Evaluation of case-pack sizes in grocery retailing using a Markov Chain approach Department of...

Evaluation of case-pack sizes in grocery retailing using a Markov Chain approach

Department of OperationsCatholic University Eichstätt-IngolstadtAuf der Schanz 49, 85049 Ingolstadt, Germany

Heinrich Kuhn

Thomas Wensing

Michael Sternbeck

SMMSO 2015, Volos, Greece

Optimizing case-pack sizes in grocery retailing using a Markov Chain approach

Department of OperationsCatholic University Eichstätt-IngolstadtAuf der Schanz 49, 85049 Ingolstadt, Germany

Heinrich Kuhn

Thomas Wensing

Michael Sternbeck

SMMSO 2015, Volos, Greece

Agenda

1. INTRODUCTION

2. MODEL DEVELOPMENT

3. OPTIMIZATION APPROACH

4. NUMERICAL STUDY

5. CONCLUSIONS AND FUTURE RESEARCH

Logistics costs distribution in retail chains

– 5 –

Warehousing

28%

(secondary) Transportation

24%

In-store Logistics

48%

1. INTRODUCTION

see Kuhn/Sternbeck (2013, OMR)

ConsumerDistribution center Transportation Store

Retail system

Case-Pack Size

– 6 –

Case-pack size of a productProducts delivered to stores are generally combined in case packs that are used as order and distribution unit

Case-pack sizes influence in-store processes

How to dimension the Case Pack (CP) from an in-store operations perspective?

Store

1. INTRODUCTION

DC

Instore Activities

– 8 –

SKU 1 SKU 2

Shelf on sales floor

Product delivery

Opening case pack

Filling the shelf

Storing overflow inventory

1. INTRODUCTION

SKU 1 SKU 2

Backroom store

Case pack

Single unit

Refilling when shelf space becomes available

Introductory Example

– 9 –

Status quoq = 12

Simulated scenarioq = 6

Number of units that have to be stored in the backroom was reduced substantially by 79.5% ̶ total instore logistics costs for this SKU were reduced by almost 48 %

1. INTRODUCTION

see Sternbeck (2014, JBE)

Shelf Size = 14 Shelf Size = 14

Two main research questions arise:

(A) How does case-pack size (q) influence

instore logistics costs ?

(B) What is the optimum

case-pack size (qopt) ?

Assuming an (r,s,nq) inventory policy

… and a given replenishment /delivery pattern

– 10 –

1. INTRODUCTION

1

1,5

2

2,5

3

3,5

4

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Costs

Case-pack size, q

qopt

Pattern Monday Tuesday Wednesday Thursday Friday Saturday1 X X X X X X2 X X X X X ---3 X --- X --- X X3 X --- X --- X ---4 X --- --- X --- ---5 --- --- X --- --- ---

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Inventory

Time

(r,s,nq) policy

q 2q

r

s

Litrature

Relevance of Case-Pack Size in Retail Trade

van der Laan, Joost W., Optimal Case-pack Quantity of FMCG products, Retail Economics, September 2011, http://retaileconomics.com/case-pack-quantity/

Kuhn, H., Sternbeck M.G., Integrative retail logistics: An exploratory study, Operations Management Research, Vol. 6, No. 1, 2013, pp. 2-18.

(r,s,nq) Inventory Policy

Tempelmeier, H., Fischer, L., Approximation of the probability distribution of the customer waiting time under an (r, s, q) inventory policy in discrete time. IJPR 48 (21), 2010, 6275–6291.

Shang, K. H., Zhou, S. X., Optimal and heuristic echelon (r, nq, t) policies in serial inventory systems with fixed costs. Operations Research 58 (2), 2010, pp. 414–427.

Zheng, Y.-S., Chen, F., Inventory policies with quantized ordering. Naval Research Logistics Quarterly 39, 1992, pp. 285–305.

Optimum Case-Pack Size Models

Sternbeck, M.G., A store-oriented approach to determine order packaging quantities in grocery retailing, forthcoming in: Journal of Business Economics, 2015

Wen, N., Graves, St.C., Ren, Z.J., Ship-pack optimization in a two-echelon distribution system, European Journal of Operational Research, Vol. 220, No. 3, 2012, pp. 777-785

1. INTRODUCTION

– 11 –

http://retaileconomics.com/case-pack-quantity/

Agenda

1. INTRODUCTION



4. NUMERICAL STUDY


Inventory Model – Control

– 13 –

Shelf Size 16Display Stock 8

q 5

l 3

r {Mo, We, Sa}

s (14,-,12,-,-,10)


demand

supply

• Stochastic demand

• Length of period = one day

• Lost sales

• Deterministic lead time (l)

• Replenishment policy:Generalization of the (r, s, nq) inventory policy:

- On certain days of the week (e.g., Mo, We, Sa)

- check the inventory position (IP) and place an order

- if IP is equal to or lower than the reorder level (s) for the particular weekday.

s141210

Inventory Model – Cost Drivers

– 14 –

Shelf Size: 16Display Stock: 8

q 5

l 3

r {Mo, We, Sa}

s (14,-,12,-,-,10)

What are the crucial instore logistics cost drivers ?

