New Retailing Problem for an Integrated Food Supply Chain in the Baking Industry
Abstract
:1. Introduction
1.1. Revenue-Sharing Contract
1.2. Buy-Back Contract
1.3. Quantity-Flexibility Contract
1.4. Food Security
2. Problem Description
3. Notations and Assumptions
Assumptions
- The article considers a supply chain system comprising of one manufacturer (supplier) and one retailer.
- The retailer has remaining inventory at the end of a season; the whole amount will be sold back to the central kitchen.
- The manufacturer considers the differential pricing strategy under O2O environment, .
- The manufacturer considers the basics of price elasticity strategy, .
- The buy-back price has to be lower than the wholesale price, .
- The items expected sales at a varying rate of quantity , where and . Here denotes the first derivative of with respect to . Note that means that expected sales are increasing over time.
4. Model Formulation
- Temperature control
- Temperature coefficient
- The quality degradation cost () at central kitchen
4.1. Retailer’s Total Profit per Unit Time
- Sales revenue (SR): The sales revenue per replenishment cycle is expressed as .
- Ordering cost (OC): The retailer’s ordering cost per replenishment cycle is .
- Purchasing cost (PC): The retailer’s purchasing cost per replenishment cycle is .
- Freight cost (FC): Fixed cost of shipment F, and various transportation costs. Namely, the retailer’s freight cost per replenishment is .
- Goodwill cost (GC): Goodwill cost of the retailer is .
- Marginal cost (MC): The retailer’s marginal cost per replenishment cycle is .
- Holding cost (HC): Based on Yang et al. [59], the retailer’s inventory level in a replenishment cycle, the retailer’s holding cost is calculated as .
- Case I: Revenue-sharing contract
- Case II: Buy-back contract
- Case III: Quantity-flexibility contract
- Case 1:
- Case 2:
- Case 3:
4.2. Manufacturer’s Total Profit per Unit Time
- Sales revenue (SR): The manufacturer’s sales revenue per replenishment cycle is expressed as .
- Wholesale value (WV): .
- Setup cost (SC): The manufacturer’s setup cost per replenishment cycle is .
- Quality degradation function (): Similar to Rong et al. [61], the manufacturer’s degradation function per replenishment is .
- Goodwill cost (GC): Goodwill cost of the manufacturer is .
- Holding cost (HC): Based on Yang et al. [59], the manufacturer’s inventory level in a replenishment cycle. The manufacturer’s holding cost is calculated as .
- CASE I. Revenue-sharing contract
- CASE II. Buy-back contract
- CASE III. Quantity-flexibility contract
- Case 1:
- Case 2:
- Case 3:
4.3. The Joint Total Profit per Unit Time
5. Solution Procedure
5.1. Determination of the Optimal for Given and
- 1.
- if, then the solutionwhich maximizesnot only exists but also is unique, where.
- 2.
- if, then the solutionwhich maximizesnot only exists but also is unique, where.
5.2. Determination of the Optimal for Given and
- 1.
- if, then the solutionwhich maximizesnot only exists but also is unique, where.
- 2.
- if, then the solutionwhich maximizesnot only exists but also is unique, where.
6. Application Example
6.1. New Retailing Framework
- Online mobile payment
- Product standardization in central kitchen
- Immediate distribution for personal services
- Big data as a service (BDaaS)
- Customer image capture
6.2. Food Supply Chain-Case Study
6.3. Alogorithm
- Step 1. Choose the initial value of .
- Step 2. Evaluate the solution of according to Equations (23)–(25).
- Step3. Use Propositions 1 to determine and the corresponding value of .
- Step 4. Let and repeat Steps 2–3.
- Step 5. If , then return to Step 4; otherwise, execute Step 6.
- Step 6. Let ; therefore, is the optimal solution and the maximum total profit per unit time is .
