Price Differentiation and Inventory Decisions in a Socially Responsible Dual-Channel Supply Chain with Partial Information Stochastic Demand and Cannibalization
Abstract
:1. Introduction
2. Literature Review
2.1. Dual-Channel Supply Chain
2.2. Price Differentiation and Cannibalization
2.3. Corporate Social Responsibility
2.4. Partial Demand Information
3. Deterministic Demand
- (i)
- Centralized analysis: The manufacturer and seller simultaneously decide the , and
- (ii)
- Decentralized analysis: The manufacturer decides the and whereas the seller responds by setting the .
- Both the manufacturer and the retailer exhibit risk-neutral behavior and are rational decision makers.
- An information symmetry exists in the SC, hence, both players (manufacturer and retailer) have the same information.
3.1. Centralized Analysis (Deterministic Demand)
3.2. Decentralized Analysis (Deterministic Demand)
4. Stochastic Demand
4.1. Centralized Analysis
- 1.
- Given the pricing and CSR investment decisions, () the unique optimal order quantities/inventories are:
- 2.
- Given the pricing and CSR investment decisions (),is jointly concave in optimal order quantities/inventories.
- Step 1: Input , , , , , , . Select the probability distribution function for the demand.
- Step 2: Simultaneously solve (numerically) Equations (37)–(39) to determine , and
- Step 3: Set
- Step 4: Determine order quantity/inventory using Equation (32).
4.2. Decentralized Analysis
- 1.
- Maximum price,that satisfies
- 2.
- where.
- Step 1: Input , , , , , , , and choose the probability distribution for the demand.
- Step 2: Simultaneously solve (numerically) Equations (44)–(47) to determine , and
- Step 3: Set
- Step 4: Determine order quantity/inventory such that , where . and . Also, , .
5. Stochastic Demand with Partial Demand Information
5.1. Centralized Analysis
5.2. Decentralized Analysis
6. Numerical Analysis
6.1. Deterministic Demand
6.2. Stochastic Demand
6.3. Impact of Differentiation Price
7. Conclusions, Limitations, and Future Research Suggestions
Funding
Conflicts of Interest
Appendix A. Proof of Proposition 1
Scenarios | Remarks |
---|---|
, | Yields , which fails to achieve price differentiation. Therefore, discarded. |
, | Infeasible, since Equation (A4) is violated. |
, | A unique solution is obtainable, , since . Thus, , |
, | Infeasible, since Equation (A4) is violated, since , thus |
Appendix B. Proof of Proposition 2
Appendix C. Proof of Proposition 3
- Part (1)
- Part (2)
Appendix D. Proof of Proposition 4
Appendix E. Proof of Proposition 5
- Part (1)
- Part (2)
Appendix F. Proof of Proposition 6
Appendix G. Proof of Proposition 7
Appendix H. Proof of Proposition 8
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Literature | SC Configuration (Closed-Loop, Network, Others) | SC Coordination Contracts (Revenue-Sharing, Cost-Sharing, Others) | Societal Consideration (Greening, Corporate Investment, Govt. Incentives, Others) | Market Demand Behavior (Deterministic, Stochastic, Uncertain) | SC Players Attitude (Risk-Less, Risk-Neutral, Risk-Averse) | Decisions (Pricing, Inventory, Others) |
