Question

a manufacturer experiences a strong seasonal demand pattern, driven by the winter holiday season. the company has a 6 month production plan, where the monthly demands dt are provided in the table below. the unit cost, fixed setup cost, and monthly holding cost for each unit is provided in the table below. based on this information, what is the optimal production schedule for the 6 month period using the wagner - whitten algorithm. (similar to problem 9)

t	1	2	3	4	5	6
$c_t$	$1,000	$1,000	$1,000	$1,000	$1,000	$1,000
$a_t$	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000
$h_t$	$1	$1	$1	$1	$1	$10

build lot for lot, so build period 1 in period 1, period 2 in period 2, period 3 in period 3, etc.
build periods 1, 2, 3, & 4 in period 1, build periods 5 & 6 in period 5.
build periods 1 & 2 in period 1, build period 3 in period 3, build period 4 in period 4, build periods 5 & 6 in period 5

10 pts

question 18
the economic lifetime of a particular model of phone is only 6 to 12 months. for a new model of phone that is about to be released, a company needs to negotiate a contract with a screen provider. the company is forecasting the demand of the phone to be a normal distribution with a mean of 3.1 million units with a standard deviation of 250,000 units. the net profit from each units sale is $525. each screen has a cost of $175 and are not expected to be available for salvage. use the news vendor model to determine the purchase quantities of screens where the cost of lost sales and cost of excess materials are balanced. (similar to problem 11)

Explanation:

Step1: Recall Wagner - Whitten algorithm concept

The Wagner - Whitten algorithm aims to find the optimal production schedule to minimize total cost (setup + production+ holding) over a planning horizon.

Step2: Analyze cost components

The cost components are unit cost $c_t$, fixed setup cost $A_t$ and holding cost $h_t$. The unit cost is constant at $1000$, setup cost at $15000$ and holding cost varies ($1$ for first 5 months and $10$ for 6th month).

Step3: Evaluate options

• Option 1 (Build lot - for - lot): High setup costs as there is a setup in each period.
• Option 2 (Build periods 1, 2, 3, & 4 in period 1, build periods 5 & 6 in period 5): High holding costs for early - produced units for long periods.
• Option 3 (Build periods 1 & 2 in period 1, build period 3 in period 3, build period 4 in period 4, build periods 5 & 6 in period 5): Balances setup and holding costs well. Producing in batches when demand patterns allow can reduce setup frequency while not incurring excessive holding costs.

Answer:

Build periods 1 & 2 in period 1, build period 3 in period 3, build period 4 in period 4, build periods 5 & 6 in period 5