Research Article Joint Pricing and Inventory Management of Interbasin Water Transfer Supply Chain

Hindawi Complexity Volume 2020, Article ID 3954084, 16 pages https://doi.org/10.1155/2020/3954084

Xue Chen1 and Zhisong Chen 1,2

1Business School, Nanjing Normal University, Qixia District, Nanjing 210023, China 2Stern School of Business, New York University, 44 West Fourth Street, New York 10012, NY, USA

Correspondence should be addressed to Zhisong Chen; [email protected]

Received 19 June 2020; Revised 7 August 2020; Accepted 19 August 2020; Published 7 September 2020

Academic Editor: Shouwei Li

Copyright © 2020 Xue Chen and Zhisong Chen. )is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Four game-theoretical decision models without/with backlogging for the interbasin water transfer (IBWT) supply chain considering water delivery loss under joint pricing and inventory management (JPIM) are first developed, analyzed, and compared; then, the corresponding numerical and sensitivity analyses are conducted and compared; finally, the managerial insights and practical implementations are summarized in this paper. )e research results indicate that (1) a revenue and cost sharing contract could effectively coordinate the IBWT supply chain and improve the operational performance of the IBWT supply chain under JPIM; (2) the partial backlogging strategy of water demand could effectively improve the operational performance of the IBWT supply chain under JPIM; (3) coordination strategy with partial backlogging is the best strategy for improving the operational performance of the IBWT supply chain under JPIM; (4) reducing water delivery loss rate and operational costs and increasing backlogging ratio are beneficial to improving the operational performance of the IBWT supply chain under JPIM.

1. Introduction relationship is an urgent problem for the IBWT projects. Furthermore, due to the random water demand, the order To alleviate the shortage of water resources in arid and quantity may mismatch with water demand. )e water semiarid areas, various kinds of interbasin water transfer demand may be lower than the order quantity, and the (IBWT) projects have been constructed and operated all holding cost of excess water inventory will thus be incurred; over the world, such as the South-to-North Water Diversion on the contrary, the water demand may be higher than the (SNWD) Project in China, the California State Water order quantity, and the shortage cost of excess water demand Project, the Central Arizona Project and the Colorado River will thus be incurred. Hence, how to jointly make optimal Aqueduct in the US, the Indira Gandhi Canal and the Telugu pricing and inventory decisions to achieve operational Ganga Project in India, the Snowy Mountains Scheme in performance improvement is also an important issue for the Australia, the North Sinai Development Project in Egypt, IBWT projects. and the National Water Carrier in Israel [1, 2]. In the From the perspective of supply chain management, the practical operation management of the IBWT project, the available research has explored the subsidy policy and the existing rigid water price mechanism for the IBWTproject is operational strategy of the IBWT green supply chain under decoupled from the water supply-demand relationship and social welfare maximization [3, 4], the impact of the supply cannot effectively exert the regulatory role of the market capacity constraint and fairness concern on the operational mechanism and coordinate the interests of all parties in- decisions and outcomes of the IBWT supply chain under volved. )us, how to optimize pricing to achieve operational random precipitation [5], and the impact of fully/partial performance improvement under a flexible water price backlogging on the operational decisions and outcomes of mechanism that is linked to the water supply-demand IBWT green supply chain coordination considering water 2 Complexity delivery loss under random precipitation [6]. However, the supply chain under social welfare maximization [3, 4], joint pricing-inventory management decisions and opera- impact of the supply capacity constraint and fairness con- tional strategies for an IBWTsupply chain considering water cern on the operational decisions and outcomes of the IBWT delivery loss and partial backlogging are rarely investigated supply chain under random precipitation [5], and impact of in the current literatures and practices. fully/partial backlogging on the IBWT green supply chain )erefore, this paper will try to explore a novelty re- coordination considering water delivery loss under random search issue regarding the operation management of the precipitation [6]. IBWT supply chain—the joint pricing-inventory manage- Nevertheless, these existing literatures regarding IBWT ment (JPIM) decisions and operational strategies for the supply chain management neither explored the equilibrium/ IBWT supply chain considering water delivery loss and coordination strategies of the IBWT supply chain under partial backlogging under random water demand. JPIM, nor investigated the impact of the partial backlogging, In the following sections, the related literatures are the choice of operational strategies, and the water delivery reviewed first in Section 2; the theoretical modeling nota- loss on the operational performance of the IBWT supply tions and assumptions for a generic IBWT supply chain are chain. )is paper tries to address the shortcomings in the defined in Section 3; four game-theoretical decision models available literatures and explore the operational strategies for for the IBWT supply chain without/with backlogging under an IBWT supply chain without/with partial backlogging joint pricing-inventory management (JPIM) are developed, under JPIM. An equilibrium decision model and a coor- analyzed, and compared in Section 4; the corresponding dination decision model for the IBWT supply chain without numerical and sensitivity analyses for all models are backlogging/with partial backlogging under JPIM are de- implemented, and the corresponding results are compared veloped, solved, and compared, respectively, to explore the in Section 5; the managerial insights and practical imple- optimal operational strategies and optimal joint pricing and mentations are then summarized in Section 6; finally, the inventory decisions for the IBWT supply chain. theoretical and practical contributions are summarized. 3. Modeling Notations and Assumptions 2. Literature Review An IBWTdistribution system is a typical “embedded” supply Currently, the interaction relationships among multiple chain structure. In this supply chain system, a horizontal stakeholders in the IBWT projects are investigated through water supply system embeds itself in a vertical water dis- game theory, such as the water conflict game-theoretical tribution system (see Figure 1). In the horizontal water model of the SNWD project [7], game-theoretical model of supply system, a local supplier and an external supplier work the IBWT project considering both the water quantity and as a joint IBWT supplier via an efficient cooperation water quality [8], water allocation option contract for the mechanism. Water resources are transferred and supplied by IBWT projects [9], and incentive-compatible payment de- the local supplier from the water source to the external sign for the SNWD project [10]. supplier within the trunk channel and then distributed to Besides, cooperative game theory is applied to achieve water resource distributors of all water intakes via river Pareto improvement in the IBWT projects, such as the channels and artificial canals. Finally, the water resources are crisp and fuzzy Shapley game model for the IBWT water sold by each distributor to the water resource consumers in allocation [11], cooperative game model for the IBWT his/her service region. )e water distributor and the cor- water allocation [12], IBWT water resource allocation responding water market in the ith water intake are indexed using the least core game [13], and robust multiobjective by i � 1, 2, ... , n. It is assumed that there are m distributors bargaining game model for the IBWT water resource al- supplied by the local supplier and n–m distributors supplied location [14]. by the external supplier. Currently, theories and techniques of supply chain On this basis, the parameters used in the models are management (SCM) have been applied in the IBWTprojects defined as follows: to investigate the interactions among multiple stakeholders th cdi � the water transfer cost from the i water intake to and develop equilibrium/coordination operational mecha- th nisms, such as optimal pricing and coordination schemes for the i distributor th the SNWD supply chain [15], coordination mechanism ck � the water transfer cost from the (k − 1) water based on revenue sharing contract for the SNWD supply intake to the kth water intake within the horizontal chain with strategic customer [16], asymmetric Nash bar- supply chain, k � 1, 2, ... , n gaining model for the SNWD supply chain [17], two-echelon th δk � the water delivery loss rate from the (k − 1) water water inventory model with inflow forecasting updates in an intake to the kth water intake within the horizontal IBWT project [18], two-tier pricing and allocation schemes ... supply chain, and δk ∈ (0, 1), k � 1, 2, , n for the SNWD supply chain [19], competition intensity in c � the fixed cost for the ith water intake of the IBWT the water supply chain under two contracts [20], power fi supplier structures for the competitive water supply chains [21], m optimal pricing and ordering strategies for dual competing cfl � the fixed cost for the local supplier, cfl � �i�1 cfi water supply chains under three contracts [22], subsidy cfe � the fixed cost for the external supplier, n policies and operational strategies for the IBWT green cfe � �i�m+1 cfi Complexity 3

