Sustainable Integrated Inventory Model for Substitutable Deteriorating Items Considering Both Transport and Industry Carbon Emissions

Abstract

Sustainable integrated inventory management policy focuses on reducing the environmental impact of the manufacturing and transport sector. This study develops an integrated single-manufacturer single-buyer inventory model for substitutable deteriorating items considering transport and industry carbon emissions. This article categorizes carbon emissions into two parts: direct and indirect emissions. We also assume two mutually substitutable items, and substitution is considered on the buyer’s side. If one of the items is out of stock, the demand for that item can be partially satisfied by the stock of the other item; else, demand will be lost. The purpose of this study is to minimize the integrated cost of the supply chain with total carbon emissions produced by industry and transport sectors and to determine the optimal number of deliveries, order level and carbon emission quantity. A solution procedure is developed to find the optimal values of the policy. Numerical experiments and sensitivity analyses are presented to demonstrate the proposed model.

Keywords

Integrated inventory model / sustainability / deteriorating items / substitutable items / carbon emission

References

[1] Aazami A, Saidi-Mehrabad M. A production and distribution planning of perishable products with a fixed lifetime under vertical competition in the seller-buyer systems: A real-world application. Journal of Manufacturing Systems, 2021, 58: 223-247. May 2020

[2] Anupindi R, Dada M, Gupta S. Estimation of consumer demand with stock-out based substitution: An application to vending machine products. Marketing Science, 1998, 17(4): 406-423.

[3] Banerjee A. Economic-lot-size model for purchaser and vendor. Decision Sciences, 1986, 17: 292-311.

[4] Battini D, Persona A, Sgarbossa F. A sustainable EOQ model: Theoretical formulation and applications. International Journal of Production Economics, 2014, 149: 145-153.

[5] Bazan E, Jaber M Y, Zanoni S. Supply chain models with greenhouse gases emissions, energy usage and different coordination decisions. Applied Mathematical Modelling, 2015, 39(17): 5131-5151.

[6] Bazan E, Jaber M Y, Zanoni S. Carbon emissions and energy effects on a two-level manufacturer-retailer closed-loop supply chain model with remanufacturing subject to different coordination mechanisms. International Journal of Production Economics, 2017, 183: 394-408.

[7] Bouchery Y, Ghaffari A, Jemai Z, Dallery Y. Including sustainability criteria into inventory models. European Journal of Operational Research, 2012, 222(2): 229-240.

[8] Cai J, Tadikamalla P R, Shang J, Huang G. Optimal inventory decisions under vendor managed inventory: Substitution effects and replenishment tactics. Applied Mathematical Modelling, 2017, 43: 611-629.

[9] Daryanto Y, Wee H M, Astanti R D. Three-echelon supply chain model considering carbon emission and item deterioration. Transportation Research Part E: Logistics and Transportation Review, 2019, 122: 368-383.

[10] Drezner Z, Gurnani H, Pasternack B A. An EOQ model with substitutions between products. Journal of the Operational Research Society, 1995, 46(7): 887-891.

[11] Fu Y C, Yeh C W. An integrated producer-buyer supply chain with delivery cost under stochastic transportation time. Applied Mathematical Modelling, 2017, 44: 676-687.

[12] Ghare P M, Schrader G F. A model for an exponentially decaying inventory. Journal of Industrial Engineering, 1963, 14: 238-243.

[13] Glock C H. A multiple-vendor single-buyer integrated inventory model with a variable number of vendors. Computers and Industrial Engineering, 2011, 60(1): 173-182.

[14] Goyal S K. An integrated inventory model for a single supplier-single customer problem. International Journal of Production Research, 1977, 15(1): 107-111.

[15] Goyal S K, Giri B C. Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 2001, 134(1): 1-16.

[16] Hsiao H I, Tu M, Yang M F, Tseng W C. Deteriorating inventory model for ready-to-eat food under fuzzy environment. International Journal of Logistics Research and Applications, 2017, 20(6): 560-580.

[17] Hua G, Cheng T C E, Wang S. Managing carbon footprints in inventory management. International Journal of Production Economics, 2011, 132(2): 178-185.

[18] Jaber M Y, Glock C H, El Saadany A M A. Supply chain coordination with emissions reduction incentives. International Journal of Production Research, 2013, 51(1): 69-82.

[19] Kim S W, Bell P C. Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution. Omega, 2011, 39(5): 528-538.

[20] Krommyda I P, Skouri K, Konstantaras I. Optimal ordering quantities for substitutable products with stock-dependent demand. Applied Mathematical Modelling, 2015, 39(1): 147-164.

[21] Lee S, Kim D. An optimal policy for a single-vendor single-buyer integrated production-distribution model with both deteriorating and defective items. International Journal of Production Economics, 2014, 147: 161-170. PART A

[22] Lin C, Lin Y. A cooperative inventory policy with deteriorating items for a two-echelon model. European Journal of Operational Research, 2007, 178(1): 92-111.

[23] Lou Z, Hou F, Lou X, Ma T (2021). Game-theoretical models of a two-echelon supply chain involving two substitutable products. Journal of Systems Science and Systems Engineering 1–14.

[24] Lu L. A one-vendor multi-buyer integrated inventory model. European Journal of Operational Research, 1995, 81(2): 312-323.

[25] Marchi B, Zanoni S, Zavanella L E, Jaber M Y. Supply chain models with greenhouse gases emissions, energy usage, imperfect process under different coordination decisions. International Journal of Production Economics, 2019, 211: 145-153.

[26] McGillivray A R, Silver E A. Some concepts for inventory control under substitutable demand. INFOR Journal, 1978, 16(1): 47-63.

[27] Mishra U, Wu J Z, Sarkar B. A sustainable production-inventory model for a controllable carbon emissions rate under shortages. Journal of Cleaner Production, 2020, 256: 120268.

