Network equilibrium models for conflicting objectives tradeoff

There exists extensive literature on the conflicting objective analysis in supply chain network management. Many methods have been used to improve the supply efficiency of a supply chain with conflicting objectives, including such things as weighting method, penalty cost function, quality deterioration, marginal value of time, discarding cost, and exponential score. These works include Chan and Chung (2004), Yu and Nagurney (2013), Masoumi, Yu, and Nagurney (2017), Kadziński, Tervonen, Tomczyk, and Dekker (2017), De Treville et al. (2014). This section reviews only the works associated with time-cost and service-cost conflicting objectives analysis in supply chain network management.

This section reviews two streams of literature in the following section. One stream deals with the coordination of operational cost, processing time, and service level in a supply chain network. In this stream of research, the supply chain network equilibrium model with time- and service-cost competition involves product quality (in which the processing time affects the product quality, for example, fresh produce supply chain network and nuclear medicine supply chains), profit loss (in which the processing time affects firms’ operational cost, for example, penalty and overtime cost), and company reputation (Nagurney et al., 2014), even processing

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time is treated as an important factor to affect the service level. A recent article by Nagurney et al. (2018) is worth much attention because the dynamics of quality are treated as a strategic variable in supply chain network with time-cost competition. Importantly, the dynamics of quality in time-cost competition has been used as a marketing tool. In practice, some retailers use freshness as a key competitive advantage, for example, German company Globus (Entrup et al., 2005) and Lucky in California (So, 2000). Under quality information asymmetry, Li, Nagurney, and Yu (2017) develop an adaptive model for producers at the supply markets to adapt their decisions over time in response to consumer learning of quality. Fresh food deterioration is a distinct characteristic in the food supply chain network. Yu and Nagurney (2013) develop a network-based food supply chain network model with a focus on fresh produce deterioration. Nagurney and Nagurney (2012) develop a supply chain network equilibrium network model for the design of nuclear medicine supply chains by deriving formulae for the arc and path multipliers that capture the underlying physics of radioisotope decay affected by processing time. Taking into consideration discarding costs, Masoumi, Yu, and Nagurney (2012) construct a generalized network oligopoly model for supply chains of pharmaceutical products by using arc multipliers. Widodo et al. (2005) and Ahumada and Villalobos (2011) implement a loss function in the objective functions to handle the processing time cost in supply chains. Relatedly, a product’s marginal value of time, the rate at which a product loses value over time, is used to minimize lost value in perishable product supply chains (Blackburn & Scudder, 2009).

Service/price options decisions in the firm level setting have been discussed extensively, including single firm optimization (Mussa & Rosen, 1978) and competition among firms (Lederer and Li, 1997; Easton & Moodie, 1999; So, 2000). The above problems are described as profit maximization problems at the service level and cost constraints in a monopoly or oligopoly setting (in which time is also an important factor affecting the service level). These works focus on optimization problems at the firm level-the coordination of inter-supply chain competition is not considered. The basic setting for these works is that the processing time and service level can be linearly or nonlinearly converted into some kind of operational cost from a firm’s perspective so that the problem remains in single objective realm. Furthermore, heterogenous customer choice behaviors are not considered.

In supply chain network management literature, much of the network equilibrium literature considers time-cost tradeoff problems where operational time acquiescently can be converted into the operational cost at the firm level. Masoumi, Yu, and Nagurney (2012) further construct a generalized network oligopoly model for perishable products by introducing a concept called arc multiplier. A loss function (Ahumada & Villalobos, 2011) and a product’s marginal value of time (Blackburn & Scudder, 2009) are two common tools to convert a processing time into

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cost in time-cost supply chains. Masoumi et al. (2012) develop a pharmaceutical product network model, and Yu and Nagurney (2013) model a food supply chain network. Both consider discarding costs affected by the operational time on each link from firm’s perspective.

Studies in time-cost tradeoff supply chains have illustrated different methods to optimize the profits of firms in time-cost tradeoff supply chains in consideration of operational time, including linear and nonlinear conversions (Sabri & Beamon, 2000; Masoumi et al., 2017;

Kadziński et al., 2017). There is much literature that focuses on the Pareto front of time-cost tradeoff supply chains (See, Farahani & Elahipanah, 2008). The basic assumption is providing a series of optimal options for decision makers to choose in terms of the decision maker’s preference. These studies focus on internal supply efficiency in a time-cost tradeoff supply chain, whereby customers' preferences or the connection between supply and demand are not considered. However, in a supply chain constituted by different time-cost tradeoff individual firms, it is possible to collaborate time-cost arrangements at the supply chain level based on customer heterogeneity.