1) Physical Inventory

2) Display Stock Undershoot

3) Backroom Activity

4) Backroom Inventory

5) Case Pack Handling


demand

supply

(1)

(2)

(3)

(5)

(3,4)

Inventory Model – Cost Drivers

– 15 –

Shelf Size: 16Display Stock: 8

q 5

l 3

r {Mo, We, Sa}

s (14,-,12,-,-,10)

How do cost drivers develop with increasing case-pack size (q)

1) Physical Inventory ↑

2) Display Stock Undershoot ↓

3) Backroom Activity ↑ ↓

4) Backroom Inventory ↑

5) Case Pack Handling ↓


demand

supply

(1)

(2)

(3)

(5)

(3,4)

0

10

20

30

40

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

%

Case-pack size, q

Physical inventory

Backstore inventory

Under-shooting DS

Case-pack handling

Backstore activity

Inventory Model – Cost Function

– 16 –

1) Physical Inventory : I

2) Display Stock (DS) Undershoot (U )U := MAX(0, DS – I )

3) Backstore Activity (B1) B1 := 1 if B1>0 and A*>0

B1 := 0 otherwise

4) Backstore Inventory (B2)B2 := MAX(0, I – SP**)

5) Case Pack Handling (H) H := A/q

* New Arrivals (A)** Shelf Size (SP)


– 18 –

w_x, i,

n or 0

w_y, max(0,i–

d), n and 0, respectively

P(d=D) Case 1:

w_y is neither order issue nor

order arrival period

w_x, i, 0

w_y, max(0,i–

d), n*

P(d=D) Case 2: w_y is order issue period

n* = min(n|n*q ≥s-max(0, i – d))

w_x, i, n

w_y,i*,0

P(d=D) Case 3: w_y is order arrival period

i*= max(0, i – d+n*q)

Inventory Model – States and Transitions

Note: For a clearer presentation, we assume that only one order can be outstanding and order issue periods cannot be equal to arrival periods.


w : Mo, Tu, We, Th, Fr, Sa

sw = ( 14, - , 12, - , - , 10)Day

Open order of size n*q

Phys. inventory

Analytical Model - Approach

• Markov Chain– State defined by

• weekday (w)

• inventory level (I)• arriving or outstanding

case packs (n)

– Transitions follow from deterministic arrivals and stochastic demands

– 19 –

Solid arrows refer to transition probability 0.5, dotted arrows to certain transition.

q 2

l 1

r (-,x,-)

s (-,1,-)

D 0 or 1, equally distributed


Agenda

1. INTRODUCTION



4. NUMERICAL STUDY


0

10

20

30

40

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

%

Case-pack size, q

Physical inventory

Backstore inventory

Under-shooting DS

Case-pack handling

Backstore activity

Optimization Approach

– 22 –

3. Optimization Approach

In-store logistic costs ↑↓ when case pack size q

increase

1) Physical Inventory ↑

2) Display Stock Undershoot ↓

3) Backroom Activity ↑ ↓

4) Backroom Inventory ↑

5) Case Pack Handling ↓

Declining cost function (dec)

Total Cost Function

Increasing cost function (inc)

Optimization Procedure

Optimization Approach

– 23 –

0

0,1

0,2

0,3

0,4

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

final CUB

qmin qmax

C(q)

Cdec(q)

Cinc(q)

CP size, qqstartqopt

P3

Costs

P1

P4P2

First step-

Iteration left

Second step-

Iteration right

initial CUB

3. Optimization Approach

Agenda

1. INTRODUCTION



4. NUMERICAL STUDY


Numerical Study – Cases

4. Numerical Study

Stores (A, B, … , H)Products (1, 2, … , 6)

Changes of

current CP sizes

when

optimal CP sizes

are applied-7

23

-3

-19

1

-11

1

33

-2

-14

32

-10

29

-2

-6

6

-6 -6

-2

-13

9

-9 -8

-4

-9

4

-2

27

-7

29

-2

-14

-2

-16

-8

30

-1

-7

6

-3-6

15

-2

-8

9

-21

Product ID

65

21

4321

HGFEDCBA

Product ID Product category Sales category Sales (volume)Current case-

pack size

1 Pet food low sales 322 Personal care medium sales 123 Pet food high sales 324 Personal care very low sales 65 Personal care very high sales 166 Food high sales 12

Store Store size Store size (m2) Store salesA small medium salesB medium low salesC large medium salesD medium high salesE medium medium salesF medium very high salesG medium medium salesH medium high sales

Numerical Study – Product 1, Store H

– 26 –

4. Numerical Study

0

1

2

3

4

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Curr. unit

Case-pack size, q

Physical inventory (I)

Backroom inventory (B)

Undershooting DS (U)

Case-pack handling (H)

Backroom activity (A)

Total

Cost functions

Numerical Study – Product 1, Store H

– 27 –

q = 32

qopt = 11

4. Numerical Study

Shelf Size = 23

Shelf Size = 23

32

12

32

6

1612

1613

19

4

38

5

Product ID

Case

–pa

ck si

ze

21 43 65

Optimal case-pack size (one-size-for-all-stores) Current case-pack size

-23.3%

-3.2%

-20.7%

Total costs optimal case-pack

sizes tailored to each store

Total costs one case-pack

size for all stores

Total costs status quo

Numerical Study – One-Size-for-all-Stores

– 28 –

4. Numerical Study

Agenda

1. INTRODUCTION



4. NUMERICAL STUDY


Contribution, current status and further research

Optimizing case pack size Areas for further research

▪ The presented model fills a gap in literature and opens the opportunity to evaluate case-pack-sizes in respect to retail in-store logistics costs.

▪ Relevant in-store cost drivers are considered, i.e., physical inventory, display stock undershoot, backroom inventory, backroom activity, case pack handling.

▪ Numerical analyses of a real case study show that case-pack sizes should be reduced for some products as well as increased for other products.


▪ Integration of unpacking and/or packing costs in the DC

▪ Integration of case pack size related picking costs in the DC

▪ Synchronization of case pack sizes across stores

▪ Agreements with fast moving consumer goods companies in respect of “optimal” case-pack sizes

– 30 –

…many thanks for your attention

– 32 –

Evaluation of case-pack sizes in grocery retailing using a Markov Chain approach Department of...

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