Horizontal supply chain: IBWT water resource joint supplier

Pump Local supplier Pump Pump Water supplier Pump

Reservoirs 1 Reservoirs 2… Reservoirs j … Reservoirs J Water source Water

Distributor Distributor Distributor Distributor Distributor Distributor Distributor Distributor 1 2 i … m m + 1 m + 2 m + k … n

Water -intake Vertical supply chain: ibwt water distribution water ibwt chain: supply Vertical 1st 2nd ith mth (m + 1)th (m + 2)th (m + k)th nth market market market market market market market market

Figure 1: A generic interbasin water transfer supply chain system.

c � the fixed cost for the IBWT supplier, i k− 1 f TCi(Qi) � Qi �k�1[ck�j�0 (1 − δj)]; hereinto, δ0 � 0. c � c + c � �n c f fl fe i�1 fi )erefore, the total transfer cost of the water demand (order w � the wholesale price of water resources transferred quantity) of the ith water intake is from the local supplier to the external supplier i k− 1 i TCi(qi) � ((�k�1[ck �j�0 (1 − δj)]/ �k�1(1 − δk))qi). De- w � i k− 1 i i the wholesale price of water resources transferred fining C � (� [c � (1 − δ )]/ � (1 − δ )), then from the IBWT supplier to the ith distributor i k�1 k j�0 j k�1 k (q ) � C q th TCi i i i. Following Howe and Linaweaver [23, 24], pi � the retail price of water resources sold from the i Petruzzi and Dada [25], and Wang et al. [26], the water distributor to the consumers in his service region th demand for the i distributor is di(pi), and � − b κh the holding cost coefficient, and 0 < κh < 1 di(pi) � yi(pi)xi. Hereinto, yi(pi) � aipi , where ai is the th hi � the unit cost of holding water inventory for the i potential maximum water demand quantity and b is the distributor, and hi � κhpi price elasticity of the expected demand. xi is a random disturbance defined in the range [A, B] with B > A > 0. )e κs � the shortage cost coefficient, and 0 < κh < κs < 1 th cumulative distribution function (CDF) and the probability si � the shortage cost of unmet water demand for the i density function (PDF) of xi are Fi(·) and fi(·), and the distributor, and si � κspi mean value and the standard deviation of xi are μi and σi. Qi � the original pumping quantity from the water Following Petruzzi and Dada [25], Wang et al. [27], and th source to the i water intake Wang [28], zi � (qi/yi(pi)) is defined as the “water stock th th qi � the order quantity of the i water intake factor” for the i distributor; thus, the order quantity th τ � the bargaining powers of the local supplier, and function of water resources for the i water intake is q � y (p )z x τ ∈ (0, 1) i i i i. )e distribution of i satisfies the IGFR (increasing generalized failure rate) condition: λ � the bargaining powers of the ith water intake of the (dg(xi)/dxi) > 0, where gi(xi) ≡ xi(fi(xi)/[1 − Fi(xi)]), IBWT supplier, and λ ∈ (0, 1) and there exists a unique solution to the maximal expected As mentioned above, the unmet water demand may be problem. Many distributions, such as normal distribution partially backlogged due to the capacity constraint of the and exponential distribution, satisfy the IGFR condition IBWT project. )e backlogging ratio of unmet water de- [27, 29, 30]. mand for the ith distributor is φ, and φ ∈ [0, 1]. )e rela- Based on the foregoing modeling notations and as- th th tionship between the water demand of the ith water intake q sumptions, the profit functions of the i distributor, the i i th and the original pumping quantity Qi is water intake of the IBWTsupplier, and the i water intake of i the IBWT supply chain with partial backlogging can be qi � Qi �k�1 (1 − δk), and the total transfer cost of the original pumping quantity Qi is formulated as follows: 4 Complexity

z , p � � p y p �E �z , x �� − p y p �E� z − x �+ � + � �p − w + c �� − p �y p �E� x − z �+ � ΠDi i i i i i min i i κh i i i i i φ i i di κs i i i i i

− wi + cdi �yipi �zi, w � � w − C �y p �z + w − C �y p �E� x − z �+ � − c , ( ) ΠSi i i i i i i φ i i i i i i fi 1 z , p � � p y p �E �z , x �� − p y p �E� z − x �+ � + � �p − C + c �� − p �y p �E� x − z �+ � ΠSCi i i i i i min i i κh i i i i i φ i i di κs i i i i i

− Ci + cdi �yipi �zi − cfi.