---|---|---|---|---|---|---|
[85] | Channel selection in supply chain | None | Greening investment | Deterministic | Risk-less | Pricing |
[71] | Multi-period network | None | CRS investment | Deterministic | Risk-less | Multi-criteria (Pricing, Quantity, CSR activities) |
[86] | Multi-level supply chain network | None | CSR activities | Deterministic | Risk-less | Pricing, CSR activities |
[87] | Supply chain network | None | Emission reduction | Deterministic | Risk-less | Pricing, CRS activities |
[88] | Single product, Single channel | Wholesale price via subgames | CSR activities | Deterministic | Risk-less | Pricing, CRS activities |
[89] | Multi-agent network | None | CSR activities | Uncertain (supply-side disruptions, social risks) | Risk-less | Pricing, CRS activities |
[90] | Multi-level global supply chain network | None | CSR activities | Deterministic | Risk-less | Pricing, CSR investment |
[3] | Dual-channel supply chain | Franchise-fee | Consumer-surplus | Deterministic | Risk-less | Quantity, replenishment cycles |
[4] | Dual-channel, Three echelon | Quantity discount, Franchise fee | None | Deterministic | Risk-less | Quantity, replenishment cycles |
[91] | Single product, Single channel | Discount | Consumer-surplus | Deterministic | Risk-less | Pricing |
[64] | Multi-channel, Multi-echelon | Two-part tariff | Consumer-surplus | Deterministic | Risk-less | Pricing |
[65] | Duopolistic retailers, Two-layer supply chain | Two-part tariff | Consumer-surplus | Deterministic | Risk-less | Pricing |
[66] | Three-echelon supply chain | All unit quantity discount | None | Deterministic | Risk-less | Pricing |
[63] | Three-layer supply chain | Revenue-sharing | Consumer-surplus | Deterministic | Risk-less | Pricing |
[67] | Single product, Single channel | Profit division | Consumer-surplus | Deterministic | Risk-less | Pricing |
[68] | Single product, Single channel | All unit quantity discount | Consumer-surplus | Deterministic | Risk-less | Pricing |
[69] | Closed-loop supply chain | Revenue-sharing | Consumer-surplus | Deterministic | Risk-less | Pricing |
[76] | Single channel, Multiple retailers | Cost-sharing | CSR investment, Consumer-surplus | Deterministic | Risk-less | Pricing |
[23] | Single channel, Single product | Revenue-sharing | CSR activities | Stochastic | Risk-neutral | Pricing |
[72] | Single product, Single channel | Profit-sharing | CSR activities | Stochastic | Risk-neutral | Pricing, CRS investment, Inventory |
[92] | Two-period manufacturer-retailer supply chain | two-part tariff contracts | Cost learning effects | Deterministic | Risk-neutral | Pricing |
[93] | Single product, Single channel | Transfer payment mechanism | CSR activities | Deterministic | Risk-neutral | Pricing, CSR effort |
