Forecasting, Markdown and Replenishment Optimization: An Integrated Framework for

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

©2013. Predictix. All Rights Reserved. 1

October 9, 2013

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."


Agenda ■  Problem Overview ■  Integrated Framework & Benefits ■  Forecasting ■  Markdown Optimization (MDO)

»  Problem Description »  Optimization Model »  Illustrative Example

■  Replenishment Optimization »  Problem Description »  Optimization Model »  Post Optimization Processes


■  Problem Overview ■  Integrated Framework & Benefits ■  Forecasting ■  Markdown Optimization (MDO)




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


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


Integrated Framework


Forecas(ng Engine

Replenishment Engine

Markdown Engine

Client

Data Staging

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


Forecasting Process


3 Years of Sales & Promo History

Classifica9on

Mul9-‐level Regression

Compute Trend and Level

(Smoothing)

Compute Forecasts

Forecast Type

Promo and Seasonality Coefficients

Base Sales Level and Trend

Forecasts

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)


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



!   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




1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

7 8 9

7 8 9

DC 1

DC 2

DC 3

Store 1

Store 2

Store m

.

.

.

.

Outlet 1

Outlet 2

DC1

DC2

DC3

Online sales

Regular stores

Outlets

Alloca9ons from DCs Ini9al store inventories

Weeks

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


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


Illustrative Results – Optimal DC stock allocation


DC1

DC2

DC3

Outlet store 1

Store group 1

Outlet store 2

Store group 2

Outlet store 3

Store group 3

17

306

323

153 11

142

15

284

299

Initial DC Inventory

Illustrative Results – Optimal Markdown Plan


DC1

DC2

DC3

323

153

299

0.0 0.0 0.2 0.2 0.3 0.3 0.3 0.3 0.4 0.4

0.3 0.3 0.4 0.4 0.4 0.4

12/30 1/6 1/13 1/20 1/27 2/3 2/10 2/17 2/24 3/3

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

Store Group 1

Outlet stores

Ini9al outlet store inventory is 0

Ini9al regular store inventory is 137

17

11

15

306

Illustrative Results – Optimal Solution at Store Level


0.0 0.0 0.2 0.2 0.3 0.3 0.3 0.4

12/30 1/6 1/13 1/20 1/27 2/3 2/10 2/17 2/24

14 13 12 11 9 7 5 3 0

1 $18.22

1 $18.22

1 $14.58

1 $14.58

2 $25.51

2 $25.51

2 $25.51

2 $25.51

3 $32.80

Revenue from sales = $200.43 Revenue from salvage products = $0.00 Total revenue = $200.43

2

13

Ini9al store inventory = 2 Allocated inventory from DC1 = 13 Total star9ng inventory = 15

0.3

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


Supply Chain Network


Vendor 1 Vendor 2

Ordering DC 1

Ordering DC 2

DC 1 DC 2 DC 3

Store 1

Store 2

Store 3

Store 4

Store 5

Store 6

Store 7

Store 8

Vendor 3

Vendor 4

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, …)


Supply Chain Network – Nodes and Arcs


T H

W

Store

Servicing DC

Ordering DC

Vendor

W F

W

H F S

H

W

Store demand forecast

Shipment

Shipment

Shipment

W

T

Order

Order

Order

Online demand forecast

(Sellable) Inventory

Inventory

Inventory

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


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


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


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


Illustrative Results – Total Inventory Movement


0

5000

10000

15000

20000

25000

30000

35000

40000

4/3/12 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

Store inventory

DC inventory

Inventory in motion

Illustrative Results – Store Inventory Movement


0

1

2

3

4

5

6

7

8

9

10

4/2/12 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

Inventory

Display minimum

Safety stock

Q & A


Forecasting, Markdown and Replenishment Optimization: An Integrated Framework for

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