Joint Decisions of Inventory Optimization and Order Allocation for OmniChannel MultiEchelon Distribution Network
Abstract
:1. Introduction
2. Literature Review
2.1. OmniChannel and Inventory Optimization Policy
2.2. Order Allocation and Fulfillment
3. Problem Description and Modelling
3.1. Problem Description
3.2. Problem Assumptions and Parameter Definitions
 (1)
 A single kind of product with the same quality and price is considered;
 (2)
 The online and offline demands of each node are stochastic and independent and follow a normal distribution;
 (3)
 Each node adopts a periodic review policy and the replenishment between different echelons had the lead time;
 (4)
 Each node has a different distribution region, and the distribution region between nodes of the same echelon does not overlap, and between different echelon nodes the upper nodes will cover the whole region of lower replenishment nodes;
 (5)
 We measure the location and the shortest delivery time of online customers by the closest node in the distribution range and choose the node with minimum cost within distribution networks to fulfill online orders;
 (6)
 Except suppliers, each echelon node in the distribution network has the inventory capacity limit;
 (7)
 Lateral transshipments are only conducted after the realization of actual demands: we adopt an emergency transshipment policy;
 (8)
 For offline orders, it only occurs stockout when the store node requests lateral transshipment and still cannot be satisfied; for online orders, it occurs stockout only when the node whose total cost including the stockout cost is still the lowest. The loss will be calculated at that node.
3.3. The OmniChannel MultiEchelon Joint Optimization Model
4. The GABased Solution Approach
 (1)
 Encoding
$${Q}_{ukt}$$

$${y}_{{k}^{\prime}kt}$$

$${z}_{knt}$$

 (2)
 Initializing
 (3)
 Fitness function
 (4)
 Selection
 (5)
 Crossover and mutation
5. Numerical Experiments
5.1. Network Setup
5.2. Numerical Results
5.2.1. Algorithm Performance Analysis
5.2.2. Computational Results
5.3. Managerial Insights
5.3.1. Impact of Demand Fluctuation Ratio
5.3.2. Impact of Time Penalty Coefficient
6. Conclusions
6.1. Concluding Remarks
6.2. Theoretical Contributions
6.3. Research Limitations and Future Directions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. The Optimization Model—Decentralized Inventory and Closest Allocation (<DI, CA>)
Appendix A.2. The Optimization Model—Integrated Inventory and Closest Allocation (<II, CA>)
Appendix A.3. The Optimization Model—Decentralized Inventory and MinimumCost Allocation (<DI, MA>)
Appendix B
Strategies  TC (¥)  Service Level  Echelons  $\mathit{T}{\mathit{C}}_{\mathit{n}}\text{}\left(\text{\xa5}\right)$  CR (¥)  CT (¥)  CH (¥)  CF (¥)  CS (¥) 

<DI, CA>  60,928.6  92.90%  CDCs  23,178.15  9750.4    3984.75  9443   
RDCs  21,778.6  7675.6    3429  10,674    
Stores  15,971.85  4110.6    2003.25  6408  3450  
<II, CA>  54,659.64  95.40%  CDCs  20,722.95  8250    3029.95  9443   
RDCs  20,889.85  7156.35    3059.5  10,674    
Stores  13,046.84  4114.5  398.34  1926  6368  240  
<DI, MA>  56,225.45  95.70%  CDCs  32,853.85  9399.5    4340.35  19,114   
RDCs  13,936.95  6554.95    2756  4626    
Stores  9434.65  3757.65    1833  3664  180  
<II, MA>  53,262.18  98.10%  CDCs  30,217.65  8360    2743.65  19,114   
RDCs  13,962.3  6581.3    2737  4644    
Stores  9082.23  3624.8  57.68  1705.75  3664  30 
Nodes  The Average Inventory Level $\mathbf{of}\text{}\mathbf{Each}\text{}\mathbf{Strategy}\text{}\left({\mathit{Q}}_{\mathit{n}\prime \mathit{n}}\right)$  The Total Cost (¥) $\mathbf{of}\text{}\mathbf{Each}\text{}\mathbf{Strategy}\text{}\left(\mathit{T}{\mathit{C}}_{\mathit{n}}\right)$  

<DI, CA>  <II, CA>  <DI, MA>  <II, MA>  <DI, CA>  <II, CA>  <DI, MA>  <II, MA>  
1  4186  3500  4555  3500  12,080.65  10,845.85  16,791.8  15,649.6 
2  4678  4000  5326  4100  11,097.5  9877.1  16,062.05  14,568.05 
3  1379  1300  841  835  5980.5  5779.05  1493.4  1510.4 
4  1285  1360  1285  1365  4152.45  4308.7  4208.3  4364.5 
5  1844  1600  1402  1402  5848.9  5227.2  2447.4  2447.4 
6  1837  1750  1808  1789  5796.75  5574.9  5787.9  5640 
7  273  269  273  269  1613.9  1600.1  1613.9  1600.1 
8  182  175  116  116  996.55  1123.65  343.95  283.95 
9  267  270  267  270  1207.65  1212.75  1207.65  1215 
10  274  300  227  227  2245.75  1442.89  674.4  612.08 
11  399  360  399  360  1980.35  1845.8  1980.35  1845.8 
12  400  380  300  300  1669.3  1600.3  696.3  696.3 
13  343  320  343  320  1939.8  1849.2  1939.8  1860.5 
14  152  182  137  137  1709.6  884.6  340.05  334.8 
15  264  300  260  260  2608.95  1487.55  638.25  633.75 
Nodes  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 