[83] | Single product, Single channel, Multiple retailers | Price | CSR activities, Govt. Subsidiary | Deterministic | Risk-neutral | Pricing, CSR investment, Govt. subsidiary |
[94] | Single product, Single channel, Multiple retailers, Third party collectors | Profit-sharing | CRS investment | Deterministic | Risk-neutral | Pricing, CSR investment |
[73] | Closed-loop | Revenue-sharing | CSR investment | Deterministic | Risk-neutral | Pricing |
[95] | Closed-loop | Revenue-sharing | CSR investment | Deterministic | Risk-neutral | Pricing, CSR investment |
[7] | Single channel, Market differentiation | None | Greening investment | Stochastic | Risk-neutral | Pricing, Greening effort, Inventory |
[6] | Dual-channel, Market differentiation | Cost-sharing, Revenue-sharing | Greening investment | Deterministic | Risk-averse | Pricing, Greening effort |
[96] | Single product, Single channel | Profit-sharing | CSR investment | Stochastic | Risk-neutral | Pricing, CSR (effort) investment, Inventory |
[97] | Single product, Closed-loop | None | Carbon tax | Stochastic | Risk-neutral | Pricing, Carbon emission, Inventory |
This paper | Dual-channel, Market differentiation | None | CSR investment | Stochastic | Risk-neutral | Pricing, CSR (effort) investment, Inventory |
Parameters | Description |
---|---|
Cost of manufacturing per unit | |
Maximum perceived cumulative deterministic (riskless) demand (Market share), | |
Price sensitivity, | |
Coefficient of Corporate Social Responsibility (CSR) investment impact on demand, | |
Cannibalization (demand leakage) proportion, | |
Adjusted price-and CSR dependent deterministic demand in retail (regular) channel | |
Adjusted price-and CSR dependent deterministic demand in online (direct) channel demand | |
Mean of stochastic demand factor, , = online | |
Standard deviation of stochastic demand factor, , , = online | |
Probability distribution function of price-and CSR dependent stochastic demand in market segment , = online/direct | |
Cumulative Probability distribution function of price-and CSR dependent stochastic demand in market segment , = online | |
Price-and CSR dependent stochastic demand, | |
Manufacturer’s revenue (payoff), | |
Retailer (sellers)’s revenue (payoff), | |
Supply chain (total) revenue (payoff), | |
Decisions | |
Manufacturer (m) | |
Wholesale price per unit, | |
Price per unit of standard product in direct (online) channel | |
Differentiation price, | |
Investment on CSR activities, | |
Seller/retailer (s) | |
Price per unit for a product in regular channel, | |
Order quantity (inventory) for regular channel, | |
Order quantity (inventory) for online channel, | |
Scripts and Accents | |
“ | Superscript for decentralized analysis, () |
“ | Superscript for centralized analysis, () |
“ | Accent used for a control decision, when price-and-CSR dependent demand is deterministic |
“ | Accent used for a control decision, when price-and-CSR dependent demand is stochastic with partial information (unknown distribution) |
