Shipment Consolidation Policy under Uncertainty of Customer Order for Sustainable Supply Chain Management
Abstract
:1. Introduction
2. Literature Review
3. Mathematical Models
3.1. Quantity-Based Policy to Consideration of Order Cancellation
- : fixed cost of replenish inventory
- : unit replenish cost
- : fixed cost of dispatching shipment to customer
- : unit dispatch cost
- : holding cost per unit per unit time
- : Poisson demand rate
- : order cancellation cost per unit
- : order cancellation rate per unit time ()
- : unit environmental cost during dispatch
- : dispatch quantity (integer, decision variable, )
- : number of dispatch cycles within an inventory replenishment cycle (integer, decision variable, )
- : replenishment quantity ()
- Order Cancellation Cost: Since the company will not dispatch its products until q units of demand accumulate, the order cancellation rate is . Thus, the order cancellation cost per dispatch cycle is . Since there are n dispatch cycles in a replenishment cycle, the customer waiting cost per replenishment cycle is:
- Replenishment Cost: Since the replenishment quantity, Q, is equal to (see Figure 1), the replenishment cost is:
- Dispatch Cost: Since the dispatch quantity is , the dispatch cost in a dispatch cycle is . There are n dispatch cycles during a replenishment cycle, and, thus, the dispatch cost during the cycle is:
- Inventory Holding Cost: At the beginning of a replenishment cycle, the inventory level is . This implies that the inventory level is kept at throughout the first dispatch cycle, and incurs expected holding cost of . For the ith dispatch cycle, the expected holding cost is . Hence, the total expected inventory holding cost is given by:Using the above results, the expected cost during a replenishment cycle is computed by:Conversely, the expression for the long-run average profit, , is given by:
- The simple enumeration algorithm (SEA_Q)
3.2. Time-Based Policy to Consideration of Order Cancellation
- : dispatch cycle time (decision variable)
- : number of dispatch cycles within an inventory replenishment cycle
- : replenishment quantity (integer, decision variable)
- : demand during dispatch cycles
- Order Cancellation Cost: Since the company will not dispatch its products until T units of time lapses, the order cancellation rate is . Thus, the order cancellation cost per dispatch cycle is . Since there are n dispatch cycles in a replenishment cycle, the customer waiting cost per replenishment cycle is:
- Replenishment Cost: The expected replenishment quantity is equal to the expected total demand within a replenishment cycle (see Figure 2). The expected replenishment cost is computed by:
- Dispatch Cost: The expected dispatch quantity in a dispatch cycle is , and the expected dispatch cost in a dispatch cycle is . There are dispatch cycles during a replenishment cycle, and, thus, the expected dispatch cost during a replenishment cycle is computed by:
- Inventory Holding Cost: Let I(t) denote the inventory level at time t.Since holding cost is h, the inventory holding cost is given by:Using the above results, the expected cost during a replenishment cycle is computed by:Conversely, the expression for the long-run average profit, TP(Q,T), is given by:
- The simple enumeration algorithm (SEA_T)
4. Numerical Results
4.1. Sensitivity Analysis
4.2. Comparison of the Quantity-Based and the Time-Based Policies
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Quantity-Based Policy | Time-Based Policy | |||||
---|---|---|---|---|---|---|
n | q | Total Cost | T | Total Cost | ||
