Background
Introduction
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Development and implementation of a general and integrated model of inventory management and distribution in a three-level regional blood transfusion network (regional blood center or main base, community blood centers, hospital).
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Simultaneous implementation of blood inventory management and distribution by blood group and consumer in a wide regional and three-level network.
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Designing the best logistic model possible that can be applied to all participants (hospitals and central bases) in the regional blood transfusion network.
Literature review
The difference with the proposed research model | The implementation of the Model | Method | Purpose | The examined stage of the chain | Authors | |||||
---|---|---|---|---|---|---|---|---|---|---|
Model implementation dimensions | method | purpose | The stage under review | distribution | inventory | collection | ||||
☑ | ☑ | American Blood Transfusion Organization | Dynamic planning | Designing ordering policies | ☑ | [26] | ||||
☑ | Blood bank of Turkey | Simulation | Examining the blood bank inventory management policies | ☑ | [27] | |||||
☑ | ☑ | ☑ | Solving the numerical example | Integer programming Proximity search | Routing | ☑ | [28] | |||
☑ | ☑ | ☑ | Testing the designed model using data from the Stanford Blood Services Center | LIFO Analysis FIFO Analysis | Improving inventory management policies and reducing the amount of expired items | ☑ | ☑ | [29] | ||
☑ | ☑ | Collecting bases in urban and rural environments in French cities | Simulation | Developing blood collection Scenarios | ☑ | [30] | ||||
☑ | ☑ | Testing the model with real data from several hospitals | Simulation | Reducing blood expiration rate and optimizing ordering policies | ☑ | [31] | ||||
☑ | National Blood Center of Iran | Simulation Taguchi | Improving the efficiency of the blood supply chain | ☑ | [32] | |||||
☑ | ☑ | ☑ | Solving the numerical example | Integrated integer linear programming | Increasing the efficiency of the supply chain | ☑ | [33] | |||
☑ | ☑ | Implementing the model in Saskatchewan, Canada | Simulation | Designing a blood distribution network model | ☑ | [34] | ||||
☑ | ☑ | ☑ | Implementing the model in a hospital | Two-stage stochastic programming | Reducing the costs of expiration, waste and shortage | ☑ | [35] | |||
☑ | ☑ | ☑ | Solving the numerical example | Possible optimization | Increasing chain efficiency | ☑ | [36] | |||
☑ | ☑ | A distribution network with 8 customers and 3 vehicles | Branch and cut | Blood routing | ☑ | [20] | ||||
☑ | ☑ | Sari blood transfusion network | Mixed integer programming - Robust probabilistic planning method | Blood routing | ☑ | [21] | ||||
☑ | ☑ | ☑ | Special region in Italy | Binary programming | Organizing blood management system | ☑ | [37] |
Methods
Description of the model
Research algorithm
Designing inventory management model by RBC organization
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Wastes are divided into two categories: wastes resulting from blood expiration and wastes from non-use of blood. Additionally, each frequency is individually entered into the model
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The supply of blood is subject to fluctuating demand.
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For each hospital and CBC, a specified initial blood stock level is established.
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Specific precautionary stock levels are set for every CBC and hospital.
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Blood may be transferred between CBC.
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The region of the model is considered to consist of 54 hospitals and six CBC.
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A shortage penalty for the supplier is taken into consideration due to the high level of uncertainty in the demand.
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A regional network utilizes a centralized structure
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The circular policy is the one employed by the regional network. The blood is transported to the hospital as part of the circular system, but the blood bank at the CBC is still in charge of the blood units can transport them to other hospitals. In other words, goods can be sent to the main blood transfusion center.