Expected value of random variable, such that |
Decisions/Outcomes | Remarks/Conditions | |
---|---|---|
, if | ||
, if | ||
if , | ||
if |
Decisions/Outcomes | Remarks/Conditions | |
---|---|---|
, | ||
if , and | ||
, if and | ||
- | ||
, if | ||
if , |
Decisions/Outcomes | Remarks/Conditions | |
---|---|---|
, if | ||
, if | ||
, if | ||
if , | ||
, if , | ||
if , | ||
if , |
Decisions/Outcomes | Remarks/Conditions | |
---|---|---|
, if | ||
, if , | ||
, if , | ||
if , | ||
if, | ||
, if and |
Decentralized Analysis | Centralized Analysis | |||||||||||||||
0 | 0 | 11.43 | 8.21 | 10.36 | 0.00 | 857.14 | 2571.43 | 918.37 | 12,857.10 | 13,775.50 | 10.00 | 7.50 | 0.00 | 2000.00 | 2000.00 | 15,000.00 |
2 | 0 | 11.44 | 8.22 | 10.36 | 18.42 | 858.37 | 2575.11 | 921.00 | 12,875.50 | 13,796.50 | 10.01 | 7.50 | 25.08 | 2003.34 | 2003.34 | 14,924.70 |
4 | 0 | 11.47 | 8.23 | 10.39 | 74.32 | 862.07 | 2586.21 | 928.95 | 12,931.00 | 13,860.00 | 10.03 | 7.52 | 101.35 | 2013.42 | 2013.42 | 14,695.30 |
6 | 0 | 11.51 | 8.26 | 10.43 | 169.64 | 868.31 | 2604.92 | 942.45 | 13,024.60 | 13,967.00 | 10.08 | 7.54 | 231.91 | 2030.46 | 2030.46 | 14,300.80 |
8 | 0 | 11.58 | 8.29 | 10.48 | 307.79 | 877.19 | 2631.58 | 961.83 | 13,157.90 | 14,119.70 | 10.14 | 7.57 | 422.22 | 2054.79 | 2054.79 | 13,722.10 |
10 | 0 | 11.67 | 8.33 | 10.56 | 493.83 | 888.89 | 2666.67 | 987.65 | 13,333.30 | 14,321.00 | 10.22 | 7.61 | 680.53 | 2086.96 | 2086.96 | 12,930.10 |
0 | 0.05 | 11.44 | 8.24 | 10.37 | 0.00 | 808.51 | 2595.74 | 860.12 | 12,766.00 | 13,626.10 | 10.04 | 7.58 | 0.00 | 1868.85 | 2065.57 | 14,754.10 |
2 | 0.05 | 11.45 | 8.25 | 10.38 | 18.16 | 809.66 | 2599.43 | 862.56 | 12,784.10 | 13,646.70 | 10.05 | 7.59 | 24.27 | 1871.92 | 2068.97 | 14,681.30 |
4 | 0.05 | 11.47 | 8.26 | 10.40 | 73.26 | 813.12 | 2610.56 | 869.96 | 12,838.80 | 13,708.80 | 10.07 | 7.60 | 98.03 | 1881.19 | 2079.21 | 14,459.40 |
6 | 0.05 | 11.52 | 8.29 | 10.44 | 167.21 | 818.97 | 2629.31 | 882.51 | 12,931.00 | 13,813.50 | 10.12 | 7.62 | 224.25 | 1896.84 | 2096.51 | 14,078.00 |
8 | 0.05 | 11.59 | 8.32 | 10.50 | 303.34 | 827.29 | 2656.02 | 900.53 | 13,062.40 | 13,962.90 | 10.18 | 7.65 | 408.12 | 1919.19 | 2121.21 | 13,519.00 |
10 | 0.05 | 11.67 | 8.36 | 10.57 | 486.59 | 838.24 | 2691.18 | 924.52 | 13,235.30 | 14,159.80 | 10.26 | 7.69 | 657.46 | 1948.72 | 2153.85 | 12,754.80 |
0 | 0.1 | 11.44 | 8.27 | 10.39 | 0.00 | 760.56 | 2619.72 | 803.41 | 12,676.10 | 13,479.50 | 10.08 | 7.66 | 0.00 | 1741.94 | 2129.03 | 14,516.10 |
2 | 0.1 | 11.45 | 8.28 | 10.39 | 17.90 | 761.64 | 2623.41 | 805.68 | 12,693.90 | 13,499.60 | 10.09 | 7.67 | 23.49 | 1744.75 | 2132.47 | 14,445.60 |
4 | 0.1 | 11.48 | 8.29 | 10.42 | 72.23 | 764.87 | 2634.56 | 812.54 | 12,747.90 | 13,560.40 | 10.11 | 7.68 | 94.87 | 1753.25 | 2142.86 | 14,230.90 |
6 | 0.1 | 11.53 | 8.32 | 10.46 | 164.84 | 770.33 | 2653.35 | 824.17 | 12,838.80 | 13,663.00 | 10.16 | 7.70 | 216.97 | 1767.59 | 2160.39 | 13,862.10 |