7. Numerical Example
7.1. Comparison among Decisions in Online and Offline Stratedgy
7.2. Sensitivity Analysis
7.3. The Discussion of Results
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
System Parameters | |
Retailer’s base demand. | |
Manufacturer’s production rate, where . | |
Manufacturer’s ordering cost per order. | |
Manufacturer’s the setup cost per order. | |
Self-price sensitivity. | |
Cross-price sensitivity. | |
Retailer’s price per unit offline. | |
Retailer’s price per unit online. | |
Goodwill cost of the manufacturer. | |
Goodwill cost of the retailer, . | |
Fixed costs per shipment. | |
All-unit freight charged per unit. | |
Retailer’s unit wholesale price, where . | |
Manufacturer’s unit production cost. | |
Retailer’s the marginal cost. | |
Manufacturer’s holding cost per unit per unit time. | |
Order quantity. | |
Expected sales. | |
Buy-back price of unsold items (paid by the manufacturer toward the retailer). | |
New wholesale price. | |
Wholesale price. | |
Revenue-sharing fraction, . | |
Quantity-flexibility fraction, . | |
The ratio between the COP at the cooling temperature, set by the manufacturer for treating the product (i.e.). | |
Total profit of the retailer during cycle time. | |
Total profit of the manufacturer during production cycle. | |
Decision Variables | |
Optimal order quantity for supply chain coordination, . | |
Number of shipments from the supplier to the retailer per production. | |
Optimal temperature . |
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Reference | Model | Demand | Revenue-Sharing Contract | Buy-Back Contract | Quantity-Flexibility Contract |
---|---|---|---|---|---|
Pang et al. [23] | Supply chain | Sales effort dependent | V | ||
Tsao & Lee [24] | Supply chain | Uncertain and promotion-sensitive | V | ||
Zhao & Wu [25] | Stochastic | V | |||
Cachon & Lariviere [26] | Supply chain | Price-dependent | V | ||
Sang [27] | Supply chain | Fuzzy demand | V | ||
Yao et al. [28] | Supply chain | Price-dependent demand | V | ||
Govindan & Malomfalean [29] | Supply chain | Constant | V | V | V |
Gong [28] | Supply chain | Stochastic | V | ||
Wang & Zipkin [30] | Supply chain | Constant | V | ||
Hou et al. [32] | Supply chain | Constant | V | ||
Ding et al. [33] | EOQ | Price-dependent demand | V | ||
Tibrewala et al. [34] | Supply chain | Stochastic | V | ||
Zhang et al. [35] | Supply chain | Stochastic | V | ||
Dai et al. [36] | Supply chain | Stochastic | V | ||
Sainathan & Groenevelt [37] | Supply chain | Constant | V | V | V |
Tsay & Lovejoy [38] | Supply chain | Stochastic | V | ||
Li & Kouvelis [39] | Supply chain | Constant | V | V | |
Sethi et al. [40] | Supply chain | Stochastic | V | ||
Wu [41] | Supply chain | Stochastic | V | ||
Milner & Kouvelis [42] | Supply chain | Stochastic | V | ||
Bag et al. [43] | EPQ | Stochastic | V | ||
Li et al. [44] | Supply chain | Constant | V | ||
Lian & Deshmukh [45] | Supply chain | Stochastic | V | ||
Present article | Food supply chain | Constant | V | V | V |
= 1000 | = 2000 | = 9 | = 170 |
= 160 | = 0.1 | = 80 | = $10 |
= $5 | = $8 | = $0.1 | = $5 |
= $15 | = $1 | = 0.55 | = 0.4 |
= 6 | = 5 | = 40 | = 100 |
= 0.5 | = $4 | ||
Online + Offline | Case I | Case II | Case III |
---|---|---|---|
46.3743 | 45.3534 | 47.8674 | |
2.4070 | 2.29413 | 2.30921 | |
32 | 32 | 10 | |
TPB | 13,108.8 | 10,937.5 | 13,754.8 |
TPFck | 18,921.1 | 6683.78 | 2019.6 |
TP | 29,692.4 | 17,621.3 | 15,774.4 |
Offline | Case I | Case II | Case III |
42.1495 | 43.634 | 46.8146 | |
2.29675 | 2.34995 | 2.38194 | |
30 | 30 | 12 | |
TPB | 1338.26 | 10,672.1 | 14,880.1 |
TPFck | 909.386 | 561.133 | 1214.06 |
TP | 2247.646 | 11233.3 | 16,094.2 |
Para. | % | CASE I | CASE II | CASE III | |||
---|---|---|---|---|---|---|---|
−50% | (46.54, 2.61, 34) | (13,005.1, 20, 060.3) | (45.89, 2.21, 32) | (10, 955.2, 7439.55) | (48.14, 2.43, 10) | (11,692.5, 2123.1) | |
