Supply Chain Network Sustainability. Competition and Frequencies of Activities from Production to Distribution

Transcription

1 Under Competition and Frequencies of Activities from Production to Distribution Anna Nagurney 1,2, Min Yu 3, and Jonas Floden 2 1 Department of Operations and Information Management Isenberg School of Management University of Massachusetts Amherst, Massachusetts, USA 2 School of Business, Economics and Law University of Gothenburg, Gothenburg, Sweden 3 Pamplin School of Business Administration University of Portland, Oregon, USA INFORMS Annual Meeting, San Francisco, CA November 9-12, 2014

2 This talk is based on the paper: Nagurney, A., Yu, M., Floden, J., Supply chain network sustainability under competition and frequencies of activities from production to distribution. Computational Management Science 10(4), where a full list of references can be found.

3 Acknowledgments The research was supported, in part, by the School of Business, Economics and Law at the University of Gothenburg through its Visiting Professor Program. This support is gratefully acknowledged.

4 Outline Background and Motivation An Overview of the Relevant Literature The Sustainable Supply Chain Network Model Under Competition and Frequencies The Algorithm Numerical Examples Summary and Conclusions

5 Background and Motivation Supply chains have revolutionized the manner in which goods are produced, stored, and distributed around the globe and serve as critical infrastructure networks for economic activities.

6 Background and Motivation Today, there are over 7 billion people on our planet with more than half of the world s population residing in cities.

7 Background and Motivation Today, there are over 7 billion people on our planet with more than half of the world s population residing in cities.

8 Background and Motivation Today, there are over 7 billion people on our planet with more than half of the world s population residing in cities. The quantification of environmental impacts associated with supply chains is essential to sustainability.

9 Background and Motivation In urban areas alone, the freight transportation may account for 20-30% of the total vehicle distance traveled; and 16-50% of the emissions from transportation. The transportation sector in North America is second only to electricity generation in terms of CO 2 emissions generated. The United States: 7.8% of total emissions in 2008; Canada: 8% of total CO 2 emissions in 2007 In the European Union 27, transport emissions (freight and other) comprised 19.7% of the GHG emissions for 2010.

10 Background and Motivation Manufacturing and industrial processes release GHGs, which the Environmental Protection Agency (EPA) estimates are equivalent to approximately 350 million metric tons of carbon dioxide emissions 5% of the total US greenhouse gas emissions. Industrial processes, including manufacturing, accounted for 7.3% of the GHG emissions in 2010 in the European Union 27.

11 Background and Motivation In 2011, Hennes & Mauritz (H&M) achieved its target of a 5% year-on-year reduction in its carbon emissions. The company s CO 2 -equivalent emissions per million SEK ($148, 500) of sales were 3.16 metric tons, down from 3.33 in The reduction was achieved through Reducing the transportation of goods via air by 32%; Improving energy efficiency in its stores; and offsetting using Gold Standard-verified carbon reduction projects.

12 Background and Motivation Since Procter & Gamble (P&G) has more than halved the environmental impact through Energy usage CO 2 emissions Water usage Waste disposal It has redesigned its network through the location of its distribution centers in Europe as well as its use (and loadage) of transport modes.

13 Background and Motivation Ford is targeting a 30% reduction in carbon dioxide emissions per vehicle from its factories by 2025 after a 37% cut from 2000 to ICA, a Swedish grocery chain, reduced emissions by centralizing its distribution network. The suppliers are all routed to a single central warehouse from which ICA then sends one large consolidated truck to the store. More tonne-kms but fewer vehicle-kms, which has resulted in lower emissions, an estimated reduction of 20%.

14 Relevant Literature Sustainable Supply Chains: Beamon (1999), Sarkis (2003), Corbett and Kleindorfer (2003), Nagurney and Toyasaki (2005), Sheu, Chou, and Hu (2005), Kleindorfer, Singhal, and van Wassenhove (2005), Nagurney, Liu, and Woolley (2007), Seuring and Muller (2008), Linton, Klassen, and Jayaraman (2007), Nagurney and Woolley (2010), Boone, Jayaraman, and Ganeshan (2012) Network Economics: Nagurney and Nagurney (2011), Nagurney, Masoumi, and Yu (2012), Nagurney and Nagurney (2012), Nagurney and Yu (2012), Nagurney (2013), Yu and Nagurney (2013)

15 The Sustainable Supply Chain Network Model Under Competition and Frequencies The profit-maximizing firms compete noncooperatively in an oligopolistic manner. Firms produce substitutable, but differentiated, products. Pharmaceuticals High technology Fashion apparel Food products All the firms are concerned with their environmental impacts along their supply chains, but, possibly, to different degrees.