1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 
2  1  1  0  0  0  0  0  0  0  0  0  0  0  0  0 
3  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0 
4  1  1  0  1  0  0  0  0  0  0  0  0  0  0  0 
5  0  1  0  0  1  0  0  0  0  0  0  0  0  0  0 
6  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0 
7  1  0  1  0  0  0  1  1  0  0  0  0  0  0  0 
8  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0 
9  0  0  0  1  0  0  0  0  1  0  0  0  0  0  0 
10  1  0  0  1  0  0  0  0  0  1  0  0  0  0  0 
11  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0 
12  0  1  0  0  1  0  0  0  0  0  0  0  0  0  0 
13  0  0  0  0  0  0  0  0  0  0  1  0  1  0  0 
14  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0 
15  1  1  0  0  0  0  0  0  0  0  0  0  0  0  1 
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Sets  

$S$  Sets of suppliers, $s\in S$ 
$W$  Sets of central distribution centers, $\text{}w\in W$ 
$U$  Sets of regional distribution centers, $u\in U$ 
$K$  Sets of stores, $k\in K$ 
$T$  Sets of time periods, $t\in T$ 
Parameters  
$i$  i = r for offline demand; i = e for online demand 
${D}_{nt}^{i}$  Demand of site n for i demand in the beginning of period t, n = {w, u, k}, i = {r, e} 
${A}_{n}^{i}$  Inventory capacity of site n for i demand, n = {w, u, k}$,\text{}{A}_{n}$=${A}_{n}^{r}+{A}_{n}^{e}$ 
${g}_{n}$  Unit replenishment cost at site n, n = {w, u, k} 
${h}_{n}$  Unit inventory holding cost at site n, n = {w, u, k} 
${d}_{n{n}^{\prime}}$  The distance from site n to site ${n}^{\prime}$, n = ${n}^{\prime}$=$\left\{w,u,k\right\}$ 
${c}_{n{n}^{\prime}}$  Unit transshipment cost from site n to site ${n}^{\prime}$, n = ${n}^{\prime}$ = $\left\{k\right\}$ 
${f}_{n{n}^{\prime}}$  Unit delivery cost for online demand of site n to be fulfilled by site ${n}^{\prime}$, n = ${n}^{\prime}$ = $\left\{w,u,k\right\}$ 
${\mathsf{\theta}}_{n{n}^{\prime}}$  ${\mathsf{\theta}}_{n{n}^{\prime}}\in \left[0,1\right]$, the probability of order loss when online orders of site n allocate to site ${n}^{\prime}$, n = ${n}^{\prime}$ = $\left\{w,u,k\right\}$ 
${b}_{n}^{i}$  Unit stockout cost for i demand of site n, n = {w, u, k}, i = {r, e} 
${L}_{{n}^{\prime}n}$  Lead–time from site ${n}^{\prime}$ to site n, ${n}^{\prime}$ = {s, w, u}, n = $\left\{w,u,k\right\}$ 
Decision Variables  
${Q}_{{n}^{\prime}nt}^{i}$  The replenishment amount from site ${n}^{\prime}$ to site n for i demand in the beginning of period t, $\text{}{n}^{\prime}$ = {s, w, u}, n = $\left\{w,u,k\right\}$, i = {r, e} 
${x}_{kt}^{r}$  The amount of inventory used to fulfill offline demand by store k in the period t, $k\in K$ 
${v}_{n{n}^{\prime}t}^{e}$  The amount of inventory used to fulfill online demand of site n by site ${n}^{\prime}$ in the period t, n = ${n}^{\prime}$ = $\left\{w,u,k\right\}$ 
${y}_{n{n}^{\prime}t}$  The amount of transshipment inventory from site n to site ${n}^{\prime}$ in the period t, n = ${n}^{\prime}$ = $\left\{k\right\}$ 
${z}_{n{n}^{\prime}t}$  Binary variable which is equal to 1 if the online demand of site n is fulfilled by site ${n}^{\prime}$ in period t, 0 otherwise, n = ${n}^{\prime}$ = $\left\{w,u,k\right\}$ 
${I}_{nt}^{+}$  The inventory on hand of site n at the end of period t, n = $\left\{w,u,k\right\}$ 
${B}_{nt}^{i}$  The stockout amount of site n for i demand at the end of period t, n = $\left\{w,u,k\right\}$, i = {r, e} 
Parameter  CDCs  RDCs  Stores 

