A company manufactures and sells four families of products (, B, , ). The company tries to optimize its operations using IQR. The time required to sell 10,000 units of a product family in all POS (points-of-sales) follows Normal distribution with the parameters shown in Table 1.

a) Describe how queuing models can help the company solve this problem. State your assumptions.

b) Draw a diagram of the companys operations and indicate the queuing models used (using Kendalls notation).

c) Calculate IQR based on the inventory in Table 3 and explain its meaning.

d) What is the inventory level for each product family? State your assumptions.

e) How can IQR be improved? What factors have a negative impact on selected parameters?

Table 1 Demand data (time required to sell 10,000 units) Mean (days/10000units) 4 Variance (days/10000unit)2 9 Product family 12 16 Each product family is manufactured in a dedicated production facility, where final product inventory is kept and from where demand is served. The distributions of the time required for manufacturing 10,000 units in each facility are shown in Table 2. Table 2 Supply data (time required to produce 10,000 units) Product family Distribution Mean Variance ays/10000units (days/10000units)2 Exponential Normal Exponential Normal 49 16 64 25 13 The inventory targets and finished product prices for each family are shown in Table 3. Table 3 Inventory data Price ($/unit) 1.0 2.0 1.5 3.5 Product family Target (units) 2500 13000 13,000 5000 Table 1 Demand data (time required to sell 10,000 units) Mean (days/10000units) 4 Variance (days/10000unit)2 9 Product family 12 16 Each product family is manufactured in a dedicated production facility, where final product inventory is kept and from where demand is served. The distributions of the time required for manufacturing 10,000 units in each facility are shown in Table 2. Table 2 Supply data (time required to produce 10,000 units) Product family Distribution Mean Variance ays/10000units (days/10000units)2 Exponential Normal Exponential Normal 49 16 64 25 13 The inventory targets and finished product prices for each family are shown in Table 3. Table 3 Inventory data Price ($/unit) 1.0 2.0 1.5 3.5 Product family Target (units) 2500 13000 13,000 5000