TY - JOUR
T1 - Production/inventory competition between firms with fixed-proportions co-production systems
AU - He, Shuang
AU - Zhang, Jian
AU - Zhang, Juliang
AU - Cheng, T. C.E.
N1 - Funding Information:
This work was supported in part by the National Natural Science Foundation of China under grant numbers 71962026 and 71661167009 , NSFC/RGC under grant number N_PolyU531/16 , the Humanities and Social Sciences Foundation of Ministry of Education of China under grant number 19YJA630111 , Natural Science Foundation of Inner Mongolia under grant number 2019MS07004 , and Beijing Logistics Informatics Research Base . Cheng was also supported in part by The Hong Kong Polytechnic University under the Fung Yiu King-Wing Hang Bank Endowed Professorship in Business Administration.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021
Y1 - 2021
N2 - We study the production/inventory competition problem between two manufacturers each adopting the co-production system to process a raw material into two products in fixed proportions that are substitutable between the manufacturers. We first consider the one-period problem where the demands for the two manufacturers’ products are uncertain and independent. The unmet demand of one manufacturer's product can be met by the other manufacturer's leftover stock of the same product, if available, and is lost otherwise. The manufacturers compete for the substitute demands by choosing their own purchase/processing quantities. We show the existence of the unique Nash equilibrium processing quantity, and examine the impact of competition by comparing the total equilibrium quantity of the game with that of the centralized-decision case. We then study the multi-period production/inventory competition problem in which the manufacturers make decisions in each period according to the initial inventory levels of the products and the rivals’ decisions. We show the existence and uniqueness of the Nash equilibrium strategy and that the equilibrium strategy has the simple base-stock structure. We then consider the case where the manufacturers’ demands are correlated. In addition, studying the case where the manufacturers are capacitated, we show that the unique Nash equilibrium exists and has a modified base-stock structure. We further generalize the results to the infinite-period case and the case with more than two products. Finally, numerical studies are conducted to investigate the impacts of the model parameters on the equilibrium outcomes and get some managerial insights from the analytical findings.
AB - We study the production/inventory competition problem between two manufacturers each adopting the co-production system to process a raw material into two products in fixed proportions that are substitutable between the manufacturers. We first consider the one-period problem where the demands for the two manufacturers’ products are uncertain and independent. The unmet demand of one manufacturer's product can be met by the other manufacturer's leftover stock of the same product, if available, and is lost otherwise. The manufacturers compete for the substitute demands by choosing their own purchase/processing quantities. We show the existence of the unique Nash equilibrium processing quantity, and examine the impact of competition by comparing the total equilibrium quantity of the game with that of the centralized-decision case. We then study the multi-period production/inventory competition problem in which the manufacturers make decisions in each period according to the initial inventory levels of the products and the rivals’ decisions. We show the existence and uniqueness of the Nash equilibrium strategy and that the equilibrium strategy has the simple base-stock structure. We then consider the case where the manufacturers’ demands are correlated. In addition, studying the case where the manufacturers are capacitated, we show that the unique Nash equilibrium exists and has a modified base-stock structure. We further generalize the results to the infinite-period case and the case with more than two products. Finally, numerical studies are conducted to investigate the impacts of the model parameters on the equilibrium outcomes and get some managerial insights from the analytical findings.
KW - Base-stock policy
KW - Co-production system
KW - Dynamic game
KW - Inventory
UR - http://www.scopus.com/inward/record.url?scp=85110553446&partnerID=8YFLogxK
U2 - 10.1016/j.ejor.2021.06.041
DO - 10.1016/j.ejor.2021.06.041
M3 - Journal article
AN - SCOPUS:85110553446
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
ER -