increases | increases | increases | increases | No impact | increases | |
No impact | increases | increases | No impact | increases | increases | |
h | decreases | decreases | increases | decreases | decreases | increases |
No impact | decreases | increases | No impact | decreases | increases |
i | Quantity-Based Policy | Time-Based Policy | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
n | q | Total Cost (TC) | (=TCi − TCi−1) | T | Total Cost (TC) | (=TCi − TCi−1) | |||||
1 | 5 | 4 | 4 | 16.36 | - | - | 11 | 1.74 | 25.61 | - | - |
2 | 10 | 6 | 4 | 20.45 | 4.09 | 0.82 | 11 | 2.26 | 29.67 | 4.06 | 0.81 |
3 | 15 | 7 | 4 | 23.85 | 3.40 | 0.68 | 10 | 2.66 | 32.04 | 3.07 | 0.61 |
4 | 20 | 8 | 6 | 26.73 | 2.88 | 0.58 | 10 | 2.96 | 34.44 | 2.40 | 0.48 |
5 | 25 | 8 | 8 | 29.20 | 2.47 | 0.49 | 10 | 3.22 | 36.55 | 2.11 | 0.42 |
6 | 30 | 8 | 8 | 31.34 | 2.14 | 0.43 | 10 | 3.46 | 38.49 | 1.94 | 0.39 |
7 | 35 | 9 | 9 | 33.21 | 1.87 | 0.37 | 10 | 3.67 | 40.25 | 1.76 | 0.35 |
8 | 40 | 10 | 9 | 34.86 | 1.65 | 0.33 | 9 | 3.90 | 40.50 | 1.60 | 0.32 |
9 | 45 | 10 | 9 | 36.33 | 1.47 | 0.29 | 9 | 4.08 | 42.04 | 1.54 | 0.31 |
10 | 50 | 11 | 9 | 37.64 | 1.31 | 0.26 | 9 | 4.26 | 43.41 | 1.37 | 0.27 |
11 | 55 | 12 | 9 | 38.82 | 1.18 | 0.24 | 9 | 4.42 | 44.71 | 1.30 | 0.26 |
12 | 60 | 12 | 9 | 39.89 | 1.07 | 0.21 | 9 | 4.58 | 45.96 | 1.25 | 0.25 |
13 | 65 | 13 | 9 | 40.86 | 0.97 | 0.19 | 9 | 4.73 | 47.16 | 1.20 | 0.24 |
14 | 70 | 14 | 10 | 41.74 | 0.88 | 0.18 | 9 | 4.87 | 48.31 | 1.15 | 0.23 |
15 | 75 | 14 | 11 | 42.55 | 0.81 | 0.16 | 8 | 5.05 | 47.59 | 1.07 | 0.21 |
i | Quantity-Based Policy | Time-Based Policy | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
n | q | Total Cost (TC) | (=TCi − TCi−1) | T | Total Cost (TC) | (=TCi − TCi−1) | |||||
1 | 2 | 5 | 6 | 17.17 | - | - | 11 | 1.74 | 25.61 | - | - |
2 | 4 | 6 | 5 | 19.22 | 2.05 | 1.03 | 11 | 1.62 | 28.61 | 3.00 | 1.50 |
3 | 6 | 7 | 4 | 20.83 | 1.61 | 0.81 | 11 | 1.51 | 31.75 | 3.14 | 1.57 |
4 | 8 | 8 | 4 | 22.21 | 1.38 | 0.69 | 12 | 1.34 | 35.07 | 3.32 | 1.66 |
5 | 10 | 9 | 3 | 23.42 | 1.21 | 0.61 | 12 | 1.32 | 38.54 | 3.38 | 1.69 |
6 | 12 | 10 | 3 | 24.50 | 1.08 | 0.54 | 12 | 1.25 | 41.98 | 3.44 | 1.72 |
7 | 14 | 11 | 3 | 25.50 | 1.00 | 0.50 | 12 | 1.19 | 45.50 | 3.52 | 1.76 |
8 | 16 | 12 | 3 | 26.43 | 0.93 | 0.47 | 12 | 1.13 | 49.09 | 3.59 | 1.80 |
9 | 18 | 13 | 2 | 27.30 | 0.87 | 0.44 | 12 | 1.09 | 52.71 | 3.62 | 1.81 |
10 | 20 | 14 | 2 | 28.12 | 0.82 | 0.41 | 12 | 1.04 | 56.38 | 3.67 | 1.84 |
11 | 22 | 15 | 2 | 28.90 | 0.78 | 0.39 | 12 | 1.00 | 60.09 | 3.71 | 1.86 |
12 | 24 | 16 | 2 | 29.66 | 0.76 | 0.38 | 12 | 0.97 | 63.82 | 3.73 | 1.87 |
13 | 26 | 17 | 2 | 30.38 | 0.72 | 0.36 | 12 | 0.94 | 67.58 | 3.76 | 1.88 |
14 | 28 | 18 | 1 | 31.08 | 0.70 | 0.35 | 12 | 0.91 | 71.37 | 3.79 | 1.90 |
15 | 30 | 19 | 1 | 31.75 | 0.67 | 0.34 | 12 | 0.88 | 75.17 | 3.80 | 1.90 |
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Kang, K.; Hong, K.-s.; Kim, K.H.; Lee, C. Shipment Consolidation Policy under Uncertainty of Customer Order for Sustainable Supply Chain Management. Sustainability 2017, 9, 1675. https://doi.org/10.3390/su9091675
Kang K, Hong K-s, Kim KH, Lee C. Shipment Consolidation Policy under Uncertainty of Customer Order for Sustainable Supply Chain Management. Sustainability. 2017; 9(9):1675. https://doi.org/10.3390/su9091675
Chicago/Turabian StyleKang, Kyunghoon, Ki-sung Hong, Ki Hong Kim, and Chulung Lee. 2017. "Shipment Consolidation Policy under Uncertainty of Customer Order for Sustainable Supply Chain Management" Sustainability 9, no. 9: 1675. https://doi.org/10.3390/su9091675