Modeling simultaneous substitution flows

[nzligul]

Hello,

In my model, there are two different brands of the same medicine. Patients generate demand for the brand reimbursed by their insurance. However, even if there is sufficient national stock, the specific brand demanded in some regions may not be available at the pharmacy level. In such cases, after waiting for some period, patients may get an alternative brand. Because of this, I assume that under normal conditions, there is always some level of substitution flow between the two brands. This flow increases when stock levels are low, and if one brand is completely out of stock, all the demand shifts to the other brand. While modeling this, I noticed a problem: defining simultaneous flows in two directions unintentionally inflates total demand. For example, demand moves from Brand B to Brand A, and then flows back to Brand B.

Eventually, I plan to expand this model to include more brands using subscripts. Then the substitution decision will also be affected by the price. I have attached the simplified version of the model. What would be the best way to model such substitution flows? Would it be better to separate “Original Demand” and “Substitute Demand” into distinct stocks for each brand?

[Administrator]

I'm not familiar with this kind of healthcare so I can only offer some general advice.

I think I'd look at the stock of each medicine rather than the demand. Then the outflow from this stock is the "fulfilment rate", but if that cannot be met, try taking any remaining medicine B. That would be fairly simple.

In reality, does demand actually shift between medicines? I can see how the attractiveness of medicine A might be higher than medicine B, that might influence the demand for this.

Sorry I cannot offer any more advice. Here in the UK, we don't get to choose the brand of medicine.

[nzligul]

Hello,

I have made some simplifications in my model. There is no demand shift during normal times; demand only shifts to the next cheapest product when inventory is unavailable. For example, consider three products A, B, and C, with the following properties:

• Brands: A, B, C

• Price[Brand]: 2, 4, 5

• Demand[Brand]: 50, 30, 20

• Inventory[Brand]: 10, 60, 50

Brands B and C have sufficient inventory, so their demands are fulfilled from their own stock. However, Brand A has a demand of 50 but only 10 units in inventory. The remaining 40 units will be fulfilled from other brands’ inventories, if available.

Since fulfillment from other brands depends on their prices, Brand B, being cheaper than C, will provide inventory first. Brand B has 60 units initially, so 30 units can be allocated to help Brand A (The other 30 is for its own demand). Still, Brand A needs 10 more units, which will then be fulfilled from Brand C’s inventory.

I tried using allocation functions, but couldn't correctly allocate these demands. Since I am particularly interested in modeling the fulfillment through other brands within the same time step (i.e., no delay to the next period; fulfillment from both own and other brands occurs simultaneously), I would appreciate your suggestions. This is intended to be a dynamic process where demand and inventory levels change over time. How should I formulate this relationship in Vensim DSS?

[tomfid]

I'm puzzled by your statement that "defining simultaneous flows in two directions unintentionally inflates total demand. For example, demand moves from Brand B to Brand A, and then flows back to Brand B." In your example, demand is conserved. If demand shifts from A to B, the demand for B increases but A decreases correspondingly. I think the "demand" stocks actually increase because the inflow of prescriptions remains constant for some time after stockouts cause a decrease in the outflows of fulfillment.