−25% | (46.42, 2.59, 33) | (13,098.2, 19, 661.3) | (45.86, 2.22, 32) | (10, 945.1, 7223.54) | (48.02, 2.36, 10) | (12,991.3, 2117.9) | |
0 | (46.37, 2.40, 32) | (13,108.8, 18, 921.1) | (45.35, 2.29, 32) | (10, 937.5, 6683.78) | (47.86, 2.30, 10) | (13,754.8, 2019.6) | |
25% | (46.32, 2.39, 32) | (14,098.2, 18, 842.2) | (43.83, 2.36, 32) | (10, 627.5, 6791.53) | (42.78, 2.26, 10) | (17,128.4, 2007.1) | |
50% | (46.28, 2.38, 32) | (14,099.3, 18, 432.7) | (43.80, 2.36, 32) | (10, 628.5, 6975.53) | (42.66, 2.21, 10) | (17,195.0, 2001.6) | |
−50% | (46.44, 2.56, 32) | (14,740.1, 19, 253.6) | (46.49, 2.27, 32) | (17, 035.2, 7043.44) | (48.50, 2.29, 10) | (17,115.6, 1921.5) | |
−25% | (46.41, 2.49, 32) | (14,418.5, 19, 252.7) | (46.16, 2.27, 32) | (13, 830.6, 7025.41) | (48.20, 2.29, 10) | (13,910.8, 1940.4) | |
0 | (46.37, 2.40, 32) | (13,108.8, 18, 921.1) | (45.35, 2.29, 32) | (10, 937.5, 6683.78) | (47.86, 2.30, 10) | (13,754.8, 2019.6) | |
25% | (46.33, 2.38, 32) | (9775.51, 18,250.9) | (43.53, 2.43, 32) | (7421.73, 6989.81) | (-,-,-) | (-,-) | |
50% | (46.29, 2.31, 32) | (9454.01, 18,250.1) | (43.22, 2.44, 32) | (4217.41, 6972.22) | (-,-,-) | (-,-) | |
−50% | (46.37, 2.40, 32) | (14,102.1, 18,921.1) | (45.35, 2.29, 32) | (10,851.1, 6683.78) | (-,-,-) | (-,-) | |
−25% | (46.37, 2.40, 32) | (13,099.5, 18,921.1) | (45.35, 2.29, 32) | (10,854.5, 6683.78) | (-,-,-) | (-,-) | |
0 | (46.37, 2.40, 32) | (13,108.8, 18,921.1) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
25% | (46.37, 2.40, 32) | (10,094.5, 18,921.1) | (45.35, 2.29, 32) | (11,149.5, 6683.78) | (-,-,-) | (-,-) | |
50% | (46.37, 2.40, 32) | (10,092.1, 18,921.1) | (45.35, 2.29, 32) | (11,172.1, 6683.78) | (-,-,-) | (-,-) | |
−50% | (47.67, 2.43, 32) | (13,184.3, 19,282.1) | (45.93, 2.40, 32) | (10,976.9, 7067.72) | (-,-,-) | (-,-) | |
−25% | (47.00, 2.41, 32) | (13,140.2, 19,267.1) | (45.38, 2.40, 32) | (10,951.4, 7037.41) | (-,-,-) | (-,-) | |
0 | (46.37, 2.40, 32) | (13,108.8, 18,921.1) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
25% | (45.76, 2.09, 33) | (10,054.8, 18,236.4) | (43.33, 2.29, 33) | (10,901.1, 6678.07) | (-,-,-) | (-,-) | |
50% | (45.17, 1.93, 33) | (10,013.4, 18,220.9) | (40.38, 2.29, 33) | (10,820.5, 6596.76) | (-,-,-) | (-,-) | |
−50% | (48.50, 2.33, 31) | (13,238.7, 19,299.7) | (45.83, 2.46, 31) | (10,977.9, 6604.68) | (-,-,-) | (-,-) | |
−25% | (47.40, 2.38, 32) | (13,166.6, 19,276.1) | (45.71, 2.45, 31) | (10,966.7, 6655.55) | (-,-,-) | (-,-) | |
0 | (46.37, 2.40, 32) | (13,108.8, 18,921.1) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
25% | (45.41, 2.45, 33) | (10,029.9, 18,227.2) | (43.03, 2.26, 32) | (10,586.2, 6960.57) | (-,-,-) | (-,-) | |
50% | (44.50, 2.47, 34) | (9964.94, 18,202.2) | (42.25, 2.21, 32) | (10,546.9, 6914.61) | (-,-,-) | (-,-) | |
−50% | (46.56, 2.30, 32) | (10,081.7, 19,590.1) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
−25% | (46.44, 2.31, 32) | (10,064.3, 19,580.8) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
0 | (46.37, 2.40, 32) | (13,108.8, 18,921.1) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
25% | (46.28, 2.42, 32) | (13,139.9, 18,912.4) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
50% | (46.19, 2.43, 32) | (13,182.9, 18,872.9) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
−50% | (43.85, 0.07, 34) | (13,626.1, 17,007.4) | (45.35, 0.06,34) | (10,626.1, 7007.54) | (-,-,-) | (-,-) | |
−25% | (43.85, 1.07, 33) | (13,626.1, 17,007.4) | (45.35, 1.06,34) | (10,626.1, 7007.54) | (-,-,-) | (-,-) | |
0 | (46.37, 2.41, 32) | (13,108.8, 18,921.1) | (45.35, 2.29,32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
25% | (-,-,-) | (-,-) | (-,-,-) | (-,-) | (-,-,-) | (-,-) | |
50% | (-,-,-) | (-,-) | (-,-,-) | (-,-) | (-,-,-) | (-,-) | |
−50% | 26.3743 | (10,069.1, 6335.23) | (26.37, 0.67, 32) | (10,069.1, 7335.23) | (-,-,-) | (-,-) | |