8 | 0.1 | 11.59 | 8.35 | 10.51 | 298.98 | 778.10 | 2680.12 | 840.88 | 12,968.30 | 13,809.20 | 10.22 | 7.73 | 394.72 | 1788.08 | 2185.43 | 13,321.80 |
10 | 0.1 | 11.68 | 8.39 | 10.58 | 479.51 | 788.32 | 2715.33 | 863.13 | 13,138.70 | 14,001.80 | 10.29 | 7.77 | 635.55 | 1815.13 | 2218.49 | 12,583.90 |
0 | 0.15 | 11.45 | 8.30 | 10.40 | 0.00 | 713.29 | 2643.36 | 748.20 | 12,587.40 | 13,335.60 | 10.12 | 7.74 | 0.00 | 1619.05 | 2190.48 | 14,285.70 |
2 | 0.15 | 11.46 | 8.31 | 10.41 | 17.65 | 714.29 | 2647.06 | 750.30 | 12,605.00 | 13,355.30 | 10.13 | 7.74 | 22.75 | 1621.62 | 2193.96 | 14,217.40 |
4 | 0.15 | 11.49 | 8.32 | 10.43 | 71.21 | 717.30 | 2658.23 | 756.65 | 12,658.20 | 13,414.90 | 10.15 | 7.76 | 91.87 | 1629.39 | 2204.47 | 14,009.50 |
6 | 0.15 | 11.53 | 8.35 | 10.47 | 162.51 | 722.38 | 2677.05 | 767.40 | 12,747.90 | 13,515.30 | 10.19 | 7.78 | 210.04 | 1642.51 | 2222.22 | 13,652.60 |
8 | 0.15 | 11.60 | 8.38 | 10.53 | 294.72 | 729.61 | 2703.86 | 782.85 | 12,875.50 | 13,658.40 | 10.25 | 7.81 | 381.97 | 1661.24 | 2247.56 | 13,130.10 |
10 | 0.15 | 11.68 | 8.42 | 10.60 | 472.59 | 739.13 | 2739.13 | 803.40 | 13,043.50 | 13,846.90 | 10.33 | 7.85 | 614.71 | 1685.95 | 2280.99 | 12,417.20 |
0 | 0.2 | 11.46 | 8.33 | 10.42 | 0.00 | 666.67 | 2666.67 | 694.44 | 12,500.00 | 13,194.40 | 10.16 | 7.81 | 0.00 | 1500.00 | 2250.00 | 14,062.50 |
2 | 0.2 | 11.47 | 8.34 | 10.42 | 17.41 | 667.59 | 2670.38 | 696.38 | 12,517.40 | 13,213.80 | 10.16 | 7.82 | 22.04 | 1502.35 | 2253.52 | 13,996.30 |
4 | 0.2 | 11.49 | 8.35 | 10.45 | 70.22 | 670.39 | 2681.56 | 702.23 | 12,569.80 | 13,272.10 | 10.19 | 7.83 | 89.00 | 1509.43 | 2264.15 | 13,794.90 |
6 | 0.2 | 11.54 | 8.38 | 10.49 | 160.23 | 675.11 | 2700.42 | 712.14 | 12,658.20 | 13,370.40 | 10.23 | 7.85 | 203.44 | 1521.39 | 2282.09 | 13,449.30 |
8 | 0.2 | 11.61 | 8.41 | 10.54 | 290.55 | 681.82 | 2727.27 | 726.37 | 12,784.10 | 13,510.50 | 10.29 | 7.88 | 369.82 | 1538.46 | 2307.69 | 12,943.80 |
10 | 0.2 | 11.69 | 8.45 | 10.61 | 465.81 | 690.65 | 2762.59 | 745.30 | 12,949.60 | 13,694.90 | 10.37 | 7.93 | 594.88 | 1560.98 | 2341.46 | 12,254.60 |
Decentralized Analysis | Centralized Analysis | |||||||||||||||
0 | 0 | 11.36 | 8.14 | 10.29 | 890.03 | 2538.17 | 0.00 | 597.62 | 12,162.00 | 12,759.60 | 9.93 | 7.42 | 2043.97 | 1955.45 | 0.00 | 14,317.10 |
2 | 0 | 11.37 | 8.15 | 10.30 | 891.28 | 2541.87 | 17.82 | 599.57 | 12,179.80 | 12,779.40 | 9.94 | 7.42 | 2047.30 | 1958.83 | 24.40 | 14,341.40 |
4 | 0 | 11.40 | 8.16 | 10.32 | 895.03 | 2553.04 | 71.91 | 605.49 | 12,233.50 | 12,839.00 | 9.96 | 7.44 | 2057.38 | 1969.06 | 98.58 | 14,415.00 |
6 | 0 | 11.44 | 8.18 | 10.36 | 901.35 | 2571.87 | 164.18 | 615.54 | 12,324.10 | 12,939.60 | 10.01 | 7.46 | 2074.39 | 1986.34 | 225.60 | 14,539.20 |
8 | 0 | 11.51 | 8.22 | 10.41 | 910.37 | 2598.68 | 297.94 | 630.00 | 12,453.10 | 13,083.10 | 10.07 | 7.49 | 2098.70 | 2011.02 | 410.83 | 14,716.80 |
10 | 0 | 11.60 | 8.26 | 10.49 | 922.23 | 2633.98 | 478.15 | 649.30 | 12,622.90 | 13,272.20 | 10.15 | 7.53 | 2130.84 | 2043.64 | 662.34 | 14,951.60 |