[28] Mishra U, Wu J Z, Sarkar B. Optimum sustainable inventory management with backorder and deterioration under controllable carbon emissions. Journal of Cleaner Production, 2021, 279: 123699.

[29] Mishra U, Wu J Z, Tsao Y C, Tseng M L. Sustainable inventory system with controllable non-instantaneous deterioration and environmental emission rates. Journal of Cleaner Production, 2020, 244: 118807.

[30] Mishra V K. Optimal ordering quantities for substitutable deteriorating items under joint replenishment with cost of substitution. Journal of Industrial Engineering International, 2017, 13(3): 381-391.

[31] Misra R B. Optimum production lot size model for a system with deteriorating inventory. International Journal of Production Research, 1975, 13(5): 495-505.

[32] Rasouli N, Nakhaikamalabadi I. Joint pricing and inventory control for seasonal and substitutable goods mentioning the symmetrical and asymmetrical substitution. International Journal of Engineering, 2014, 27(9): 1385-1392.

[33] Rau H, Wu M Y, Wee H M. Integrated inventory model for deteriorating items under a multi-echelon supply chain environment. International Journal of Production Economics, 2003, 86(2): 155-168.

[34] Salameh M K, Yassine A A, Maddah B, Ghaddar L. Joint replenishment model with substitution. Applied Mathematical Modelling, 2014, 38(14): 3662-3671.

[35] Sarkar B, Ganguly B, Sarkar M, Pareek S. Effect of variable transportation and carbon emission in a three-echelon supply chain model. Transportation Research Part E: Logistics and Transportation Review, 2016, 91: 112-128.

[36] Sarkar B, Saren S, Sarkar M, Seo Y W. A Stackelberg game approach in an integrated inventory model with carbon-emission and setup cost reduction. Sustainability, 2016, 8(12): 1244.

[37] Sarkar S, Giri B C. A vendor-buyer integrated inventory system with variable lead time and uncertain market demand. Operational Research, 2020, 20(1): 491-515.

[38] Sebatjane M, Adetunji O. Optimal lot-sizing and shipment decisions in a three-echelon supply chain for growing items with inventory level-and expiration date-dependent demand. Applied Mathematical Modelling, 2021, 90: 1204-1225.

[39] Shah N H, Chaudhari U, Cárdenas-Barrón L E. Integrating credit and replenishment policies for deteriorating items under quadratic demand in a three-echelon supply chain. International Journal of Systems Science: Operations & Logistics, 2020, 7(1): 34-45.

[40] Singh R, Mishra V K. Sustainable optimal ordering quantity for non-instantaneous deteriorating items under joint replenishment with substitution and carbon emission. Kybernetes, 2021, 51(1): 442-465.

[41] Taleizadeh A A, Niaki S T A, Barzinpour F. Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm. Applied Mathematics and Computation, 2011, 217(22): 9234-9253.

[42] Tang C S, Yin R. Joint ordering and pricing strategies for managing substitutable products. Production and Operations Management, 2007, 16(1): 138-153.

[43] Tiwari S, Daryanto Y, Wee H M. Sustainable inventory management with deteriorating and imperfect quality items considering carbon emission. Journal of Cleaner Production, 2018, 192: 281-292.

[44] U.S. Environmental Protection Agency US EPA. (2019). Sources of Greenhouse Gas Emissions [Government report]. Retrieved from https://www.epa.gov/ghgemissions/sources-greenhouse-gas-emissions.

[45] Van den Berg R, De Langen P W. Environmental sustainability in container transport: The attitudes of shippers and forwarders. International Journal of Logistics Research and Applications, 2017, 20(2): 146-162.

[46] Wahab M I M, Mamun S M H, Ongkunaruk P. EOQ models for a coordinated two-level international supply chain considering imperfect items and environmental impact. International Journal of Production Economics, 2011, 134(1): 151-158.

[47] Wangsa I D, Tiwari S, Wee H M, Reong S. A sustainable vendor-buyer inventory system considering transportation, loading and unloading activities. Journal of Cleaner Production, 2020, 271: 122120.

[48] Wee H M, Jong J F, Yang P C. A discussion on economic ordering policy of deteriorated item for vendor and buyer. Production Planning and Control, 2006, 17(8): 792-795.

[49] Whitin T. M (1957). Theory of Inventory Management. Princeton University Press.

[50] Wu B, Sarker B R. Optimal manufacturing and delivery schedules in a supply chain system of deteriorating items. International Journal of Production Research, 2013, 51(3): 798-812.

[51] Xu M, Zuo X. An optimal dynamic advertising model with inverse inventory sensitive demand effect for deteriorating items. Journal of Systems Science and Systems Engineering, 2017, 26(5): 593-608.

[52] Yan C, Banerjee A, Yang L. An integrated productiondistribution model for a deteriorating inventory item. International Journal of Production Economics, 2011, 133(1): 228-232.

[53] Yang P C, Wee H M. Economic ordering policy of deteriorated item for vendor and buyer: An integrated approach. Production Planning and Control, 2000, 11(5): 474-480.

[54] Yu Y, Chu F, Chen H. On improving an integrated inventory model for a single vendor and multiple buyers with a relaxed material ordering cycle policy. Journal of Systems Science and Systems Engineering, 2006, 15(3): 298-313.

[55] Yu Y, Wang Z, Liang L. A vendor managed inventory supply chain with deteriorating raw materials and products. International Journal of Production Economics, 2012, 136(2): 266-274.

[56] Zanoni S, Mazzoldi L, Jaber M Y. Vendor-managed inventory with consignment stock agreement for single vendor-single buyer under the emission-trading scheme. International Journal of Production Research, 2014, 52(1): 20-31.