Unit Replenishment Cost (¥)  1.1  1.55  1.95 
Unit Inventory Holding Cost (¥)  0.7  1  1.5 
Unit Transshipment Cost (¥)      2 
Unit Stockout Cost (¥)  30  30  30 
Nodes  Coordinate  $({\mathit{u}}_{\mathit{n}\mathit{r}},{\mathit{\sigma}}_{\mathit{n}\mathit{r}}^{2},{\mathit{A}}_{\mathit{n}}^{\mathit{r}})$  $({\mathit{u}}_{\mathit{n}\mathit{e}},{\mathit{\sigma}}_{\mathit{n}\mathit{e}}^{2},{\mathit{A}}_{\mathit{n}}^{\mathit{e}})$ 

1  (32, 82)  (, , 4500)  (45, 20, 1500) 
2  (29, 49)  (, , 6000)  (30, 10, 1000) 
3  (17, 84)  (, , 1000)  (24, 16, 500) 
4  (50, 80)  (, , 1000)  (15, 6, 500) 
5  (41, 41)  (, , 1500)  (18, 10, 500) 
6  (20, 44)  (, , 1500)  (20, 8, 500) 
7  (10, 72)  (20, 7, 150)  (16, 5, 150) 
8  (10, 90)  (15, 5, 120)  (8, 4, 100) 
9  (49, 94)  (25, 10, 200)  (10, 2, 100) 
10  (55, 90)  (30, 12, 200)  (9, 5, 100) 
11  (42, 23)  (28, 9, 250)  (15, 7, 150) 
12  (53, 37)  (33, 14, 300)  (10, 6, 100) 
13  (12, 29)  (20, 6, 200)  (17, 6, 150) 
14  (20, 30)  (18, 5, 100)  (6, 4, 100) 
15  (22, 30)  (35, 10, 200)  (8, 3, 100) 
Node  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 

Corresponding Replenishment Node  0  0  1  1  2  2  3  3  4  4  5  5  6  6  6 
Lead time/days  8  9  3  4  4  3  1  1  1  1  2  2  2  1  1 
Methods  GA  CPLEX  

(Population Size, Iteration)  (100, 200)    
Crossover  0.7  0.8    
mutation  0.01  0.05  0.01  0.05   
Result  61,179.64  61,221.40  61,105.38  60,928.60  60,899.35 
Computation time (s)  124.55  146.91  132.25  120.16  201.08 
$\mathbf{Strategies}\text{}\left(\mathit{\omega}\right)$  $\mathit{T}\mathit{C}{\mathit{\%}}_{\mathit{\omega}}$  $\mathbf{S}\mathbf{e}\mathbf{r}\mathbf{v}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{Level}{\mathit{\%}}_{\mathit{\omega}}$  Echelons  $\mathit{T}{\mathit{C}}_{\mathit{n}}{\mathit{\%}}_{\mathit{\omega}}$  $\mathit{C}\mathit{R}{\mathit{\%}}_{\mathit{\omega}}$  $\mathit{C}\mathit{T}{\mathit{\%}}_{\mathit{\omega}}$  $\mathit{C}\mathit{H}{\mathit{\%}}_{\mathit{\omega}}$  $\mathit{C}\mathit{F}{\mathit{\%}}_{\mathit{\omega}}$  $\mathit{C}\mathit{S}{\mathit{\%}}_{\mathit{\omega}}$ 

<II, CA>  10.29  2.69  CDCs  10.59  15.39    23.96     
RDCs  4.08  6.76    10.78      
Stores  18.31  0.09  M  3.86  0.62  93.04  
<DI, MA>  7.72  3.01  CDCs  −41.74  3.60    −8.92  −102.41   
RDCs  36.01  14.60    19.63  56.66    
Stores  40.93  8.59    8.50  42.82  94.78  
<II, MA>  12.58  5.60  CDCs  −30.37  14.26    31.15  −102.41   
RDCs  35.89  14.26    20.18  56.49    
Stores  43.14  11.82  M  14.85  42.82  99.13 
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Qu, T.; Huang, T.; Nie, D.; Fu, Y.; Ma, L.; Huang, G.Q. Joint Decisions of Inventory Optimization and Order Allocation for OmniChannel MultiEchelon Distribution Network. Sustainability 2022, 14, 5903. https://doi.org/10.3390/su14105903
Qu T, Huang T, Nie D, Fu Y, Ma L, Huang GQ. Joint Decisions of Inventory Optimization and Order Allocation for OmniChannel MultiEchelon Distribution Network. Sustainability. 2022; 14(10):5903. https://doi.org/10.3390/su14105903
Chicago/Turabian StyleQu, Ting, Tianxiang Huang, Duxian Nie, Yelin Fu, Lin Ma, and George Q. Huang. 2022. "Joint Decisions of Inventory Optimization and Order Allocation for OmniChannel MultiEchelon Distribution Network" Sustainability 14, no. 10: 5903. https://doi.org/10.3390/su14105903