Specifications | A | O | B | AB |
---|---|---|---|---|
Network architecture | (3:5:1) | (3:7:1) | (3:9:1) | (3:8:1) |
MSE | 0.013 | 0.0092 | 0.0099 | 0.0072 |
CBC | i | Distribution Ffunction | |||
---|---|---|---|---|---|
A | O | B | AB | ||
Mashhad | 1 | Na | Na | Na | Na |
Sabzevar | 2 | Pb | Pb | Pb | Pb |
Torbat Heydarieh | 3 | Pb | Pb | Pb | Pb |
Gonabad | 4 | Pb | Pb | Pb | Pb |
Neyshabur | 5 | Pb | Pb | Pb | Pb |
Ghuchan | 6 | Pb | Pb | Pb | Pb |
Central Base | i | Target inventory values | |||
A | O | B | AB | ||
Mashhad central | 1 |
\(160\le S\le 240\)
|
\(152\le S\le 228\)
|
\(120\le S\le 180\)
|
\(52\le S\le 78\)
|
Sabzevar central | 2 |
\(64\le S\le 96\)
|
\(56\le S\le 84\)
|
\(24\le S\le 36\)
|
\(26\le S\le 39\)
|
Torbat Heydarieh central | 3 |
\(64\le S\le 96\)
|
\(56\le S\le 84\)
|
\(32\le S\le 48\)
|
\(20\le S\le 29\)
|
Gonabad central | 4 |
\(24\le S\le 36\)
|
\(24\le S\le 36\)
|
\(20\le S\le 30\)
|
\(16\le S\le 24\)
|
Neyshabur central | 5 |
\(24\le S\le 36\)
|
\(16\le S\le 24\)
|
\(16\le S\le 24\)
|
\(15\le S\le 22\)
|
Ghuchan central | 6 |
\(24\le S\le 36\)
|
\(16\le S\le 24\)
|
\(16\le S\le 24\)
|
\(12\le S\le 18\)
|
Central base | i | Reorder point values | |||
A | O | B | AB | ||
Mashhad central | 1 |
\(15\le R\le 25\)
|
\(13\le R\le 23\)
|
\(5\le R\le 15\)
|
\(3\le R\le 13\)
|
Sabzevar central | 2 |
\(5\le R\le 15\)
|
\(5\le R\le 15\)
|
\(0\le R\le 10\)
|
\(1\le R\le 9\)
|
Torbat Heydarieh central | 3 |
\(5\le R\le 15\)
|
\(5\le R\le 15\)
|
\(0\le R\le 10\)
|
\(0\le R\le 10\)
|
Gonabad central | 4 |
\(0\le R\le 10\)
|
\(0\le R\le 10\)
|
\(0\le R\le 7\)
|
\(0\le R\le 7\)
|
Neyshabur central | 5 |
\(0\le R\le 10\)
|
\(0\le R\le 10\)
|
\(0\le R\le 7\)
|
\(0\le R\le 7\)
|
Ghuchan central | 6 |
\(0\le R\le 10\)
|
\(0\le R\le 10\)
|
\(0\le R\le 7\)
|
\(0\le R\le 7\)
|
Symbol | Definition |
---|---|
\({UI}_{ir}\)
| Consumption distribution (demand) function of central base i for blood group r |
\({UA}_{ri}\)
| Hospital demand distribution function i for blood group r |
\({s}_{ri}\)
| Target inventory level of each consumer and supplier i in blood group r |
\({R}_{ri}\)
| Reorder point of each consumer and supplier i in blood group r |
\({LF}_{r}\)
| Shelf life of products |
\({s}_{ri}^{*}\)
| The best level of inventory of the target hospital or central base i in blood group r |
\({R}_{ri}^{*}\)
| Reorder point of each consumer and supplier i in blood group r |
\({Sh}_{ri}\)
| Number of deficiencies of each consumer and supplier i in blood group r |
\({O}_{ri}\)
| Number of expired blood consuming or supplying i for blood group r |
Implementation of inventory management model on a daily in CBC’s and hospitals
-
There is blood exchange between central bases (CBCs) in the logistics network.
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In a logistics network, a supplier delivers blood to multiple consumers (hospitals under its cover and other central bases).
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It is impossible to exchange blood units between hospitals.
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The supplier uses a heterogeneous transport network (fleet) with vehicles that differ in capacity and cost to distribute blood to consumers.
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Each blood unit has a specific expiration date and after that it will be unusable.
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It is possible for consumers to return expired or unused blood.
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Consumer requests have to be submitted within a specified time frame.
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The inventory capacity of each consumer for each blood is recognized by the supplier.
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A cost of shortage penalty is considered for the supplier because of the high degree of uncertainty in the demand value.
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The level of initial blood supply in each consumer is known.
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Precautionary reserve is specified for each supplier and consumer.