16 The Sustainable Supply Chain Network Topology M 1 1 D 1 1,1 D 1 1,2 Firm 1 Firm I 1 I Manufacturing 6 6M 1 n 1 M I 6 M 1 6M I n M I Transportation 6 6D 1 nd 1,1 D1,1 I 6 6D I nd I,1 Storage 6 6D 1 n D 1,2 D1,2 I 6 6D I n D I,2 Distribution 6 R 1 R nr 6

17 Conservation of Flow Equations f a : the flow on link a; x p : the nonnegative flow on path p joining (origin) node i with a (destination) demand market node; d ik : the demand for firm i s product at demand market R k. Relationship between link flows and path flows f a = p P x p δ ap, a L. (1) Relationship between path flows and demands x p = d ik, i, k. (2) p P i k Nonnegativity x p 0, p P. (3)

18 Frequencies γ a : the activity frequency of link a, e.g. The number of manufacturing runs needed The number of shipments The number of warehouse content replacements ū a : the existing capacity of link a. The production amount in a single manufacturing run The volumes (flows) of the product that the mode can transport f a ū a γ a, a L, (4)

19 Demand Prices Demand Price Functions ρ ik = ρ ik (d) = ˆρ ik (x), i, k. (5) The functions capture the demand-side competition of the competitive supply chain network.. The functions are assumed to be continuous, continuously differentiable, and monotone decreasing.

20 Operational Costs Total Operational Cost Functions ĉ a = ĉ a (f ), a L. (6) ĝ a = ĝ a (γ a ), a L. (7) The total cost expressions capture supply-side competition among the firms for resources used in the manufacture, transportation, storage, and distribution of their products. The operational cost functions is assumed to be convex and continuously differentiable.

21 Emissions Emission-Generation Functions ê a = ê a (f a, γ a ), a L. (8) The emission functions are assumed to correspond to GHG emissions as in carbon emissions. The model are also relevant to other emissions, including particulate matter (PM). These functions are also assumed to be convex and continuously differentiable.

22 The Profit Function of Firm i Maximize n R k=1 ˆρ ik (x) p P i k x p a L i ĉ a (f ) a L i ĝ a (γ a ). (9) The Environmental Impact of Firm i Minimize ê a (f a, γ a ). (10) a L i

23 The Utility Function of Firm i U i = n R k=1 ˆρ ik (x) p P i k x p a L i ĉ a (f ) a L i ĝ a (γ a ) ω i a L i ê a (f a, γ a ). Each firm weights its generated emissions in an individual way. In the case of governmental regulations, the ω i s would correspond to a tax on emissions (carbon or related). In this oligopoly competition problem, the strategic variables are the product flows and the activity frequencies, Y i (X i, Γ i ) and Y {{Y i } i = 1,..., I } (11)

24 Supply Chain Network Cournot-Nash Equilibrium A path flow and link frequency pattern Y K = I i=1 K i is said to constitute a supply chain network Cournot-Nash equilibrium if for each firm i; i = 1,..., I : where Ŷ i Û i (Y i, Ŷ i ) Û i (Y i, Ŷ i ), Y i K i, (12) (Y 1,..., Y i 1, Y i+1,..., Y I ) and K i {Y i Y i R n P i +n L i + }. An equilibrium is established if NO firm can unilaterally improve its profit by changing its product flows throughout its supply chain network, given the product flow decisions of the other firms.

25 Variational Inequality Formulation Variational Inequality (Path Flows) Determine (x, γ, λ ) K 1 satisfying: I n R i=1 k=1 p Pk i + + I i=1 a L i [ Ĉ p (x ) x p + ω i Ê p (x, γ ) x p + a L i λ aδ ap ˆρ ik (x ) n R ˆρ il (x ) x q [x p xp ] x p l=1 q Pl i [ ] ĝ a (γa ) Ê p (x, γ ) + ω i ū a λ a γ a γ a [γ a γ a ] I ū a γa xq δ aq [λ a λ a] 0, (x, γ, λ) K 1, q P i=1 a L i where K 1 {(x, γ, λ) x R n P +, γ R n L +, λ R n L + }. (13)

26 Variational Inequality Formulation Variational Inequality (Link Flows) Determine (f, d, γ, λ ) K 2, such that: [ I ĉ b (f ) f a i=1 a L i b L [ i I n R + ρ ik (d ) + + i=1 k=1 I [ ĝa (γa ) i=1 a L i I i=1 γ a ê a (fa, γa ) + ω i f a n R l=1 ρ il (d ) dil d ik + λ a ] ê a (fa, γa ) + ω i ū a λ a γ a ] [f a f a ] [d ik d ik] ] [γ a γ a ] a L i [ū a γ a f a ] [λ a λ a] 0, (f, d, γ, λ) K 2, (14) where K 2 {(f, d, γ, λ) x 0, and (1) and (2) hold, and γ 0, λ 0}.