On this basis, the profit functions of the IBWT supplier, scenario without backlogging; the super/subscript b repre- the local supplier, the external supplier, and the IBWT sents the scenario with partial backlogging. supply chain with partial backlogging can be formulated as follows: n 4.1. Game-4eoretical Decision Models without Backlogging. Π w � � � Π w �, Under the scenario without backlogging, the backlogging S i Si i th i�1 ratio of unmet water demand for the i distributor is φ � 0. m n Two game-theoretical decision models of the IBWT supply w , w � � � w � + w � y p �z , chain without backlogging under JPIM considering water ΠLS i ΠSi i i i i i�1 i�m+1 delivery loss, including the equilibrium and coordination (2) n n decision models, are developed, analyzed, and compared in w , w � � � w � − w � y p �z , ΠES i ΠSi i i i i this section. i�m+1 i�m+1 n z , p � � � z , p �. ΠSC i i ΠSCi i i 4.1.1. Equilibrium Decision Model without Backlogging. i�1 Under this scenario, the detailed decision sequences are as follows: the local and external suppliers will first bargain 4. Game-Theoretical Decision Models over the wholesale price of the water resources within the IBWT horizontal supply chain via Nash bargaining theory Based on the modeling notations and assumptions in Section [32–35] to achieve cooperative operations; then, the IBWT 3, two game-theoretical decision models without back- supplier decides the usage price of water resources for each logging/with partial backlogging for the IBWT supply chain water distributor in the IBWT vertical supply chain; finally, under JPIM considering water delivery loss, including the each water distributor independently and simultaneously equilibrium and coordination decision models, are devel- decides the stock factor and the retail price of water re- oped, analyzed, and compared in this section. In the models sources for the consumer it serves. to follow, note that the super/subscript d represents an )e two-stage Stackelberg and Nash bargaining game equilibrium decision; the super/subscript c represents a model for the IBWT supply chain without backlogging can coordination decision; the super/subscript o represents the be formulated as

τ 1− τ max Ω(w) ��Πod�wod, qod, w �� Πod�wod, qod, w �� , w LS i i ES i i

⎪⎧ Πod�wod, qod, w � + Πod�wod, qod, w � � Πod�wod, qod �, ⎪ LS i i ES i i S i i ⎪ ⎪ ⎪ od od od od ⎪ ⎪⎧ wi , pi , zi and qi are derived from solving the following problem, ⎪ ⎪ ⎪ ⎪ (3) ⎨⎪ ⎪ o ⎪ ⎧⎪ �w , podw �, zod�, s.t. ⎪ ⎪ max ΠS i i i i ⎪ ⎨ ⎪ wi ⎪ . . ⎪ ⎪ s t ⎪ ⎨⎪ ⎪ ⎪ od od ⎪ ⎪ ⎪ p w � and z are derived from solving the following problem, ⎪ ⎪ ⎪ i i i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ o ⎩⎪ ⎩⎪ ⎩⎪ max Π z , p �. Di i i zi,pi Complexity 5

Solving this two-stage Stackelberg and Nash bargaining then, the IBWT supplier provides the distributors a revenue od problem, we can get the equilibrium usage price wi in sharing contract in which the IBWTsupplier charges a lower th od the i water intake, the equilibrium retail price pi and the usage price wi to the water distributors; if the distributors od th equilibrium stock factor zi for the i water distributor, the accept the contract, they will place orders with quantity od th equilibrium ordering quantity qi for the i water distrib- qi to the IBWT supplier and decide the retail price of water o utor, and the bargaining wholesale price wd. Furthermore, resources pi and the stock factor of water resources zi; the profits of the local supplier, the external supplier, the finally, they will share a proportion of their net revenues IBWTsupplier, the ith water distributor, and the IBWTsupply (1 − ϕ) to the IBWT supplier, where ϕ is the revenue od od od od od chain can be calculated as ΠLS, ΠES, ΠS , ΠD , and ΠSC keeping rate of the water distributors, 0 ≤ ϕ ≤ 1. )e revenue i th (see Table 1 for the detailed analytical results, and their shared by the i distributor to the IBWT supplier is Ti � + derivations can be seen in sec10Supplementary Materials (1 − ϕ)piyi(pi)�E[min�zi, xi �] − κhE[(zi − xi) ]− κsE[(xi− + th (available here)). zi) ]}. )us, the profit functions of the i distributor and the IBWT supplier are as follows: Πoc (z , p ) � Πo (z , p ) − T Di i i Di i i i and Πoc(w ) � �n Πoc(w ) � �n [Πo (w ) + T ]. 4.1.2. Coordination Decision Model without Backlogging. S i i�1 Si i i�1 Si i i Under this scenario, the detailed decision sequences are as )e two-stage coordination and Nash bargaining game follows: the local and external suppliers will first bargain model for the IBWT supply chain without backlogging can over the wholesale price of water resources within the IBWT be formulated as horizontal supply chain to achieve cooperative operations;

− max Ω(w) � �Πoc woc, qoc, w ��τ�Πoc woc, qoc, w ��1 τ, w LS i i ES i i

⎧⎪ oc woc, qoc, w � + oc woc, qoc, w � � ocwoc, qoc �, ⎪ ΠLS i i ΠES i i ΠS i i ⎪ ⎪ ⎪ woc, qoc, Πoc woc, qoc, w �, Πoc woc, qoc, w � and Πocwoc, qoc � ⎪ i i LS i i ES i i S i i ⎪ ⎪ ⎪ are derived from solving the following problem, ⎪ ⎪ ⎪ − ⎪ ⎧⎪ o oc od λ oc od 1 λ ⎪ ⎪ max πi (ϕ) ��ΠS (ϕ) − ΠS � �ΠD (ϕ) − ΠD � , ⎪ ⎪ ϕ i i i i ⎪ ⎪ ⎪ ⎪ (4) ⎨ ⎪ oc oc oc s.t. ⎪ ⎧⎪ ΠS (ϕ) + ΠD (ϕ) � ΠSC , ⎪ ⎪ ⎪ i i i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ oc oc oc oc oc oc oc ⎪ ⎪ ⎪ w (ϕ), p , z , q , Π (ϕ), Π (ϕ) and Π ⎪ ⎨ ⎪ i i i i Si Di SCi ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ are derived from solving the following problem, ⎪ ⎪ s.t. ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧⎪ max Πoc z , p �, ⎪ ⎪ ⎪ ⎪ Di i i ⎪ ⎪ ⎪ ⎨⎪ zi,pi ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩⎪ ⎪ o ⎩ ⎩ ⎩ max ΠSCzi, pi �. zi,pi

on Solving this two-stage coordination and Nash bar- price wc . Furthermore, the proﬁts of the local supplier, gaining problem, we can obtain the equilibrium usage the external supplier, the IBWT supplier, the ith water oc th price wi in the i water intake, the equilibrium retail distributor, and the IBWT supply chain can also be oc oc th oc oc oc oc oc price pi and the equilibrium stock factor zi for the i computed as ΠLS, ΠES, ΠS , ΠD , and ΠSC (see Table 1 for oc i water distributor, the equilibrium ordering quantity qi the detailed analytical results, and their derivations can be for the ith water distributor, and the bargaining wholesale seen in Supplementary Materials). 6