Symbol | Definition |
---|---|
\({c}_{ij}\)
| The distance between the consumer i and j |
\({\widetilde{\upsilon }}_{ijk}\)
| The cost of transferring each unit between consumer i and j for vehicle type k |
\({cap}_{k}\)
| The capacity of vehicle type k |
\({A}_{tri}\)
| Consumer demand i from blood group r on day t |
M | Big number |
\({M}{\prime}\)
| Database and consumers collection |
\({{\varvec{x}}}_{{\varvec{i}}{\varvec{j}}{\varvec{k}}{\varvec{t}}}\)
| It gets 1 if consumer j is served by device k in period t exactly after consumer i; |
\({z}_{ikt}\)
| It gets 1 if consumer i is served by device k in period t, otherwise 0 |
\({q}_{irkt}\)
| The amount of blood group r received by consumer i by device k over time t |
\({w}_{ikt}\)
| The artificial variable shows the nth consumer served by the truck. |
Results
The results of implementing optimal inventory management model for Mashhad central base
Estimation of the demand of hospitals
Maximum order quantity of each consumer
Aria | Naja | ||||||
A | O | B | AB | A | O | B | AB |
5.9033 | 6.2099 | 6.3102 | 9.5644 | 13.375 | 12.3732 | 11.894 | 4.96506 |
Artesh | Javad Alaima Tabarsi | ||||||
A | O | B | AB | A | O | B | AB |
5.6583 | 5.3546 | 5.7140 | 6.7367 | 7.0481 | 7.0481 | 4.4305 | 4.1943 |
Imam Zaman | Dr. Sheikh | ||||||
A | O | B | AB | A | O | B | AB |
10.9070 | 11.1917 | 11.7953 | 6.3161 | 26.209 | 14.8823 | 11.63375 | 8.8947 |
The results of the target inventory of Mashhad central base and the hospitals covered by it
Database | Target Inventory Amount | |||
---|---|---|---|---|
AB | B | O | A | |
Mashhad Central Base | 65 | 132 | 200 | 195 |
Aria Hospital | 3 | 6 | 8 | 7 |
Artesh Hospital | 2 | 3 | 4 | 3 |
Imam Zaman Hospital | 3 | 7 | 12 | 9 |
Javad Al-aemeh Tabrasi Hospital | 1 | 2 | 3 | 3 |
Dr.Sheikh Hospital | 4 | 12 | 16 | 10 |
Reorder point
Reorder Point Value | Database Name | |||
---|---|---|---|---|
A | O | B | AB | |
20 | 15 | 8 | 5 | Mashhad CBC |
2 | 2 | 2 | 1 | Aria Hospital |
1 | 1 | 1 | 1 | Artesh Hospital |
2 | 3 | 3 | 1 | Imam Zaman Hospital |
1 | 1 | 1 | 1 | Naja |
4 | 4 | 4 | 1 | Dr. Sheikh Hopsital |
The results of implementing the routing model of Mashhad central base
Vehicle types (K) | Vehicle number | Capacity of vehicle type k (capk) |
---|---|---|
Small | 3 | 90 |
Medium | 2 | 150 |
Large | 1 | 300 |
Consumers of Mashhad | ||||
---|---|---|---|---|
Vehicle type | Distribution route | Consumers | Blood type | The blood received (Q) |
1 | Central base, Ghaem, Imam Reza, Central base | Ghaem | A | 3 |
B | 0 | |||
AB | 2 | |||
O | 7 | |||
Imam Reza | A | 10 | ||
B | 3 | |||
AB | 6 | |||
O | 5 | |||
2 | Central base, Javad Al-aeme Tabrasi, Sina, Central base | Javad Al-aeme Tabrasi | A | 5 |
B | 1 | |||
AB | 0 | |||
O | 7 | |||
Sina | A | 0 | ||
B | 0 | |||
AB | 0 | |||
O | 5 | |||
3 | Central base, Taleghani, Shahid Hasheminejad, Central base | Taleghani | A | 0 |
B | 0 | |||
AB | 0 | |||
O | 2 | |||
Shahid Hasheminejad | A | 2 | ||
B | 8 | |||
AB | 4 | |||
O | 4 |
Validation
Step | MSE |
\({{\varvec{R}}}^{2}\) constant
| Absolute mean error | Mean relative absolute error |
---|---|---|---|---|
Training | 1.21 | 0.978 | 0.529 | 5.67 |
Validation | 1.06 | 0.995 | 0.432 | 4.96 |
Testing | 1.24 | 0.987 | 0.522 | 6.13 |
Real data | Simulation results | |
---|---|---|
Monthly average | 751.07 | 752.14 |
Standard deviation | 17.7 | 14.3 |
n | 12 | 12 |
P-value | 0.967 |
Real data | Simulation results | |
---|---|---|
Monthly average | 55.67 | 58.2 |
Standard deviation | 1.82 | 0.95 |
n | 12 | 12 |
P-value | 0.987 |