The purpose of this study was to establish a hospital supply chain management (HSCM) model in which three kinds of drugs in the same class and with the same indications were used in creating an optimal robust design and adjustable ordering strategies to deal with a drug shortage. The main assumption was that although each doctor has his/her own prescription pattern, when there is a shortage of a particular drug, the doctor may choose a similar drug with the same indications as a replacement. Four steps were used to construct and analyze the HSCM model. The computation technology used included a simulation, a neural network (NN), and a genetic algorithm (GA). The mathematical methods of the simulation and the NN were used to construct a relationship between the factor levels and performance, while the GA was used to obtain the optimal combination of factor levels from the NN. A sensitivity analysis was also used to assess the change in the optimal factor levels. Adjustable ordering strategies were also developed to prevent drug shortages.
Recently, one of the most important strategy issues for hospital administrators is to measure the performance of supply chain management (SCM). Bhatnagar and Sohal [
He and Lai [
Based on the literature summarized above, most SCM research had paid attention to the product production for suppliers, manufacturers, and customers. There is little research on HSCM. Also, in Taiwan, most of hospitals’ purchasing professionals have slight recognition or may not be familiar with the concept of supply chain [
In addition, to explore the HSCM’s performance, the total system cost (TSC) should also be taken into consideration. Lapierre and Ruiz [
Along with reducing the TSC, improving the patient safety level (PSL) is also an important issue to enhance high quality care in the performance of HSCM in Taiwan; Liao’s research on HSCM [
The study attempted to construct a HSCM model for drug delivery to avoid the drug shortage and to explore the relationship among the cost management, purchasing strategy, the logistic system, and e-health purchasing system. The concept of HSCM is based on the concept that when the actual demand occurs, the adjustable strategies for the dispatched quantity from different pharmaceutical companies will be computed to adjust the shortage demand. To achieve the optimal overall performance of the HSCM, it is necessary to pay attention to the variations in different ordering quantities and dispatched quantities of the required product when the hospital has the instability of the demand forecasting. The variations of the major parameters will be taken into consideration in order to determine the optimal supply chain’s overall performance.
Furthermore, to explore the computational technology, Liao et al. [
In this section, the HSCM and its factor level settings will be defined. In the framework of the HSCM, medical (product) purchase demands were compiled by the e-health purchasing system. Three pharmaceutical companies were contracted to supply three different drugs (drug A, drug B, and drug C). The e-health purchasing system included purchasing and coordination distribution mechanisms to compute and suggest the most robust HSCM factor level settings. The three drugs had the same indications and thus could be used to replace one another if there were a shortage. Orders for these drugs were processed in the following way: the hospitals sent their requests for each kind of drug to the e-health purchasing system, which collated the requests, computed the total quantities to be ordered, and submitted them to the pharmaceutical companies via the Internet. The pharmaceutical companies then delivered the requested quantities of the drugs ordered to the hospital. In order to circumvent the seasonal variation that affects actual demand, the pharmaceutical companies would maintain a safety stock of drugs at the warehouse’s request. The warehouse would then take any inventory shortages into consideration when filling the hospital’s orders. Small lot sizes and multiple deliveries could be implemented in order to save storage space.
Some research on HSCM performance has taken the total system cost into consideration [
In order to make the design of the HSCM as robust as possible, four steps were proposed.
In this step, in order to arrive at a robust design for the HSCM, the following important factors and their settings were considered. First, the noise and control factors were identified. In general, demand variability is difficult to control, and decision-makers always use the forecasting model to predict the quantities of the drugs that will be needed. The noise factor was identified as the demand variability, calculated using the normal probability distribution,
The control factors were the safety stock (level 1: 400 units, level 2: 500 units, and level 3: 600 units), the maximum inventory (level 1: 2,000 units, level 2: 2,500 units, and level 3: 3,000 units), the reliability of the HSCM (level 1: 99 percent, level 2: 97 percent, and level 3: 96 percent), and the transportation capacity (level 1: 250 units, level 2: 500 units, and level 3: 1,000 units).
To explore the relationship between the factor levels and performance, the mathematical function of the HSCM performance was discussed. Generally, there are two indexes of HSCM performance: the TSC and the PSL. In this study, the
The
The
The parameter settings for the simulation are summarized in Table
The parameter settings for the HSCM simulation.
|
|
|
|
|
|||
|
|
|
|
|
|||
|
|
|
Three NN models (the
The neural networks for the
Structures (input nodes-hidden nodes-output nodes) | RMSE | |
---|---|---|
Training | Testing | |
4-6-1 | 0.02982 | 0.02634 |
4-5-1 | 0.02632 | 0.02471 |
4-4-1 | 0.02444 | 0.02170 |
|
|
|
4-2-1 | 0.02651 | 0.02485 |
4-1-1 | 0.03145 | 0.03059 |
The neural networks for the
Structures (input nodes-hidden nodes-output nodes) | RMSE | |
---|---|---|
Training | Testing | |
4-6-1 | 0.03116 | 0.02824 |
4-5-1 | 0.02998 | 0.02755 |
4-4-1 | 0.02633 | 0.02463 |
|
|
|
4-2-1 | 0.02761 | 0.02537 |
4-1-1 | 0.02993 | 0.02495 |
The neural networks for the
Structures (input nodes-hidden nodes-output nodes) | RMSE | |
---|---|---|
Training | Testing | |
4-6-1 | 0.03136 | 0.02888 |
4-5-1 | 0.02872 | 0.02564 |
|
|
|
4-3-1 | 0.02766 | 0.02462 |
4-2-1 | 0.02899 | 0.02317 |
4-1-1 | 0.03100 | 0.02891 |
To complete the sensitivity analysis in order to discuss the changes in the optimal factor levels based on the optimal factor level combinations, Tables When the safety stock level was increased from 1.2 to 3, the When the maximum inventory level was increased from 1.4 to 3, the When the reliability of the HSCM was increased from 1 to 3, the When the transportation capacity was decreased from 3 to 1, the
The values for the
|
0.930 |
|
0.925 | 0.900 | 0.880 | 0.870 | 0.848 | 0.830 | 0.810 | 0.780 | 0.760 |
|
|||||||||||
Safety stock | 1 |
|
1.4 | 1.6 | 1.8 | 2 | 2.2 | 2.4 | 2.6 | 2.8 | 3 |
|
|||||||||||
|
121106 |
|
121956 | 124446 | 127345 | 129623 | 132539 | 134661 | 138439 | 144482 | 147217 |
|
|||||||||||
|
0.874 |
|
0.869 | 0.846 | 0.827 | 0.817 | 0.797 | 0.780 | 0.761 | 0.733 | 0.714 |
The values for the
|
0.910 | 0.930 |
|
0.910 | 0.900 | 0.891 | 0.881 | 0.872 | 0.861 | 0.852 | 0.843 |
|
|||||||||||
Maximum inventory | 1 | 1.2 |
|
1.6 | 1.8 | 2 | 2.2 | 2.4 | 2.6 | 2.8 | 3 |
|
|||||||||||
|
123050 | 120426 |
|
122851 | 124226 | 125583 | 126966 | 128418 | 129747 | 131421 | 132722 |
|
|||||||||||
|
0.855 | 0.874 |
|
0.855 | 0.846 | 0.837 | 0.828 | 0.819 | 0.809 | 0.801 | 0.792 |
The values for the
|
|
0.818 | 0.857 |
|
|||
HSCM reliability |
|
2 | 3 |
|
|||
|
|
122850 | 124218 |
|
|||
|
|
0.868 | 0.805 |
The values for the
|
|
0.910 | 0.900 |
|
|||
Transportation capacity |
|
2 | 1 |
|
|||
|
|
136878 | 130254 |
|
|||
|
|
0.855 | 0.846 |
To explore the adjustable ordering strategies for drugs A, B, and C, Table When there is a shortage of drug C but drugs A and B can be ordered, the When there is a shortage of drug B but drugs A and C can be ordered, the When there is a shortage of drug A but drugs B and C can be ordered, the
The control factor level combinations and their
Drugs to be ordered | Safety stock | Maximum inventory level | HSCM reliability | Transportation capacity |
|
---|---|---|---|---|---|
A, B | 430 | 2300 | 99% | 250 | 0.912 |
A, C | 420 | 2100 | 99% | 1000 | 0.924 |
B, C | 580 | 2800 | 99% | 1000 | 0.990 |
In this paper, the authors explored adjustable ordering strategies for dealing with drug shortages. The HSCM simulation model, which could handle three drugs from the same class and with the same indications, was used to find the optimal robust design and adjustable ordering strategies to cope with a drug shortage, according to the hospital’s needs and with the support of a purchasing alliance. Four steps were applied here to construct the HSCM model: the HSCM factors and their levels were taken into consideration; the relationships between the factor levels were identified; the optimal combinations of factor levels were obtained; and finally the adjustable ordering strategies to use when there was a shortage of one of the three drugs were discussed. The most significant contribution of this study is that it takes the adjustable ordering strategies of the HSCM into consideration when dealing with practical problems. The concept of adjustable ordering strategies will play an important role in future research on HSCMs. Also, some other contributions in the proposed computational technology are presented below: The study used the NN to effectively deal with complex nonlinear relationship between the factor levels and performance. In addition, GA was used to obtain the optimal combination of factor levels from the NN, from any values within the upper and lower bounds for control factors. Different settings of the same factor could be optimal for different performances. In the study, the performances of TSC and PSL are usually in conflict. A common method used for tackling the multiple performances problem is to give a weighted value to each performance, which needs to be judged and decided by a human subject. However, the desirability function proposed in the study does not need any human judgment. Therefore, it could be an attractive method in simplifying multiple performance problems because it forthright employs the upper and lower bound of each performance, without any human judgment. Also, the value of composite desirability MP derived in the study was 0.980, a value very close to 1. Hence, the desirability function in this study’s NN model for the optimization of multiresponse problems can be a very useful tool to predict surface roughness. In the study, the proposed methods, experimental design, NN, and GA, can be used for analysis, modeling, and optimization. Consequently, they can be applied in concurrent design process in HSCM.
The limitation of the study is that the control factors’ levels are based on the preference of and the control of HSCM decision-makers. However, the noise factor’s levels are in the control of external environment. Hence, while adjusting the optimal combination of factor levels, the designer must take the variations of the external environment into consideration.
The authors declare that they have no competing interests.