Table 1: Analytical results of the IBWT supply chain without backlogging. Scenario var. Result Equilibrium decision (4.1.1) Coordination decision (4.1.2) o od oc o o wi wi � ((bCi + cdi)/(b − 1)) wi � ϕc Ci − (1 − ϕc )cdi o od oc oc oc oc oc pi pi � (b/(b − 1)pi ) pi � (b/(b − 1))((Ci + cdi)zi /(1 + κs)zi − Λi(zi )) o od oc oc oc oc zi Fi(zi ) � Fi(zi ) Fi(zi ) � ((1 + κs)/b(1 + κh + κs)) + ((b − 1)Λi(zi )/b(1 + κh + κs)zi ) o od b oc oc oc oc oc − b oc qi qi � ((b − 1)/b) qi qi � yi(pi )zi � ai(pi ) zi n m wo wo � (1/ �n qod)(τΠod − �m Πod) wo � (1/ � qoc)(τΠoc − � Πoc) d i�m+1 i S i�1 Si c i�m+1 i S i�1 Si n Πo Πod � τΠod � τ �n [((b − 1)/b)b(Πoc + c ) − c ] Πoc � τΠoc � τ � [(1 − ϕo)Πoc − ϕoc ] LS LS S i�1 SCi fi fi LS S i�1 c SCi c fi n Πo Πod � (1 − τ)Πod � (1 − τ) �n [((b − 1)/b)b(Πoc + c ) − c ] Πoc � (1 − τ)Πoc � (1 − τ) � [(1 − ϕo)Πoc − ϕoc ] ES ES S i�1 SCi fi fi ES S i�1 c SCi c fi o od n od n b oc oc n oc n o oc o ΠS Π � � Π � � [((b − 1)/b) (Π + c ) − c ] Π � � Π � � [(1 − ϕ )Π − ϕ c ] S i�1 Si i�1 SCi fi fi S i�1 Si i�1 c SCi c fi o Πo Πod � ((b − 1)/b)b− 1(Πoc + c ) Πoc � ϕ (Πoc + c ) Di Di SCi fi Di c SCi fi n n Πo Πod � �n Πod � �n �[((b − 1)/b)b + ((b − 1)/b)b− 1](Πoc + c ) − c � Πoc � � Πoc � � ((C + c )/(b − 1))qoc − c SC SC i�1 SCi i�1 SCi fi fi SC i�1 SCi i�1 i di i fi o o b− 1 b ϕc NA ϕc � λ((b − 1)/b) + (1 − λ)[1 − ((b − 1)/b) ] zoc B Note oc i oc Λi(zi ) � (1 + κh + κs) �A (zi − xi)fi(xi)dxi + κs �A xifi(xi)dxi Complexity Complexity 7

4.2. Game-4eoretical Decision Models with Partial over the wholesale price of the water resources within the Backlogging. Under the scenario with partial backlogging, IBWT horizontal supply chain to achieve cooperative op- the backlogging ratio of unmet water demand for the ith erations; next, the IBWT supplier decides the usage price of distributor is φ ∈ (0, 1]. Two game-theoretical decision water resources for each water distributor in the IBWT models of the IBWT supply chain with partial backlogging vertical supply chain; then, each water distributor inde- under JPIM considering water delivery loss, including the pendently and simultaneously decides the stock factor and equilibrium and coordination decision models, are devel- the retail price of water resources for the consumer it serves; oped, analyzed, and compared in this section. finally, the unmet water demands of each market are partially backlogged and satisfied. )e two-stage Stackelberg and Nash bargaining game model for the IBWTsupply chain 4.2.1. Equilibrium Decision Model with Partial Backlogging. with partial backlogging can be formulated as Under this scenario, the detailed decision sequences are as follows: the local and external suppliers will first bargain

τ 1− τ max Ω(w) ��Πbd�wbd, qbd, w �� Πbd�wbd, qbd, w �� , w LS i i ES i i

⎧⎪ bd�wbd, qbd, w � + bd�wbd, qbd, w � � bd�wbd, qbd �, ⎪ ΠLS i i ΠES i i ΠS i i ⎪ ⎪ ⎪ ⎧⎪ wbd, pbd, zbd qbd , ⎪ ⎪ i i i and i are derived from solving the following problem ⎪ ⎪ ⎪ ⎪ (5) ⎨ ⎪ ⎧⎪ b�w , pbdw �, zbd�, s.t. ⎪ ⎪ max ΠS i i i i ⎪ ⎨ ⎪ wi ⎪ s.t. ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ pbdw � zbd , ⎪ ⎪ ⎪ i i and i are derived from solving the following problem ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩⎪ ⎩⎪ ⎩⎪ max Πb z , p �. Di i i zi,pi

Solving this two-stage Stackelberg and Nash bargaining sharing contract in which the IBWTsupplier charges a lower bd problem, we can obtain the equilibrium usage price wi in usage price wi to the water distributors; if the distributors th bd the i water intake, the equilibrium retail price pi and the accept the contract, they will place orders with quantity qi to bd th equilibrium stock factor zi for the i water distributor, the the IBWT supplier and decide the retail price of water re- bd th equilibrium ordering quantity qi for the i water distrib- sources pi and the stock factor of water resources zi; then, b utor, and the bargaining wholesale price wd. Furthermore, the unmet water demands of each market are partially the profits of the local supplier, the external supplier, the backlogged and satisfied; finally, all the distributors will IBWT supplier, the ith water distributor, and the IBWT share a proportion of their net revenues (1 − ϕ) to the IBWT bd bd bd bd supply chain can be calculated as ΠLS, ΠES, ΠS , ΠD , and supplier, where ϕ is the revenue keeping rate of the water bd i th ΠSC (see Table 2 for the detailed analytical results, and their distributors, 0 ≤ ϕ ≤ 1. )e revenue shared by the i dis- derivations can be seen in Supplementary Materials). tributor to the IBWT supplier is Ti � (1 − ϕ)piyi(pi) + + �E[min�zi, xi �] − κhE[(zi − xi) ] − κsE[(xi − zi) ]�. )us, the profit functions of the ith distributor and the IBWT 4.2.2. Coordination Decision Model with Partial Backlogging. supplier are as follows: Πbc (z , p ) � Πb (z , p ) − T and Di i i Di i i i Under this scenario, the detailed decision sequences are as bc n bc n b Π (wi) � � Π (wi) � � [Π (wi) + Ti]. follows: the local and external suppliers will first bargain S i�1 Si i�1 Si over the wholesale price of water resources within the IBWT )e two-stage coordination and Nash bargaining game horizontal supply chain to achieve cooperative operations; model for the IBWT supply chain with partial backlogging next, the IBWT supplier offers the distributors a revenue can be formulated as 8