0 | 0.05 | 11.37 | 8.17 | 10.30 | 840.70 | 2563.39 | 0.00 | 535.65 | 12,067.80 | 12,603.40 | 9.97 | 7.51 | 1910.65 | 2023.67 | 0.00 | 14,063.40 |
2 | 0.05 | 11.38 | 8.18 | 10.31 | 841.87 | 2567.10 | 17.56 | 537.44 | 12,085.30 | 12,622.80 | 9.98 | 7.51 | 1913.72 | 2027.11 | 23.59 | 14,086.90 |
4 | 0.05 | 11.40 | 8.19 | 10.33 | 845.39 | 2578.29 | 70.87 | 542.81 | 12,138.30 | 12,681.10 | 10.00 | 7.52 | 1922.98 | 2037.48 | 95.29 | 14,158.10 |
6 | 0.05 | 11.45 | 8.22 | 10.37 | 851.33 | 2597.15 | 161.78 | 551.92 | 12,227.50 | 12,779.40 | 10.05 | 7.54 | 1938.64 | 2055.00 | 218.01 | 14,278.20 |
8 | 0.05 | 11.52 | 8.25 | 10.43 | 859.79 | 2624.01 | 293.53 | 565.01 | 12,354.60 | 12,919.60 | 10.11 | 7.57 | 1961.00 | 2080.02 | 396.84 | 14,449.70 |
10 | 0.05 | 11.60 | 8.29 | 10.50 | 870.92 | 2659.35 | 470.99 | 582.55 | 12,521.90 | 13,104.50 | 10.19 | 7.62 | 1990.53 | 2113.06 | 639.45 | 14,676.40 |
0 | 0.1 | 11.37 | 8.20 | 10.32 | 792.08 | 2588.25 | 0.00 | 475.33 | 11,974.90 | 12,450.20 | 10.01 | 7.59 | 1781.70 | 2089.62 | 0.00 | 13,818.00 |
2 | 0.1 | 11.38 | 8.21 | 10.32 | 793.17 | 2591.97 | 17.31 | 476.93 | 11,992.20 | 12,469.10 | 10.02 | 7.59 | 1784.52 | 2093.10 | 22.81 | 13,840.80 |
4 | 0.1 | 11.41 | 8.22 | 10.35 | 796.47 | 2603.17 | 69.84 | 481.81 | 12,044.30 | 12,526.20 | 10.04 | 7.60 | 1793.03 | 2103.60 | 92.16 | 13,909.60 |
6 | 0.1 | 11.45 | 8.25 | 10.39 | 802.03 | 2622.06 | 159.42 | 490.03 | 12,132.30 | 12,622.30 | 10.09 | 7.63 | 1807.40 | 2121.34 | 210.79 | 14,025.70 |
8 | 0.1 | 11.52 | 8.28 | 10.44 | 809.95 | 2648.95 | 289.22 | 501.80 | 12,257.50 | 12,759.30 | 10.14 | 7.66 | 1827.92 | 2146.66 | 383.55 | 14,191.60 |
10 | 0.1 | 11.61 | 8.32 | 10.51 | 820.37 | 2684.35 | 463.99 | 517.59 | 12,422.40 | 12,940.00 | 10.22 | 7.70 | 1855.02 | 2180.09 | 617.72 | 14,410.60 |
0 | 0.15 | 11.38 | 8.23 | 10.33 | 744.14 | 2612.75 | 0.00 | 416.62 | 11,883.30 | 12,299.90 | 10.05 | 7.67 | 1656.91 | 2153.41 | 0.00 | 13,580.60 |
2 | 0.15 | 11.39 | 8.24 | 10.34 | 745.16 | 2616.47 | 17.06 | 418.05 | 11,900.40 | 12,318.40 | 10.06 | 7.67 | 1659.49 | 2156.93 | 22.08 | 13,602.60 |
4 | 0.15 | 11.41 | 8.25 | 10.36 | 748.24 | 2627.69 | 68.84 | 422.38 | 11,951.80 | 12,374.10 | 10.08 | 7.68 | 1667.29 | 2167.55 | 89.18 | 13,669.20 |
6 | 0.15 | 11.46 | 8.28 | 10.40 | 753.43 | 2646.61 | 157.12 | 429.73 | 12,038.40 | 12,468.20 | 10.12 | 7.71 | 1680.45 | 2185.48 | 203.92 | 13,781.50 |
8 | 0.15 | 11.52 | 8.31 | 10.45 | 760.83 | 2673.54 | 285.01 | 440.31 | 12,161.90 | 12,602.20 | 10.18 | 7.74 | 1699.24 | 2211.07 | 370.91 | 13,942.00 |
10 | 0.15 | 11.61 | 8.35 | 10.52 | 770.56 | 2708.97 | 457.14 | 454.45 | 12,324.30 | 12,778.80 | 10.26 | 7.78 | 1724.04 | 2244.83 | 597.07 | 14,153.70 |
0 | 0.2 | 11.38 | 8.26 | 10.34 | 696.87 | 2636.91 | 0.00 | 359.47 | 11,793.00 | 12,152.50 | 10.09 | 7.74 | 1536.07 | 2215.15 | 0.00 | 13,350.60 |
2 | 0.2 | 11.39 | 8.27 | 10.35 | 697.82 | 2640.63 | 16.82 | 360.73 | 11,809.80 | 12,170.60 | 10.09 | 7.75 | 1538.43 | 2218.70 | 21.38 | 13,372.00 |
