropriate direction and constraints tie nodes
to each other

!   In many cases, there are copies of the same node
representing the status before and after events (arrivals,
shipments, allocations, …)

25


Supply Chain Network – Nodes and Arcs
Vendor

W
Order

Ordering

DC

W

Shipment

T
Order

Servicing

DC

T

Inventory

W

Inventory

W
Order

Store

W

H
Shipment

H

Shipment

Online
demand

forecast

H

(Sellable)
Inventory

26


F

F

Store
demand

forecast

S

Replenishment Optimization

!   Objective is to maximize profit; revenue from sales minus
all Supply Chain related costs

!   Decision variables are flows on arcs representing orders,
shipments and inventory carry overs

!   Modeled as a classical network optimization problem;
hence main constraints are balancing of flows in and out
of nodes
!   Additional complexity due to business requirements

27


Replenishment Optimization Business Requirements

!   Some of the main business requirements are
»  DC nodes serve as cross-dock
»  Prioritization of inventory, in case of shortage there is an order
for fulfilling different types of inventory
»  Minimum vendor order quantities and container constraints for
global vendors
»  Part of potential lost sales are converted to actual demand

28


Replenishment Optimization

!   Estimated number of variables just for inventory is
»  10,000*100*450 ~ 450 million variables

!   Modeling it as one large MIP is not practical => split data
per vendor to use parallelization

!   We utilize Gurobi Solver with BloxOptimize package
(LogiQL)

!   Issues with splitting
»  Consolidating multiple vendor orders
»  Consolidating store orders

29


Post Optimization Processes

!   We utilize the following processes after the optimization
»  A post-processing step for adjusting shipments according to
given multiples
»  The aforementioned process alters the solution, hence
adjustments may be necessary to re-balance the flow equations
»  DC to Store shipment consolidation across vendors

30


Illustrative Results – Total Inventory Movement
40000

Store inventory

35000

DC inventory

30000

Inventory in motion

25000

20000

15000

10000

5000

0
4/3/12

31

5/3/12

6/3/12


7/3/12

8/3/12

9/3/12

10/3/12

11/3/12

12/3/12

1/3/13

2/3/13

3/3/13

Illustrative Results – Store Inventory Movement
10

Inventory

9

Display minimum

8

Safety stock

7

6
5
4
3
2
1
0
4/2/12

32

5/2/12

6/2/12


7/2/12

8/2/12

9/2/12

10/2/12

11/2/12

12/2/12

1/2/13

2/2/13

3/2/13

4/2/13

Q&A

33


Integrated Forecasting, Markdown & Replenishment Framework

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