Table 2: Analytical results of the IBWT supply chain with partial backlogging. Scenario var. Result Equilibrium decision (4.2.1) Coordination decision (4.2.2) b bd bc b b wi wi � ((bCi + cdi)/(b − 1)) wi � ϕc Ci − (1 − ϕc )cdi b bd bc bc bc bc bc bc pi pi � (b/(b − 1))pi pi � (b(Ci + cdi)/(b − 1))(((1 − φ)zi + φΝi(zi ))/((1 − φ + κs)zi − Μi(zi ))) b bd bc bc zi Fi(zi ) � Fi(zi ) Fi(zi ) b bd b bc bc bc bc bc − b bc qi qi � ((b − 1)/b) qi qi � yi(pi )zi � ai(pi ) zi wb wb � (1/ �n qbd)(τΠbd − �m Πbd) wb � (1/ �n qbc)(τΠbc − �m Πbc) d i�m+1 i S i�1 Si c i�m+1 i S i�1 Si Πb Πbd � τΠbd � τ �n [((b − 1)/b)b(Πbc + c ) − c ] Πbc � τΠbc � τ �n [(1 − ϕb)Πbc − ϕbc ] LS LS S i�1 SCi fi fi LS S i�1 c SCi c fi Πb Πbd � (1 − τ)Πbd � (1 − τ) �n [((b − 1)/b)b(Πbc + c ) − c ] Πbc � (1 − τ)Πbc � (1 − τ) �n [(1 − ϕb)Πbc − ϕbc ] ES ES S i�1 SCi fi fi ES S i�1 c SCi c fi Πb Πbd � �n Πbd � �n [((b − 1)/b)b(Πbc + c ) − c ] Πbc � �n Πbc � �n [(1 − ϕb)Πbc − ϕbc ] S S i�1 Si i�1 SCi fi fi S i�1 Si i�1 c SCi c fi Πb Πbd � ((b − 1)/b)b− 1(Πbc + c ) Πbc � ϕb(Πbc + c ) Di Di SCi fi Di c SCi fi Πb Πbd � �n Πbd � �n �[((b − 1)/b)b + ((b − 1)/b)b− 1](Πbc + c ) − c � Πbc � �n Πbc � �n �((C + c )/(b − 1))y (pbc)[(1 − φ)zbc + φΝ (zbc)] − c � SC SC i�1 SCi i�1 SCi fi fi SC i�1 SCi i�1 i di i i i i i fi b b b− 1 b ϕc NA ϕc � λ((b − 1)/b) + (1 − λ)[1 − ((b − 1)/b) ]

bc bc Fi(zi ) � (((1 − φ)(1 − φ + κs)zi + bc bc bc bc bc bc Note bφ(1 − φ + κs)Ni(zi ) + (b − 1)(1 − φ)Mi(zi ))/([(b − φ)(1 − φ + κs) + b(1 − φ)κh]zi + bφ(1 − φ + κs + κh)Νi(zi ) − (b − 1)φΜi(zi ))),Mi(zi ) � (1 + κh + κs − zbc B zbc B i bc bc i bc φ) � (zi − xi)fi(xi)dxi − (φ − κs) � xifi(xi)dxi,Ni(zi ) � � (zi − xi)fi(xi)dxi + � xifi(xi)dxi. A A A A Complexity Complexity 9

τ 1− τ max Ω(w) � �Πbc �wbc, qbc, w �� Πbc �wbc, qbc, w �� , w LS i i ES i i

⎧⎪ bc wbc, qbc, w + bc wbc, qbc, w � bc wbc, qbc , ⎪ ΠLS�i i � ΠES�i i � ΠS �i i � ⎪ ⎪ ⎪ bc bc bc bc bc bc bc bc bc bc bc ⎪ w , q , Π �w , q , w �, Π �w , q , w � and Π �w , q � ⎪ i i LS i i ES i i S i i ⎪ ⎪ ⎪ are derived from solving the following problem, ⎪ ⎪ ⎪ λ 1− λ ⎪ ⎪⎧ max πb(ϕ) ��⊓bc(ϕ) − Πbd� �Πbc (ϕ) − Πbd� , ⎪ ⎪ i Si Si Di Di ⎪ ⎪ ϕ ⎪ ⎪ ( ) ⎪ ⎪ 6 ⎨ ⎪ bc bc bc s.t. ⎪ ⎪⎧ Π (ϕ) + Π (ϕ) � Π , ⎪ ⎪ ⎪ Si Di SCi ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ bc bc bc bc bc bc bc ⎪ ⎨⎪ ⎪ wi (ϕ), pi , zi , qi , ΠS (ϕ), ΠD (ϕ) and ΠSC , ⎪ ⎪ i i i ⎪ ⎪ ⎪ ⎪ ⎪ ⎨⎪ ⎪ ⎪ are derived from solving the following problem, ⎪ ⎪ s.t.⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ bc ⎪ ⎪ ⎪ ⎧⎪ max Π zi, pi �, ⎪ ⎪ ⎪ ⎪ z ,p Di ⎪ ⎪ ⎪ ⎨ i i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩⎪ ⎪ ⎩⎪ b ⎩ ⎩ max ΠSCzi, pi �. zi,pi