−25% | 43.8481 | (10,626.1, 7007.54) | (43.84, 1.53, 32) | (10,626.1, 7007.54) | (-,-,-) | (-,-) | |
0 | 46.3743 | (13,108.8, 18,921.1) | (45.35, 2.29, 32) | (10,937.5, 6683.78) | (-,-,-) | (-,-) | |
25% | (-,-,-) | (-,-) | (-,-,-) | (-,-) | (-,-,-) | (-,-) | |
50% | (-,-,-) | (-,-) | (-,-,-) | (-,-) | (-,-,-) | (-,-) |
Increasing Parameter(s) | Case I | Case II | Case III |
---|---|---|---|
Company’s goodwill is an intangible asset owned by and associated with operation of a company. Thus, a trademark is often an important investment in protecting the intellectual property of a manufacturer. | More specifically, in a high critical ratio environment revenue sharing contracts are more profitable for the manufacturer than buyback contracts. | With goodwill cost exists, the channel coordination provides allocation of the supply chain’s profit if . | |
The contract offers accepted by the retailer, two-part tariff and quantity discount increases the efficiency of the channel in the terms of channel profit. | The contract provides an enormous motivation for retailer to give orders more than usual without concerning stock out in inventory. | With goodwill cost exists, the channel coordination provides allocation of the supply chain’s profit if . | |
The online retailer provides the freight subsidy to the manufacturer increase the profit of the total profit. | Allows a retailer to return unsold inventory up to a specified amount at an agreed upon price/freight fee, resulting in higher product availability and higher profits for both the retailer and the manufacturer. | ||
A wholesale price is plausibly below transportation fee, the members may have adopted a coordinating contract. | Focusing on the transportation costs. The retailer and the manufacturer will be covering the transportation cost. | ||
If , which a wholesale price is greater than marginal cost, which is in sharp contrast to the optimal wholesale price under a revenue-sharing contract. | The manufacturer would like to increase his own profit by increasing the wholesale price and buy-back price, where , . | ||
With revenue-sharing fraction, the manufacturer willingly reduces its wholesale price and makes money by sharing the retailer’s revenue. | If effort is significant (i.e., ), the effect dominates the quantity effect, and the wholesale price falls. | ||
To monitor the food quality in the distribution, the absolute temperature decreased by a coefficient of , the manufacturer will increase the channel profit. | To monitor the food quality in the distribution, the absolute temperature decreased by a coefficient of , the manufacturer will increase the channel profit. | ||
To monitor the food quality in the distribution, the absolute temperature decreased by a coefficient of , the manufacturer will increase the channel profit. | To monitor the food quality in the distribution, the absolute temperature decreased by a coefficient of , the manufacturer will increase the channel profit. |
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Xu, N.; Huang, Y.-F.; Weng, M.-W.; Do, M.-H. New Retailing Problem for an Integrated Food Supply Chain in the Baking Industry. Appl. Sci. 2021, 11, 946. https://doi.org/10.3390/app11030946
Xu N, Huang Y-F, Weng M-W, Do M-H. New Retailing Problem for an Integrated Food Supply Chain in the Baking Industry. Applied Sciences. 2021; 11(3):946. https://doi.org/10.3390/app11030946
Chicago/Turabian StyleXu, Ning, Yung-Fu Huang, Ming-Wei Weng, and Manh-Hoang Do. 2021. "New Retailing Problem for an Integrated Food Supply Chain in the Baking Industry" Applied Sciences 11, no. 3: 946. https://doi.org/10.3390/app11030946
APA StyleXu, N., Huang, Y. -F., Weng, M. -W., & Do, M. -H. (2021). New Retailing Problem for an Integrated Food Supply Chain in the Baking Industry. Applied Sciences, 11(3), 946. https://doi.org/10.3390/app11030946