Another stream of literature shows how to optimize the time- and service-cost tradeoff issue from the demand side. Market demands impacted by time- and service-cost tradeoff can be classified in the following several categories: (1) price-quality (Nagurney, Besik, & Yu, 2018;

Jabarzare & Rasti-Barzoki, 2019; Wang, Hu, & Liu, 2017), (2) price-lead time (Nagurney, Yu, Floden, & Nagurney, 2014; Zhu, 2015; Hua et al., 2010), (3) utility/surplus (Zhao et al., 2012;

Xia & Rajagopalan, 2009). In Nagurney et al. (2018), the dynamics of quality affected by the processing time and temperature in the food supply chain network is a single parameter in competitive demand markets. The demand functions are generated from price and quality. A supply chain network equilibrium condition is given by using variational inequalities. In time-sensitive supply chains, Jabarzare & Rasti-Barzoki (2019) demonstrate the importance of a product’s quality on demand. Wang et al. (2017), Taleizadeh, Moshtagh, & Moon (2018), Maiti

& Giri (2015) consider the influence feature of time-sensitive product’s quality on demand functions in decentralized or centralized supply chains. Along this line, Wang and Li (2012) consider both supply and demand of a supply chain by using quality deterioration functions and price-quality functions. Jin and Ryan (2012) bridge supply and demand of time-cost tradeoff supply chains through exponential score functions at the firm level and by a multinomial logit model at the demand level. In supply chain management literature, Liu et al. (2007) develop a leader-follower game model in a decentralized supply chain, in which the supplier determines the promised service and wholesale price first as a leader, and the retailer determines the retail price as a follower. They focus on two independent decision-makers at two levels in a decentralized supply chain. Then, they examine the effect of market factors (price, service, and lead time sensitivity factor) and operational factors on equilibrium solutions. Jin and Ryan

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(2012) develop an outsourced supply chain equilibrium model in which a buyer has to work with multiple suppliers, and the demand function depends on the retail prices and service levels.

In dual-channel supply chains, Hua, Wang, and Cheng (2010) develop a centralized and decentralized dual-channel supply chain model in Stackelberg game setting. In these papers, Stackelberg game is used as a competition framework setting in a decentralized supply chain.

This is close to this study. The work in Chapter 5 also assumes Stackelberg game framework in decentralized supply chains. However, these papers on time/price and service/price design focus on the firm level, while this work considers inter supply chains competition and collaboration of time-cost and service-cost tradeoff supply chains. There are two tradeoffs in a firm’s time- or service-cost and customers preference and the connection between them: how a time- or service-cost tradeoff supply chain strikes a balance between operational time/service level and operational cost to match the heterogeneous customers' preferences in a time-sensitive market environment. The answers of the above question remain still an open question. Hence, the customer behaviors are incorporated into a decentralized and centralized supply chain network. It will give an in-depth understanding about collaboration in the time- and service-cost tradeoff supply chains.

The other relevant strand of the supply chain network equilibrium model with time-cost competition involves processing time constraints in a supply chain network. In these special supply chain networks or supply chains, the processing time constraints must be strictly satisfied or strictly limited in time-windows. Nagurney et al. (2015) develop a supply chain network optimization model for a disaster relief organization for obtaining, storing, transporting, and distributing relief goods to certain disaster-prone regions in which a goal programming approach is utilized to enforce the timely delivery of relief items with respect to the pre-specified time targets at the demand points. Masoumi, Yu, and Nagurney (2017) present supply chain network optimization pre- and post-mergers and acquisition models in blood banking systems to yield the optimal path and link flows for operational and discarding costs of waste over time. Considering the optimal capacities of supply chain network activities, Nagurney, Yu, and Qiang (2011) design an equilibrium model for a supply chain network in the case of multiple products, with a particular focus on humanitarian healthcare. Govindan, Jafarian, Khodaverdi, and Devika (2014) propose a two-echelon location–routing problem with time-windows for sustainable supply chain network design and optimizing economic and environmental objectives in a perishable food supply chain network.