Solving this two-stage coordination and Nash bargaining in Yangzhou City, Jiangsu Province, the water is extracted bc problem, we can obtain the equilibrium usage price wi in from the main stream of the lower reaches of the Yangtze th bc the i water intake, the equilibrium retail price pi and the River and transferred by the Beijing-Hangzhou Grand Canal bc th equilibrium stock factor zi for the i water distributor, the and its parallel river channels to connect Hongze Lake, bc th equilibrium ordering quantity qi for the i water distrib- Luoma Lake, Nansi Lake, and Dongping Lake. After leaving b utor, and the bargaining wholesale price wc . Furthermore, Dongping Lake, there are two ways to deliver water: one is to the profits of the local supplier, the external supplier, the the north, passing through the Yellow River through a IBWT supplier, the ith water distributor, and the IBWT tunnel near Weishan, and then to Tianjin; the other is to the bc bc bc bc supply chain can also be computed as ΠLS, ΠES, ΠS , ΠD , and east, Yantai, and Weihai, via the Jiaodong water transfer bc i ΠSC (see Table 1 for the detailed analytical results, and their branch-line. )ere are 13 pumping stations in this project derivations can be seen in Supplementary Materials). with a total length of water transfer mainline at 1466.5 kilometers, a water raising capacity at 65 meters, and a water diversion scale of 14.8 billion cubic meters. )e eastern route 5. Numerical and Sensitivity Analyses project provides production and domestic water to the east Based on the game-theoretical decision modeling analysis, a of Huang-Huai-Hai Plain, Jiaodong area, and Beijing- real-world case of the eastern route of the South-to-North Tianjin-Hebei region. In the water supply area, there are 25 Water Diversion (SNWD) project in China is selected to cities at prefecture level or above from the Huaihe River, the conduct numerical and sensitivity analyses. Haihe River, and the Yellow River Basin. )e SNWD project is an important world-scale strategic In the eastern route of the SNWD project, there are six water resource engineering to solve the water shortage sections for the mainline of the project: Section 1 (Jiangdu problem in northern China. )is project is divided into the Station∼South of Nansi Lake), Section 2 (Lower Cascade of eastern route, western route, and middle route. )ese three Nansi Lake), Section 3 (Upper Cascade of Nansi Lake- routes of the SNWD project can transfer water resources ∼Changgou Pumping Station), Section 4 (Changgou separately from the Yangtze River linking Yangtze River, Pumping Station∼Dongping Lake, including East of Huaihe River, Yellow River, and Haihe River to formulate a Dongping Lake), Section 5 (Dongping Lake∼Qiutun Sluice nationwide water supply system with “Four horizontal and in Linqing City), and Section 6 (Qiutun Sluice in Linqing )ree vertical, South-North deployment, East-West mutual City∼Datun Reservoir). )ese six sections can be generalized support.” to six water intakes, i.e., n � 6. Hereinto, Sections 1-2 are )e eastern route of the SNWD project is constructed managed and operated by the local supplier (Jiangsu Water and extended based on the north water transfer project in Source Co. Ltd), and Sections 3∼6 are managed and operated Jiangsu Province. )rough the Jiangdu water control project by the external supplier (Shandong Mainline Co. Ltd), i.e., 10 Complexity m � 2 and n − m � 4. )ere are two water distributors in the analysis separately. )e main findings of the numerical service region of the local supplier and four water distrib- analysis are summarized below: utors in the service region of the external supplier. (1) Comparing the numerical analysis results between Based on the real characteristics and management equilibrium decision (Table 4) and coordination practices of the eastern route of the SNWD project in China decision (Table 5) without backlogging under JPIM, [2], the numerical and sensitivity analyses are conducted in the findings are summarized as follows: (i) )e the following sections, and the corresponding values of wholesale prices of water resources under coordi- parameters relating to the IBWT supply chain are collected nation decision are lower than those under equi- and estimated from the publicly disclosed information of the librium decision. (ii) )e retail prices of water eastern route of the SNWD project [34] and the water resources under coordination decision are lower transfer scheme for the eastern route of the SNWD project than those under equilibrium decision. (iii) )e [36]. )e parameters of water transfer costs and fixed costs water stock factors under coordination decision are can be estimated according to the cost accounting method. equal to those under equilibrium decision. (iv) )e )e parameters of the potential maximum water demand order quantities of water resources under coordi- quantity and the price elasticity of the expected demand can nation decision are higher than those under equi- be estimated based on the historical operation data. )e librium decision. (v) )e profits of the IBWT supply random distribution and corresponding parameters of the chain and its members under coordination decision random factor can also be fitted based on the historical are higher than those under equilibrium decision. operation data. )e parameter of the water delivery loss rate can be estimated based on the historical operation data. )e (2) Comparing the numerical analysis results between parameters of the holding cost coefficient and the shortage equilibrium decision (Table 6) and coordination cost coefficient can be estimated via the cost accounting decision (Table 7) with partial backlogging under method or empirical parameters. )e backlogging ratio of JPIM, the findings are summarized as follows: (i) )e unmet water demand can be calculated as total shortage wholesale prices of water resources under coordi- quantity divided by extra supply capacity. )e bargaining nation decision are lower than those under equi- powers of the local supplier and the ith water intake of the librium decision. (ii) )e retail prices of water IBWT supplier can be calculated by the market power resources under coordination decision are lower evaluation. On this basis, the lower bound of the interval of than those under equilibrium decision. (iii) )e the random factor (xi) is set at 0.00001, and the upper water stock factors under coordination decision are bounds of the interval of the random factor (xi) is set at 1, equal to those under equilibrium decision. (iv) )e i.e., A � 1E − 5,B � 1. )e random factor xi obeys normal order quantities of water resources under coordi- 2 distribution, i.e., xi ∼ N(μi, σi ). )e mean value of the nation decision are higher than those under equi- random factor μi is set at 0.10, and the standard deviation of librium decision. (v) )e profits of the IBWT supply the random factor σi is set at 0.01. )e corresponding pa- chain and its members under coordination decision rameters of mainline/branch-line water transfer costs and are higher than those under equilibrium decision. potential maximum water demand quantities are collected (3) Comparing the numerical analysis results between and estimated in Table 3. )e fixed cost of water delivery for the scenario without backlogging (Table 4) and the th c the i water intake of the IBWT supplier fi is 1,000,000. scenario with partial backlogging (Table 6) under According to the empirical parameters, the water delivery th th equilibrium decision, the findings are summarized as loss from the (i − 1) water intake to the i water intake follows: (i) )e wholesale prices of water resources within the horizontal supply chain δi is about 15%. )e th under the scenario with partial backlogging are equal backlogging ratio of unmet water demand for the i dis- to those under the scenario without backlogging. (ii) tributor φ is 0.8. )e price elasticity of the expected demand )e retail prices of water resources under the sce- b is 1.5. )e holding cost coefficient κh is 0.2, and the nario with partial backlogging are lower than those shortage cost coefficient κs is 0.5. Owing to the advantage of under the scenario without backlogging. (iii) )e the local supplier, the local supplier’s bargaining power τ is water stock factors under the scenario with partial 0.6. Likewise, due to the advantage of the IBWTsupplier, the th backlogging are lower than those under the scenario i water intake of the IBWTsupplier’s bargaining power λ is without backlogging. (iv) )e order quantities of 0.6. water resources under the scenario with partial backlogging are lower than those under the scenario without backlogging. (v) )e profits of the IBWT 5.1. Numerical Analysis. )e joint pricing-inventory oper- supply chain and its members under the scenario ational decisions and performances for all the game-theo- with partial backlogging are higher than those under retical decision models without/with backlogging are the scenario without backlogging. compared and summarized in Tables 4–7, respectively. It should be noted that the centralized decision neglects the (4) Comparing the numerical analysis results between roles of the members’ decisions and therefore is inferior to the scenario without backlogging (Table 5) and the coordination decision regarding the derived solutions. )us, scenario with partial backlogging (Table 7) under the centralized decision model is not shown in the numerical coordination decision, the findings are summarized Complexity 11

Table 3: Parameter setting.

