1. Inventory lot-sizing with supplier selection under non-stationary stochastic demand with carbon and fill rate constraints
Devendra Choudhary
Professor (Assist.)
Department of Mechanical Engineering, Govt. Engineering College Ajmer, Rajasthan

2. Outline Background Motivation Problem statement Methodology
Experimental setup
Result discussion
Managerial insights
Future scope

3. Background Inventory lot-sizing Supplier selection
Joint decision of inventory lot-sizing and supplier selection (Aissaoui et al., 2007)
Prior studies model this problem mainly under non-stationary deterministic demand process (e.g., Choudhary and Shankar, 2013 & 2014; Rezaei and Davoodi, 2011; Basnet and Leung, 2005)

4. Motivation
Most of the products exhibit non-stationary stochastic demand (Choudhary and Shankar 2015; Neale and Willems, 2009)
Supplier selection has notable influence on environmental burden of a supply chain (Sarkis, 2003; Genovese et al., 2013; Kumar et al., 2014)
Inventory lot-sizing decision may impact carbon emissions generated in a supply chain (Absi et al., 2013; Benjaafar et al., 2013)
Fill rate

5. Problem statement BUYER FIRM REGULATOR SUPPLIERS CUSTOMERS
CARBON CAP
CPRICE Os ps rs fs cs
DEMAND
N (µ, σ)
βcycle CV DP
BUYER FIRM
SUPPLIERS
REGULATOR
CARBON MARKET
CUSTOMERS

6. Methodology
Xjk ϵ {0, 1}, Ysj ϵ {0, 1}, qsj ≥ 0, qj ≥ 0, CQjk(βcycle) ≥ 0, j ϵ [1, N], k ϵ [j + 1, j + N]

7. Experimental setup System related variables βcycle ϵ {0.7, 0.9}
Attribute
Supplier 1
Supplier 2
Supplier 3
Supplier 4
Supplier 5
Order cost
450
650
400
530
Purchasing cost
2.8
2.4
2.9
2.5
3.0
Order related emission
360
552
335
384
300
Emission per unit purchased
1.6
1.4
1.7
1.9
Defect rate
0.10
0.13
0.12
0.17
0.04
System related variables
βcycle ϵ {0.7, 0.9}
suppliers’ capacity
ϵ {300, infinite}
Product related variables
DP ϵ {RAND, SIN, LCY}
CV ϵ {0.1, 0.6}
Emissions related variables
CAPhorizon ϵ {10000, 15000}
Cprice ϵ {1, 4}

8. Result discussion Fill rate (βcycle) 0.70 3089.3 1284.1 4.96 8799.6
Independent Variables
Total cost
Total inventory
Order frequency
Total emissions
Share of Supplier 1
(%)
Share of Supplier 2
Share of Supplier 3
Share of Supplier 4
Share of Supplier 5
Fill rate (βcycle)
0.70
3089.3
1284.1
4.96
8799.6
20.82
7.05
4.56
33.57
33.99
0.90
15468
2423.4
6.04
12163
25.27
4.69
3.99
25.4
41.3
Coefficient of variation (CV)
0.10
519.4
601.6
6.54
7990.5
24.91
2.7
1.57
25.7
45.13
0.60
18038
3105.9
4.46
12972
21.18
9.05
6.98
33.28
30.16
Carbon cap (CAP)
10000
15534
1855
5.5
10487
21.87
6.29
4.39
29.71
38.07
15000
3023.2
1852.5
10476
24.22
5.45
4.16
29.27
37.22
Carbon price (Cprice) 1
12339
1868.2
5.46
10509
25.2
11.74
3.57
21.56
37.93 4
6218
1839.3
5.54
10454
20.89
4.98
37.42
37.36

9. Result discussion Supplier’s capacity Limited 12544 1761.7 5.77 11326
Independent Variables
Total cost
Total inventory
Order frequency
Total emissions
Share of Supplier 1
(%)
Share of Supplier 2
Share of Supplier 3
Share of Supplier 4
Share of Supplier 5
Supplier’s capacity
Limited
12544
1761.7
5.77
11326
27.12
8.42
3.6
60.87
Unlimited
6013.3
1945.8
5.23
9636.9
18.98
11.74
0.13
55.38
14.42
Demand Pattern (DP)
LCY
10194
2025.8
6.63
10768
22.38
8.74
4.59
29.43
34.86
SIN
8294
1743.5
4.78
10215
25.55
6.73
3.28
21.74
43.68
RAND
9348
1792
5.09
10461
21.2
2.14
4.95
37.3
34.4
Average
9278.6
1853.8
5.5
23.1
5.87
4.27
29.49
37.65

10. Managerial insights
The products with stable demand (i.e., low CV), such as commodities, should be procured more frequently in small size lots from suppliers with better ordering and quality parameters especially when fill rate requirement of such products is high.
In such a business setting, frequent replenishments help in lowering inventory costs and storage related emissions.
The products with volatile demand (i.e., high CV), such as fashion products, should be procured less frequently in large size lots from suppliers offering low unit price and unitary emission, especially when fill rate requirement of such products is low.
The low replenishment frequency facilitates demand aggregation of more number of periods, and due to risk pooling effects the inventory levels decrease along with costs and emissions.

11. Managerial insights
At higher carbon cap, the supplier with lower emissions and cost parameters is preferred.
When carbon price is higher, the order should be allocated to the supplier having better emission parameters.
As it may facilitate savings in carbon emissions and providing the opportunity to sell the carbon credits in open carbon trade market and earn revenue, especially when carbon cap and carbon price are at higher level.

12. Managerial insights
If the suppliers are having limited capacity, maximum share of order quantities should go to the supplier who offers lower defect rate along with low value of ordering parameters.
When the suppliers have unlimited capacity, the replenishment orders are placed to the supplier having better emission parameters and lower unit cost at the expense of the quality level of procured lots.

13. Future scope
The present study only considers cap-and-trade regulatory mechanism
It can be extended under the strict cap, carbon tax, and carbon offset regulatory mechanisms.

14. Thank you