Some of the literature recognizes that competition is no longer between stand-alone companies, but rather a supply chain versus a supply chain (Christopher, 1992). Equilibrium models from the inter supply chain competition perspective have been further studied in the last two decades, including supply chain network economic model (Zhang, 2006), identical linear

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assembly chain model (Corbett & Karmarkar, 2001), and model extensions and applications (Nagurney, 2010; Rezapour, Farahani, & Pourakbar, 2017). However, compared with this model, most existing supply chain network equilibrium models focus on the coordination of pricing and processing time cost and service cost in a supply chain network. Combining pricing and processing time cost and service cost seems contradictory. This thesis work is not limited in the linear or nonlinear conversion between the conflicting objectives so our problem remains a single objective realm.

Table 2.2 summarizes the primary studies of related literature in objectives tradeoff supply chains in terms of the above-mentioned features the from firm’s level and demand’s level.

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Table 2.2. Literature review on a tradeoff supply chain network.

Articles Firm’s level Demand’s level Mathematical modeling Solution Approach preference consideration

Linear conversion Nonlinear conversion Linear conversion Nonlinear conversion

Nagurney et al. (2018) Price-quality function Spatial price network model Variational inequality

(Yeh & Chuang, 2011) Fitness value Mixed-integer nonlinear

programming Genetic algorithm (Chan & Chung, 2004) Pair-wise comparison

approach

Mixed-integer nonlinear programming

AHP and genetic algorithm (Chan et al., 2005) Analytic hierarchy

process Linear programming AHP and genetic

algorithm

(Nagurney et al., 2014) Price-time function Spatial price network model Variational inequality

(Yu & Nagurney, 2013) Discarding cost

function Spatial price network model Variational inequality

(Sabri & Beamon, 2000) Weighting method Mixed-integer linear

programming Heuristic method Decision maker preference

(Nagurney, 2010b) Weighting method Spatial price network model Variational inequality

(Masoumi et al., 2017) Discarding cost

function Spatial price network model Variational inequality

(Kadziński et al., 2017) Pair-wise comparison approach

Mixed-integer nonlinear programming

Evolutionary algorithm

(Frota Neto et al., 2008) Data envelopment

analysis

Mixed-integer linear

programming Integer programming

(Nagurney & Nagurney, 2010) Weighting method Spatial price network model Variational inequality

(Jabarzare & Rasti-Barzoki,

(S. Wang et al., 2017) Price-quality function Decentralized Game theory

model Stackelberg game

(Hua et al., 2010) Price/lead time function Centralized Game theory

model Stackelberg game

(Taleizadeh et al., 2018) Price-quality function Decentralized Game theory

model Stackelberg game

(X. Wang & Li, 2012) Quality deterioration

function Price-quality function Dynamic pricing model

(Maiti & Giri, 2015) Price-quality function Decentralized Game theory

model Stackelberg game

(Pekgün et al., 2017) Price-time function Queue model and Game

theory model Nash equilibrium

(Xuying Zhao et al., 2012) Linear utility/surplus

function Nonlinear programming Customer preference

(Zhu, 2015) Price/lead time function Decentralized Game theory

model Stackelberg game

(Jayaswal & Jewkes, 2016) Linear system of Centralized Game theory Analytic solution Customer preference

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equations model

(Jin & Ryan, 2012) Exponential score

function Multinomial logit model Game-theoretic duopoly

model Analytic solution

(Xia & Rajagopalan, 2009) Linear utility function Game-theoretic duopoly

model Analytic solution Customer preference

(Shang & Liu, 2011) Linear utility function Multinomial logit model Game-theoretic oligopoly

model Analytic solution

(Armony & Haviv, 2003) Linear utility function Duopoly-queueing model

(L. Liu et al., 2007) Price/lead time function Game-theoretic model Stackelberg game

(Rao et al., 2009) Price/lead time

distribution function Nonlinear programming

(Shen & Daskin, 2005) Weighting method Cost-based

location-inventory model

Heuristic solution approach based on genetic algorithm

(Boyaci & Ray, 2003) Price/lead time function Nonlinear programming

(De Treville et al., 2014) Marginal value of time Newsvendor model and

option-based model