Section (water intake) i Mainline water transfer cost (ci) Branch-line water transfer cost (cdi) Potential maximum water demand (ai) 1 0.32 0.08 1.796 + E9 2 0.24 0.10 1.218 + E9 3 0.09 0.12 1.169 + E9 4 0.14 0.76 1.941 + E9 5 0.41 0.29 1.117 + E9 6 0.81 0.40 1.525 + E9

Table 4: Numerical analysis results of equilibrium decision without backlogging. i wod pod qod Πod Πod i i i Di S 1 1.29 4.52 19,687,772 53,921,334 48,147,444 od 2 2.38 8.17 5,492,511 27,196,481 ΠLS 3 3.12 10.69 3,525,446 22,826,460 28,888,466 od 4 5.40 20.33 2,230,602 27,477,799 ΠES 5 6.59 22.72 1,087,114 14,960,682 19,258,978 od 6 10.73 36.74 721,423 16,059,575 ΠSC Sum NA NA 32,744,868 162,442,332 210,589,776 od o Note zi � 0.11, wd � 0.51

Table 5: Numerical analysis results of coordination decision without backlogging. i woc poc qoc Πoc Πoc i i i Di S 1 0.23 1.51 102,300,667 62,521,086 87,008,602 oc 2 0.45 2.72 28,539,924 31,533,966 ΠLS 3 0.60 3.56 18,318,752 26,466,983 52,205,161 oc 4 0.61 6.78 11,590,549 31,860,151 ΠES 5 1.25 7.57 5,648,811 17,346,716 34,803,441 oc 6 2.08 12.25 3,748,622 18,620,868 ΠSC Sum NA NA 170,147,325 188,349,770 275,358,372 oc o o Note zi � 0.11, wc � 0.20, ϕc � 0.67

Table 6: Numerical analysis results of equilibrium decision with partial backlogging. i wbd pbd qbd Πbd Πbd i i i Di S 1 1.29 4.42 19,598,802 55,086,318 49,317,312 bd 2 2.38 7.99 5,467,690 27,784,068 ΠLS 3 3.12 10.45 3,509,514 23,319,631 29,590,387 bd 4 5.40 19.88 2,220,522 28,071,464 ΠES 5 6.59 22.21 1,082,201 15,283,911 19,726,925 bd 6 10.73 35.93 718,163 16,406,546 ΠSC Sum NA NA 32,596,892 165,951,937 215,269,249 bd b Note zi � 0.10, wd � 0.53

as follows: (i) )e wholesale prices of water resources supply chain and its members under the scenario under the scenario with partial backlogging are equal with partial backlogging are higher than those under to those under the scenario without backlogging. (ii) the scenario without backlogging. )e retail prices of water resources under the scenario with partial backlogging are lower than those 5.2. Sensitivity Analysis. Since, in the previous analysis, under the scenario without backlogging. (iii) )e coordination decision with partial backlogging is found to be water stock factors under the scenario with partial superior to the other decisions without/with partial back- backlogging are lower than those under the scenario logging, the sensitivity analysis will focus on how the without backlogging. (iv) )e order quantities of changes in eight key parameters (including the mainline water resources under the scenario with partial transfer cost, the branch-line transfer cost, the holding cost backlogging are lower than those under the scenario coefficient, the shortage cost coefficient, the backlogging without backlogging. (v) )e profits of the IBWT ratio, the price elasticity of the expected water demand, the 12 Complexity

Table 7: Numerical analysis results of coordination decision with partial backlogging. i wbc pbc qbc Πbc Πbc i i i Di S 1 0.23 1.47 101,838,362 63,871,869 89,018,075 bc 2 0.45 2.66 28,410,950 32,215,265 ΠLS 3 0.60 3.48 18,235,969 27,038,809 53,410,845 bc 4 0.61 6.63 11,538,171 32,548,497 ΠES 5 1.25 7.40 5,623,284 17,721,496 35,607,230 bc 6 2.08 11.98 3,731,682 19,023,177 ΠSC Sum NA NA 169,378,417 192,419,112 281,437,186 bc b b Note zi � 0.10, wc � 0.20, ϕc � 0.67

water delivery loss rate, and the bargaining power of the ith Second, be it under equilibrium or coordination strat- water intake of the IBWT supplier) impact the profits under egies, the IBWT supply chain and its members would order coordination decision with partial backlogging. To capture less water resources under the scenario with partial back- the impact of the change in key parameters, we only select logging than those under the scenario without backlogging the parameters from the 1st distributor and the 1st water and could gain more profits under the scenario with partial intake to conduct sensitivity analysis, including the mainline backlogging than those under the scenario without back- transfer cost and the branch-line transfer cost. Figure 2 logging. Hence, partial backlogging of water demand is (including eight subgraphs) shows the impact of eight key beneficial to operational performance improvement for all parameters change on the profit of the IBWT supply chain the stakeholders of the IBWT supply chain under JPIM. with partial backlogging. )e findings from the sensitivity Furthermore, the higher the backlogging ratio is, the more analysis results are summarized as follows: (1) the IBWT profits the IBWT supply chain and its members could gain. supply chain profit decreases as the mainline transfer cost )us, increasing the backlogging ratio is beneficial to op- increases; (2) the IBWT supply chain profit decreases as the erational performance improvement for all the stakeholders branch-line transfer cost increases; (3) the IBWT supply of the IBWT supply chain under JPIM. chain profit decreases as the holding cost coefficient in- Finally, be it under the scenario without backlogging or creases; (4) the IBWT supply chain profit decreases as the under the scenario with partial backlogging, reducing the shortage cost coefficient increases; (5) the IBWT supply water delivery loss rate and operational costs (including chain profit increases as the backlogging ratio increases; (6) mainline transfer cost, branch-line transfer cost, holding the IBWTsupply chain profit decreases as the price elasticity cost, and shortage cost) is beneficial to operational per- of the expected water demand increases; (7) the IBWT formance improvement for all the stakeholders of the IBWT supply chain profit decreases as the water delivery loss in- supply chain under JPIM. Furthermore, a lower price creases; (8) the IBWT supplier’s profit increases and the elasticity of the expected water demand is beneficial to distributors’ profits decrease as the bargaining power of the operational performance improvement for all the stake- ith water intake of the IBWT supplier increases. holders of the IBWT supply chain under JPIM. In brief, the coordination strategy using a revenue and 6. Managerial Insights and cost sharing contract with partial backlogging outperforms all the other scenarios/strategies and is the best strategy for Practical Implications improving the operational performance of all the stake- Based on the foregoing analysis, this section will expound on holders in the IBWT supply chain under JPIM. the managerial insights and practical implications. 6.2. Practical Implications. From the practical perspective of 6.1. Managerial Insights. Based on the foregoing discussions, the IBWT project operational management, the practical the managerial insights can be derived and summarized as implications can be derived and summarized for the SNWD follows. project as follows. First, be it under the scenario without backlogging or First, a fixed water price mechanism is implemented in under the scenario with partial backlogging, the IBWT the eastern and middle routes of the SNWD project cur- supply chain and its members would make lower retail prices rently, which cannot directly reflect the linkage effect be- of water resources and order more water resources under the tween water supply and demand and water price. )is rigid coordination strategy than those under the equilibrium existing water price mechanism could not effectively exert strategy and could gain more profits under the coordination the regulatory role of the market mechanism and coordinate strategy than those under the equilibrium strategy. Hence, the interests of all operating entities involved in the oper- the coordination strategy via a revenue and cost sharing ational management of the SNWD project. )us, it is contract is beneficial to improving the operational perfor- suggested that some of the water pricing power may be mance for all the stakeholders and coordinate the IBWT transferred by the government to the main operating entities supply chain under JPIM. of the projects to give full play to the regulating role of the Complexity 13