4 | 0.2 | 11.42 | 8.28 | 10.37 | 700.69 | 2651.87 | 67.86 | 364.58 | 11,860.50 | 12,225.10 | 10.12 | 7.76 | 1545.55 | 2229.42 | 86.33 | 13,436.40 |
6 | 0.2 | 11.46 | 8.31 | 10.41 | 705.53 | 2670.80 | 154.87 | 371.10 | 11,945.90 | 12,317.00 | 10.16 | 7.78 | 1557.58 | 2247.52 | 197.37 | 13,545.20 |
8 | 0.2 | 11.53 | 8.34 | 10.46 | 712.41 | 2697.77 | 280.88 | 380.49 | 12,067.60 | 12,448.10 | 10.22 | 7.81 | 1574.73 | 2273.35 | 358.88 | 13,700.40 |
10 | 0.2 | 11.61 | 8.38 | 10.54 | 721.47 | 2733.23 | 450.44 | 393.03 | 12,227.70 | 12,620.70 | 10.29 | 7.86 | 1597.37 | 2307.42 | 577.43 | 13,905.30 |
Decentralized Analysis | Centralized Analysis | |||||||||||||||
0 | 0 | 11.37 | 8.15 | 10.29 | 0.00 | 907.14 | 2571.43 | 403.64 | 12,500.00 | 12,903.60 | 9.94 | 7.44 | 0.00 | 2050.00 | 2000.00 | 14,128.10 |
2 | 0 | 11.36 | 8.16 | 10.30 | 17.89 | 916.81 | 2566.60 | 405.76 | 12,536.40 | 12,942.10 | 9.95 | 7.44 | 24.46 | 2053.30 | 2003.30 | 14,152.50 |
4 | 0 | 11.36 | 8.17 | 10.33 | 72.16 | 945.98 | 2552.01 | 411.11 | 12,646.50 | 13,057.60 | 9.97 | 7.45 | 98.83 | 2063.26 | 2013.26 | 14,226.30 |
6 | 0 | 11.35 | 8.19 | 10.36 | 164.73 | 995.15 | 2527.42 | 416.51 | 12,833.20 | 13,249.70 | 10.01 | 7.48 | 226.14 | 2080.08 | 2030.08 | 14,350.90 |
8 | 0 | 11.34 | 8.23 | 10.42 | 298.88 | 1065.20 | 2492.40 | 416.38 | 13,101.40 | 13,517.80 | 10.07 | 7.51 | 411.73 | 2104.11 | 2054.11 | 14,528.90 |
10 | 0 | 11.33 | 8.27 | 10.49 | 479.53 | 1157.41 | 2446.30 | 402.18 | 13,458.60 | 13,860.70 | 10.15 | 7.54 | 663.62 | 2135.87 | 2085.87 | 14,764.10 |
0 | 0.05 | 11.37 | 8.18 | 10.31 | 0.00 | 857.80 | 2596.10 | 343.19 | 12,406.80 | 12,750.00 | 9.98 | 7.52 | 0.00 | 1917.21 | 2066.39 | 13,876.10 |
2 | 0.05 | 11.37 | 8.19 | 10.32 | 17.63 | 866.91 | 2591.76 | 345.14 | 12,441.80 | 12,786.90 | 9.99 | 7.52 | 23.64 | 1920.24 | 2069.74 | 13,899.70 |
4 | 0.05 | 11.37 | 8.20 | 10.34 | 71.11 | 894.39 | 2578.65 | 350.02 | 12,547.60 | 12,897.60 | 10.01 | 7.54 | 95.51 | 1929.39 | 2079.85 | 13,971.00 |
6 | 0.05 | 11.36 | 8.22 | 10.38 | 162.30 | 940.72 | 2556.55 | 354.86 | 12,726.80 | 13,081.70 | 10.05 | 7.56 | 218.50 | 1944.84 | 2096.93 | 14,091.40 |
8 | 0.05 | 11.35 | 8.26 | 10.43 | 294.43 | 1006.71 | 2525.08 | 354.44 | 12,984.30 | 13,338.70 | 10.11 | 7.59 | 397.65 | 1966.90 | 2121.31 | 14,263.30 |
10 | 0.05 | 11.33 | 8.30 | 10.50 | 472.30 | 1093.55 | 2483.66 | 340.76 | 13,326.90 | 13,667.70 | 10.19 | 7.63 | 640.59 | 1996.05 | 2153.53 | 14,490.40 |
0 | 0.1 | 11.38 | 8.21 | 10.32 | 0.00 | 809.16 | 2620.42 | 284.35 | 12,315.00 | 12,599.30 | 10.02 | 7.60 | 0.00 | 1788.71 | 2130.65 | 13,632.20 |
2 | 0.1 | 11.37 | 8.22 | 10.33 | 17.37 | 817.71 | 2616.56 | 286.13 | 12,348.60 | 12,634.70 | 10.02 | 7.61 | 22.87 | 1791.49 | 2134.04 | 13,655.00 |
4 | 0.1 | 11.37 | 8.23 | 10.35 | 70.08 | 843.54 | 2604.91 | 290.56 | 12,450.10 | 12,740.60 | 10.05 | 7.62 | 92.36 | 1799.87 | 2144.29 | 13,723.90 |
