At the beginning of each period, a company mustdetermine how many units to produce. A setup cost of $5 isincurred during each period in which production takes place.The production of each unit also incurs a $2 variable cost.All demand must be met on time, and there is a $1 per-unitholding cost on each period’s ending inventory. During eachperiod, it is equally likely that demand will equal 0 or 1 unit.Assume that each period’s ending inventory cannot exceed2 units.a Use dynamic programming to minimize the expected costs incurred during three periods. Assume that the ini-tial inventory is 0 units. b Now suppose that each unit demanded can be soldfor $4. If the demand is not met on time, the sale is lost.Use dynamic programming to maximize the expected profit earned during three periods. Assume that the ini-tial inventory is 0 units. c In parts (a) and (b), is an (s, S) policy optimal?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
At the beginning of each period, a company must
determine how many units to produce. A setup cost of $5 is
incurred during each period in which production takes place.
The production of each unit also incurs a $2 variable cost.
All demand must be met on time, and there is a $1 per-unit
holding cost on each period’s ending inventory. During each
period, it is equally likely that demand will equal 0 or 1 unit.
Assume that each period’s ending inventory cannot exceed
2 units.
a Use dynamic
costs incurred during three periods. Assume that the ini-
tial inventory is 0 units.
b Now suppose that each unit demanded can be sold
for $4. If the demand is not met on time, the sale is lost.
Use dynamic programming to maximize the expected
profit earned during three periods. Assume that the ini-
tial inventory is 0 units.
c In parts (a) and (b), is an (s, S) policy optimal?
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