27 Algorithm Euler Method Closed Form Expressions for Product Path Flows, Activity Frequencies, and Lagrange Multipliers x τ+1 p γ τ+1 a λ τ+1 a = max 0, x p τ + a τ ˆρ ik (x τ ) + n R l=1 ˆρ il (x τ ) x p q P i l x τ q Ĉp(x τ ) x p, ω i Êp(x τ, γ τ ) x p a L i λ τ a δ ap, (15a) { = max 0, γa τ + a τ (ūa λ τ a ĝ a(γa τ ) Êp(x τ, γ τ )) } ω i, (15b) γ a γ a ( = max {0, λ τ a + a τ xq τ δ aq ū a γa τ ) }. (15c) q P This computational procedure can be interpreted as a discrete-time adjustment process where the iteration corresponds to a time period.

28 Exampl 1 M 1 1 D 1 1,1 Firm 1 Firm M2 1 M M D2,1 1 D1, D2, D ,2 D 2,2 1 D ,2 D 2, R1 20 M 1 1 and M2 1 are domestic plants in the U.S.; M 1 2 and M2 2 are off-shore plants; The distribution centers and the demand market are in the U.S.

29 Exampl 1 Firm 1 cares about the emissions that it generates much more than Firm 2 does. ω 1 = 5, and ω 2 = 1. Firm 1 utilizes more advanced technologies in its supply chain activities in order to lower the emissions that it generates, but at relatively higher costs. The demand price functions for the two products at demand market R 1 are: ρ 11 (d) = d 11.2d , ρ 21 (d) = 2d 21.5d

30 Exampl 1 Link a ū a ĉ a(f ) ĝ a(γ a) ê a(f a, γ a) f f 1 γ γ 1.05f f 1 +.5γ1 2 + γ f f 2.5γ2 2 + γ 2.08f f 2 +.8γ γ f f 3 γ γ 3.1f f 3 + γ γ f f 4.5γ γ 4.15f f 4 + 2γ γ f f 5 γ5 2 + γ 5.08f f 5 + γ5 2 + γ f f 6 γ6 2 + γ 6.08f f 6 + γ6 2 + γ f f 7 1.5γ γ 7.05f f γ7 2 + γ f f 8 1.5γ γ 8.05f f γ8 2 + γ f f 9 γ γ 9.1f f 9 + γ γ f f 10 γ γ 10.1f f 10 + γ γ f f γ γ 11.08f f γ γ f f γ γ 12.08f f γ γ f f 13 γ γ 13.01f f γ γ f f 14 γ γ 14.01f f γ γ f f 15.8γ γ 15.05f f γ γ f f 16.8γ γ 16.05f f γ γ f f 17 γ γ 17.1f f γ γ f f 18 γ γ 18.1f f γ γ f f 19 γ γ 19.2f f γ γ f f 20 γ γ 20.2f f γ γ 20

31 Exampl 1 Link a fa γa λ a

32 Exampl 1 Firm 1 Firm 2 Demand Price Profit 12, , Emission Utility 10, , Given Firm 1 s effort to reduce its generated emissions, the consumers reveal their preferences for the product of Firm 1. Therefore, consumers are willing to pay more for Firm 1 s product. Firm 1 emits less pollution and has both a higher profit and a higher utility than Firm 2.

33 Exampl 1: Sensitivity Analysis Firm 1 and Firm 2 decide their product flows and activity frequencies without the consideration of their generated emissions. ω 1 = ω 2 = 0. Firm 1 Firm 2 Demand Price Profit 13, , Emission

34 Exampl 1: Sensitivity Analysis Firm 1 and Firm 2 decide their product flows and activity frequencies without the consideration of their generated emissions. ω 1 = ω 2 = 0. Firm 1 Firm 2 Demand Price Profit 13, , Emission Due to consumers preference, the profit of Firm 1 is still significantly higher than that of Firm 2.

35 Exampl 1: Sensitivity Analysis Firm 1 and Firm 2 decide their product flows and activity frequencies without the consideration of their generated emissions. ω 1 = ω 2 = 0. Firm 1 Firm 2 Demand Price Profit 13, , Emission The total emissions increase substantially.

36 Exampl 1: Sensitivity Analysis Firm 1 and Firm 2 decide their product flows and activity frequencies without the consideration of their generated emissions. ω 1 = ω 2 = 0. Firm 1 Firm 2 Demand Price Profit 13, , Emission The profit of Firm 2 is lower without the consideration of the emissions!