6 | 0.1 | 11.36 | 8.25 | 10.39 | 159.93 | 887.06 | 2585.26 | 294.88 | 12,622.10 | 12,917.00 | 10.09 | 7.64 | 211.22 | 1814.03 | 2161.59 | 13,840.30 |
8 | 0.1 | 11.35 | 8.29 | 10.44 | 290.08 | 949.06 | 2557.29 | 294.18 | 12,869.10 | 13,163.30 | 10.15 | 7.67 | 384.26 | 1834.24 | 2186.29 | 14,006.50 |
10 | 0.1 | 11.34 | 8.33 | 10.52 | 465.24 | 1030.62 | 2520.47 | 281.02 | 13,197.60 | 13,478.70 | 10.23 | 7.71 | 618.71 | 1860.92 | 2218.91 | 14,225.90 |
0 | 0.15 | 11.38 | 8.24 | 10.33 | 0.00 | 761.19 | 2644.41 | 227.07 | 12,224.40 | 12,451.50 | 10.05 | 7.68 | 0.00 | 1664.29 | 2192.86 | 13,396.00 |
2 | 0.15 | 11.38 | 8.25 | 10.34 | 17.12 | 769.21 | 2641.02 | 228.69 | 12,256.60 | 12,485.30 | 10.06 | 7.68 | 22.13 | 1666.82 | 2196.29 | 13,418.10 |
4 | 0.15 | 11.37 | 8.26 | 10.36 | 69.06 | 793.40 | 2630.80 | 232.69 | 12,354.00 | 12,586.70 | 10.08 | 7.70 | 89.36 | 1674.49 | 2206.66 | 13,484.80 |
6 | 0.15 | 11.37 | 8.28 | 10.40 | 157.60 | 834.17 | 2613.56 | 236.50 | 12,519.00 | 12,755.50 | 10.13 | 7.72 | 204.30 | 1687.43 | 2224.17 | 13,597.40 |
8 | 0.15 | 11.36 | 8.32 | 10.46 | 285.82 | 892.23 | 2589.03 | 235.56 | 12,755.80 | 12,991.40 | 10.18 | 7.75 | 371.54 | 1705.90 | 2249.15 | 13,758.10 |
10 | 0.15 | 11.34 | 8.36 | 10.53 | 458.32 | 968.61 | 2556.75 | 222.93 | 13,070.60 | 13,293.50 | 10.26 | 7.79 | 597.92 | 1730.27 | 2282.13 | 13,970.20 |
0 | 0.2 | 11.38 | 8.27 | 10.35 | 0.00 | 713.89 | 2668.06 | 171.31 | 12,135.10 | 12,306.40 | 10.09 | 7.75 | 0.00 | 1543.75 | 2253.13 | 13,167.20 |
2 | 0.2 | 11.38 | 8.28 | 10.35 | 16.88 | 721.38 | 2665.13 | 172.77 | 12,166.00 | 12,338.70 | 10.10 | 7.76 | 21.42 | 1546.06 | 2256.60 | 13,188.60 |
4 | 0.2 | 11.38 | 8.29 | 10.38 | 68.07 | 743.96 | 2656.32 | 176.36 | 12,259.40 | 12,435.70 | 10.12 | 7.77 | 86.50 | 1553.05 | 2267.08 | 13,253.20 |
6 | 0.2 | 11.37 | 8.31 | 10.41 | 155.33 | 782.02 | 2641.47 | 179.69 | 12,417.50 | 12,597.20 | 10.16 | 7.79 | 197.71 | 1564.84 | 2284.76 | 13,362.20 |
8 | 0.2 | 11.36 | 8.35 | 10.47 | 281.66 | 836.22 | 2620.32 | 178.52 | 12,644.40 | 12,822.90 | 10.22 | 7.83 | 359.42 | 1581.67 | 2310.00 | 13,517.70 |
10 | 0.2 | 11.35 | 8.39 | 10.54 | 451.56 | 907.50 | 2592.50 | 166.42 | 12,945.80 | 13,112.20 | 10.29 | 7.87 | 578.15 | 1603.86 | 2343.29 | 13,722.80 |
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Raza, S.A. Price Differentiation and Inventory Decisions in a Socially Responsible Dual-Channel Supply Chain with Partial Information Stochastic Demand and Cannibalization. Sustainability 2020, 12, 9577. https://doi.org/10.3390/su12229577
Raza SA. Price Differentiation and Inventory Decisions in a Socially Responsible Dual-Channel Supply Chain with Partial Information Stochastic Demand and Cannibalization. Sustainability. 2020; 12(22):9577. https://doi.org/10.3390/su12229577
Chicago/Turabian StyleRaza, Syed Asif. 2020. "Price Differentiation and Inventory Decisions in a Socially Responsible Dual-Channel Supply Chain with Partial Information Stochastic Demand and Cannibalization" Sustainability 12, no. 22: 9577. https://doi.org/10.3390/su12229577