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-305002

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

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)

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

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

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]

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}

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

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 10481.4 23.1 5.87 4.27 29.49 37.65

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.

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.

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.

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.

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