×108 ×108 3.2 2.86

3.1 2.84

3 2.82

2.9 2.8 Profit Profit 2.8 2.78

2.7 2.76

2.6 2.74 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 Mainline transfer cost Branchline transfer cost

Supply chain Supply chain

(a) (b) ×108 ×108 2.84 2.88

2.83 2.87

2.82 2.86

2.81 2.85

2.8 2.84 Profit Profit 2.79 2.83

2.78 2.82

2.77 2.81

2.76 2.8 0.1 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5 0.6 Holding cost coefficient Shortage cost coefficient

Supply chain Supply chain

Profit 2.79 Profit 3.5 2.78 3 2.77 2.5 2.76 2 2.75 1.5 0 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Backlogging ratio Price-elasticity of the expected demand

Supply chain Supply chain

(e) (f) Figure 2: Continued. 14 Complexity

×108 ×107 3.3 11 10 3.2 9 3.1 8

3 7 6 Profit 2.9 Profit 5 2.8 4 3 2.7 2 2.6 1 0 0.05 0.1 0.15 0.2 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Water delivery loss rate Bargaining power

Distributor 1 Distributor 5 Distributor 2 Distributor 6 Distributor 3 Distributor 7 + Distributor 4

(g) (h)

Figure 2: )e impact of key parameters’ change on the profit of the IBWTsupply chain with partial backlogging. (a) Mainline transfer cost; (b) branch-line transfer cost; (c) holding cost; (d) shortage cost; (e) backlogging ratio; (f) price elasticity; (g) water delivery loss rate; (h) bargaining power. market mechanism. In this situation, the water prices for demands of each market are partially backlogged and sat- each water intake and water market in the IBWTproject can isfied; finally, all the distributors’ net revenues will be shared be adjusted freely according to the relationship between the to the IBWT supplier. water supply and demand, which is a flexible water price Finally, the order quantity of water resources mis- mechanism. On this basis, a joint pricing and inventory matching with the random water demand would induce management (JPIM) mode could flexibly reflect the linkage unnecessary losses (including holding cost or shortage cost) effect between water supply and demand and water price and in the operational management of the IBWT project. Under regulate water supply and demand through the market the JPIM mode, a partial backlogging strategy could effec- mechanism and thus is recommended to be considered and tively reduce these unnecessary losses and thus is recom- implemented in the operational management of the SNWD mended to be adopted in the operational management of the project. eastern route of the SNWD project. )e decision makers of Second, since the asset rights of the eastern route of the the project should make a lot of effort to enhance their SNWD project belong to different entities, each interest backlogging abilities and increase the backlogging ratio to entity will tend to pursue its own interests’ maximization improve the operational performance of all the stakeholders. and will act in its own ways and lack of collaborative op- Furthermore, water delivery loss and water transfer costs eration, which will eventually lead to the reduction in op- have important impacts on the optimal operational deci- eration efficiency. Under the JPIM mode, a coordination sions/performance of the project; the decision makers of the strategy via the revenue and cost sharing contract with project should make a lot of effort to reduce water delivery partial backlogging could effectively achieve Pareto im- loss and water transfer costs in the operational management provement of all the stakeholders’ interests and thus is of the project. recommended to be adopted to coordinate all the stake- In sum, a joint pricing and inventory management holders in the eastern route of the SNWD project. )e (JPIM) mode based on the flexible water price mechanism is detailed action sequence of this coordination strategy is as recommended to be implemented, and a coordination follows: the local and the external suppliers first bargain over strategy via the revenue and cost sharing contract with the wholesale price of water resources within the IBWT partial backlogging is also recommended to be adopted to horizontal supply chain to achieve cooperative operations; improve operational efficiency for the eastern route of the next, the IBWT supplier provides the distributors a revenue SNWD project. sharing contract in which the IBWTsupplier charges a lower usage price to the water distributors; if the distributors 7. Conclusions accept the contract, they will place orders to the IBWT supplier and decide the retail price of water resources and From a perspective of supply chain management, this paper the stock factor of water resources; then, the unmet water tries to explore the issues of joint pricing-inventory Complexity 15 management decisions and operational strategies for the (Grant no. 17YJC790002), China Postdoctoral Science IBWT project considering water delivery loss and partial Foundation (Grant no. 2019M651833), Social Science backlogging. )e equilibrium and coordination decision Foundation of Jiangsu Province in China (Grant no. models without/with partial backlogging for the IBWT 19GLC003), National Key R&D Program of China (Grant supply chain considering water delivery loss under joint no. 2017YFC0404600), Natural Science Research Project of pricing and inventory management (JPIM) are developed, Colleges and Universities in Jiangsu Province (Grant no. analyzed, and compared through a game-theoretical ap- 15KJB110012), and Young Leading Talent Program of proach, and the corresponding numerical and sensitivity Nanjing Normal University. analyses for all models are implemented and compared; finally, the managerial insights and practical implementations are summarized in this paper. )e research results Supplementary Materials show that (1) a revenue and cost sharing contract could Proofs for analytical results of game-theoretical decision effectively coordinate the IBWT supply chain and improve models. 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