37 Exampl 1: Sensitivity Analysis Firm 1 and Firm 2 decide their product flows and activity frequencies without the consideration of their generated emissions. ω 1 = ω 2 = 0. Firm 1 Firm 2 Demand Price Profit 13, , Emission The profit of Firm 2 is lower without the consideration of the emissions! Sacrificing of profit may not be necessary for accomplishment in sustainability.

38 Example 2 & Example 3 Firm 1 Firm 2 M 1 1 D 1 1, M M M D2,1 1 D1, D2, D 1 1,2 D2,2 1 D 2 1,2 D , R 1

39 Example 2 & Example 3 Example 2 Firm 1 is considering the utilization of large trucks for distribution. Example 3 ū 21 = 30, ĉ 21 (f ) = f f 21, ĝ 21 (γ 21 ) = γ γ 21, ê 21 (f 21, γ 21 ) =.1f f γ γ 21. Link 21 represents the option of rail-truck intermodal transport with an even larger capacity. ū 21 = 50, ĉ 21 (f ) = f f 21, ĝ 21 (γ 21 ) = 1.5γ γ 21, ê 21 (f 21, γ 21 ) =.01f f γ γ 21.

40 Example 2 & Example 3 Example 2 Example 3 Link a fa γa λ a fa γa λ a

41 Demands Prices Profits Emissions Example 1 Example 2 Example 3 Firm Firm Firm Firm Firm 1 13, , , Firm 2 9, , , Firm Firm

42 Demands Prices Profits Emissions Example 1 Example 2 Example 3 Firm Firm Firm Firm Firm 1 13, , , Firm 2 9, , , Firm Firm Firm 1 is able to provide more products at even lower prices with the multiple modes for distribution. The profit of Firm 1 increases in both Examples 2 and 3; The profit of Firm 2 decline slightly in those two examples.

43 Demands Prices Profits Emissions Example 1 Example 2 Example 3 Firm Firm Firm Firm Firm 1 13, , , Firm 2 9, , , Firm Firm Due to the lower emission nature of intermodal transport, the rail-truck intermodal option is more appealing than the utilization of large trucks for distribution. In Example 2, the large truck transportation accounts for about 50% of the distribution; In Example 3, the intermodal transport accounts for more than 60% of the distribution. The emissions generated by Firm 1 in Example 3 are lower than in Example 2.

44 Example 3: Sensitivity Analysis At which value of ω 1, which represents Firm 1 s environmental concern, would the distribution from the distribution center D 1 2,2 to the demand market R 1 solely rely on the rail-truck intermodal transport? When ω 1 is equal to 43 (or greater) then f18 = 0.00, and also then γ18 is equal to ω 1 = 43 could also be an environmental tax. This example demonstrates how a policy-maker can effect positive environmental change through such a policy instrument.

45 Example 3: Sensitivity Analysis At which value of ω 1, which represents Firm 1 s environmental concern, would the distribution from the distribution center D 1 2,2 to the demand market R 1 solely rely on the rail-truck intermodal transport? When ω 1 is equal to 43 (or greater) then f18 = 0.00, and also then γ18 is equal to ω 1 = 43 could also be an environmental tax. This example demonstrates how a policy-maker can effect positive environmental change through such a policy instrument.

46 Example 3: Sensitivity Analysis At which value of ω 1, which represents Firm 1 s environmental concern, would the distribution from the distribution center D 1 2,2 to the demand market R 1 solely rely on the rail-truck intermodal transport? When ω 1 is equal to 43 (or greater) then f18 = 0.00, and also then γ18 is equal to ω 1 = 43 could also be an environmental tax. This example demonstrates how a policy-maker can effect positive environmental change through such a policy instrument.

47 Summary and Conclusions It is a competitive supply chain network model with multiple firms. Each firm produces a differentiated product by brand; Each weights the emissions that it generates through its supply chain network activities in an individual way; The firms seek to determine their optimal product flows and frequencies of operation so that their utilities are maximized. Multiple options for production, transport, storage, and distribution are allowed. The emission functions associated with a link depend both on the flow on the link as well as on the frequency of the link. Although the focus here is on carbon emissions, the framework is sufficiently general to handle other types of emissions.

48 Summary and Conclusions We utilize variational inequality theory for the formulation of the governing Cournot-Nash equilibrium conditions. The proposed computational procedure has nice features for implementation; and can be interpreted as a discrete-time adjustment process. The model could provide valuable information to both managerial decision-makers as well as to policy-makers.

49 Thank You! For more information, see: