Numerical example and Result

The results from the simulation and the analysis are shown below for Benin. The transportation storage device commonly used at clinics in Benin (BK-VC 1.7-CF) has a vaccine storage volume of length 10 cm, width 10 cm and height 17 cm after it is packed with conditioned ice. The average annual patient demand, which is 550, is used to determine daily demand for doses of each vaccine. Since some of the current inner packs (Tuberculosis, Measles, DTC-HepB-Hib and PCV13) are too large to be held in the BK-VC 1.7-CF, assessing the simplified ordering policies with these inner packs is impossible, and the only option is to order in vial units. However, as we saw in the storage device space analysis, 10- or 20-vial inner packs could be considered with very little increase in clinic storage requirements. Table 26 shows the actual inner pack dimensions for the 10-vial inner packs. Note that the new dimensions are calculated based on the current vial diameter and height.

Table 26. 10 vial inner pack dimensions

Vaccines Tuberculosis Tetanus Measles Oral Polio Yellow Fever DTC- HepB- Hib PCV13 Rota Length(cm) 9.25 10.6 9.25 7.5 10.6 9 8.95 7.3 Width(cm) 3.8 4.7 3.8 2.5 4.7 2.98 3.68 3.4 Height(cm) 6 5.1 6 7.5 5.1 3.7 4.1 6.9

Using the current vial unit ordering policy, we need 6.39 liters to cover all orders with a probability of 0.95, and 6.55 liters with 0.99 probability. Using the Kanban ordering policy or inner pack unit ordering policy with 10-vial inner packs for all vaccines, 6.49 liters are needed to cover all orders with the 0.95 probability, and 6.67 liters with 0.99 probability. Table 27 shows the corresponding number of inner packs of each vaccine for the simplified ordering policies.

Table 27. Number of inner packs for the simplified ordering polices

Vaccines Tuberculosis Tetanus Measles Oral Polio Yellow Fever DTC- HepB- Hib PCV13 Rota Kanban ordering 2 1 2 1 2 8 14 12 Inner pack unit ordering 2 1 2 1 2 7 16 11

Table 28 shows the number of storage devices required to hold 6.39 liters of vaccine vials for different packing efficiencies. For example, if an effective 80% of device storage space is available, five storage devices are needed. In fact, if the packing efficiency is between 80% and 90%, five storage devices will suffice.

Table 28. Number of storage devices required to hold 6.39 liters of vaccine vials

Packing efficiency 70% 80% 90% 100%

The number of the storage

devices 6 5 5 4

When 10-vial inner pack vaccines are used, we estimated that six storage devices are required for both the Kanban ordering policy and the inner pack unit ordering policy to cover 95% of vaccine delivery. With 20-vial inner packs, seven storage devices are required for both policies.

Clearly, if the inner pack size cannot be changed, the simplified ordering policies are not practical. However, if 10 or 20 vial inner pack can be used, one or two more additional transportation storage devices (vaccine carriers) would be required at each clinic.

4.5 DISCUSSION AND CONCLUSIONS

Ordering vaccines in inner pack quantities has many advantages over single vial ordering including convenience in managing inventories, fewer errors in counting and ordering, and reduced order fulfillment effort. If vaccines are stored within an inner pack, a health worker can easily distinguish vaccines from each other and more readily find the particular vaccine that the worker is looking for because there is vaccine information on the outside face of the inner pack. In addition, at the upper level distribution center, the complicated vial counting process to supply clinics will be replaced by a much simpler process of picking one, or counting just a few inner packs. Counting errors at the upper levels will decrease and order preparation and distribution time will be saved. EPI vaccines are not particularly expensive, so there is no real disadvantage to holding more vaccines at the clinic level, as long as there is sufficient storage space.

The results from Benin and Niger indicate that while there is no common inner pack size that is best for all vaccines, if we use inner packs of size 10 or 20 for all vaccines only a few more storage devices are needed. Thus, even though these simplified ordering policies increase the storage volume needed, if we choose the proper inner pack size these negative consequences can be minimized such that the additional number of storage devices needed is very small (on the order of 1%). In terms of transportation storage space, the proposed ordering policies are not practical without changing the inner pack size. However, if 10- or 20-vial inner packs are used across all vaccines, one or two more storage devices in transportation will be required to service orders with a high probability. Note that in general, a vaccine carrier is inexpensive (e.g., the 2009 price of a BK-VC 1.7-CF is US$ 12.00), so purchasing one or two devices would be very affordable for a clinic. But if transportation resources are constrained it might become necessary for an additional trip to a clinic in order to carry additional vaccine carriers. In this case the

transportation cost will increase and it might be difficult to implement due to time and resource limitations.

In conclusion, we recommend adapting simplified ordering polices based on well-known lean concepts (that are widely used in manufacturing) to a major public health sector. There are several key managerial insights relating to this recommendation. First, only replenishing using inner pack quantities reduces logistical effort and potential ordering errors at multiple levels of the supply chain. This is particularly valuable in the context of lower and middle income countries as many of the workers involved in the vaccine supply chains in these countries are not well trained in logistics systems operations. Second, while the average inventory levels do increase slightly with the simplified policies, the increase is minor and only causes minor increases (less than a few percent) in the number of cold storage devices needed at facilities if the inner pack sizes are carefully chosen. Third, transport logistics are also not impacted significantly. Thus, we can achieve significant benefits from simplified ordering policies with modest increases in operational costs by selecting proper vaccine inner pack sizes.

5.0 REDESIGN OF VACCINE DISTRIBUTION NETWORKS IN LOW AND