Problem The AB Company makes two different products, namely, A and B. Both products are made at the same workstation. Each time the workstation switches from making A to B (or from B to A) the station has to be set up for the product. Two hours are required to set up for A. An accountant has estimated that one hour of workstation time (machine plus worker) is worth about $20. The workstation takes one hour to produce one unit of A. Each finished unit of A costs $4 to store for one year. The lot size or batch size is the number of units of A produced each time the workstation is set up for A. Clearly, AB can reduce its setup costs by increasing the lot size. But then holding costs will increase. The company wants to choose the lot size that will minimize the total setup and holding cost for product A. The demand for these products exceeds AB's production capacity, but since product A is more important and profitable than B, they always choose to make enough A to meet its demand and do not make enough B to meet its demand. The demand for A is 1,000 units/year, which is spread over the year evenly. If the product is unavailable when a customer requests it, the customer will go elsewhere to purchase, and the sale is lost to AB Company (i.e., no backorders).

The following list provides more detail about the problem.

Raw Materials: Assume that raw materials for A and B are always available.

Workstation: The workstation alternates between A and B. Each time it starts a batch, it (a) sets up for the batch, (b) processes the batch, and (c) passes the batch to the appropriate finished goods inventory. The workstation does not transfer any units to the inventory until the entire batch is completed.

Workstation: Since demand exceeds capacity, you may assume that the workstation is busy continuously (setting up and producing).

Finished Goods Inventory: Holding costs are not charged until the units are in the inventory.

You may assume that the production of A is timed so that a new batch arrives in the finished goods inventory just in time for when it is needed (i.e., when they have just run out of A from the previous batch).

Begin by setting up an equation that describes the average annual setup cost for A and an equation for the average annual holding cost for A. Then combine these two equations to obtain the average annual total setup and holding cost for A.

Note: Assume that the work days are continuous, i.e. ignore the normal work hours/days in real life. Additionally, attempting to find daily holding costs for each unit is not necessary, an average will do fine, as the answer does not have to be exact or strictly realistic.