Research On Joint Optimization Method For Sustainable Facility Location And Multi-commodity Pricing

Facility locations affect the company’s market exposure and subsequently its profit,whose success is essential for the survival of the company.Rapid global industrialization has led to environmental issues and climate change,which captures world-wide attention.Nowdays,sustainability is an important issue in supply chain management.Achieving sustainability means companies concern not only economic objective,but also relevant environmental influence.In particular,carbon emission is identified by the government and consumers as one of the most important metrics on environmental influences.The government regulations about carbon emission force companies to re-examine the facility location strategy.Meanwhile with increasing globalization and heterogeneous tastes of consumers,many companies consider offering substitutable commodities and/or complementary commodities.As commodities offered by a company are commonly substitutable or complementary to each other,the demand for each commodity should depend on the prices of all commodities in the same market.The accurate characterization of the demand-price relationship is among the core ingredients to make facility location decision.In much of the existing literature,the facility location problems only focus on cases where the demand-price relationship is defined on a restricted pricing price domain.In reality,a company could set the price of one commodity extremely high,even presented with the possibility of having no demand period.Nevertheless,this commodity could still affect the demands of other commodities due to the substitutable or complementary relationship.Thus,this thesis investigates the joint optimization problem of sustainable facility location and multi-commodity pricing with concerns on carbon emission and the substitutable or complementary relationship among commodities.The main research work is summarized as follows:(1)Joint optimization method of sustainable monopolistic manufacturing facility location and multi-commodity pricingUnder carbon trading scheme,this thesis studies the facility location and multi-commodity pricing problem for a monopoly manufacturing company which produces multiple substitutable and/or complementary commodities.Firstly,based on the complementarity demand function which is defined on the entire nonnegative price domain and characterizes the demand-price relationship in a more accurate way,the joint optimization model of sustainable monopolistic manufacturing facility location and multi-commodity pricing is proposed to maximize the profit.This model is a 0-1 mixed integer non-concave quadratic program with equilibrium constraints,which is strongly NP-hard.Secondly,in order to reduce the complexity of solving the model,this program is reformulated as a 0-1 mixed integer concave program with a bounded closed set through introducing big-M coefficients and auxiliary binary variables and applying piece-wise linear envelope method.An efficient branch-and-refine algoritlun with global convergence is proposed.Finally,numerical examples illustrate the effectiveness of the proposed model and algorithm and demonstrate the effect of emission limitation and carbon trading on decisions.The results provide some strategic support and management suggestion for manufacturing company manager in the monopolistic market.(2)Joint optimization method of sustainable competitive manufacturing facility location and multi-commodity pricingAccounting for the impact of the location decisions on customers while anticipating the reaction of competitor firm is essential.This thesis considers two manufacturing companies.One manufacturing company is planning to install facilities to produce multiple substitutable and/or complementary commodities for a certain market,and another competitor manufacturing company has facilities installed and offered these multiple substitutable and/or complementary commodities to customers.The new entrant company anticipates the reaction of the competitor company to make the location and pricing decisions.After observing the decisions of the new entrant company,the competitor company adjust its supply strategy.The result is a Stackelberg leader-follower game where the new entrant company is referred to as the leader and the competitor company is the follower.Firstly,based on the complementarity demand function which is defined on the entire nonnegative price domain and characterizes the demand-price relationship in a more accurate way,the joint optimization model of sustainable competitive manufacturing facility location and multi-commodity pricing is proposed,which is a bi-level program model.The upper level model is the profit maximization model of the leader,which is a 0-1 mixed integer non-concave quadratic program with equilibrium constraints.The lower level model is the profit maximization model of the follower,which is a non-concave quadratic program with equilibrium constraints.The bi-level program is strongly NP-hard.Secondly,in order to reduce the complexity of solving the model,this program is transformed to a one-level 0-1 mixed integer non-concave quadratic program with equilibrium constraints by applying Karush-Kuhn-Tucker(KKT)condition and further reformulated as a 0-1 mixed integer concave program with a bounded closed set through introducing big-M coefficients and auxiliary binary variables and applying McCormick approximation method.An efficient Benders algorithm is proposed.Thirdly,numerical examples illustrate the effectiveness of the proposed model and algorithm and demonstrate the effect of emission limitation and carbon trading on decisions.The results provide some strategic support and management suggestion for manufacturing company manager in the competitive market.Finally,the proposed joint optimization model of sustainable competitive manufacturing facility location and multi-commodity pricing is extended to multiple followers,covering more forms of market organization.(3)Joint optimization method of sustainable cross-docking center location and multi-commodity pricingUnder carbon trading scheme,this thesis considers a two-echelon supply chain problem,where cross-docking centers of a distribution company are to be established to satisfy the demands arriving to a set of manufacturing companies from a set of customers for multiple substitutable and/or complementary commodities.Firstly,based on the complementarity demand function which is defined on the entire nonnegative price domain and characterizes the demand-price relationship in a more accurate way,the joint optimization model of sustainable cross-docking center location and multi-commodity pricing is proposed to maximize the profit of the two-echelon supply chain.This model is a 0-1 mixed integer non-concave quadratic program with equilibrium constraints,which is strongly NP-hard.Secondly,in order to reduce the complexity of solving the model,this program is reformulated as a 0-1 mixed integer concave program with a bounded closed set through introducing big-M coefficients and auxiliary binary variables and applying McCormick approximation method.An efficient branch-and-refine algorithm based on bilinear-specific branching rule with global convergence is proposed.Finally,numerical examples illustrate the effectiveness of the proposed model and algorithm and demonstrate the effect of emission limitation and carbon trading on decisions.The results provide some strategic support and management suggestion for distribution company manager in the competitive market.