Question

Problem 10-13 (Algorithmic)

Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7,300 copies. The cost of one copy of the book is $14.5. The holding cost is based on an 16% annual rate, and production setup costs are $160 per setup. The equipment on which the book is produced has an annual production volume of 23,500 copies. Wilson has 250 working days per year, and the lead time for a production run is 14 days. Use the production lot size model to compute the following values:

1. Minimum cost production lot size. Round your answer to the nearest whole number. Do not round intermediate values.
   
   Q^* =
   
2. Number of production runs per year. Round your answer to two decimal places. Do not round intermediate values.
   
   Number of production runs per year =
   
3. Cycle time. Round your answer to two decimal places. Do not round intermediate values.
   
   T =  days
   
4. Length of a production run. Round your answer to two decimal places. Do not round intermediate values.
   
   Production run length =  days
   
5. Maximum inventory. Round your answer to the nearest whole number. Do not round intermediate values.
   
   Maximum inventory =
   
6. Total annual cost. Round your answer to the nearest dollar. Do not round intermediate values.
   
   Total annual cost = $  
   
7. Reorder point. Round your answer to the nearest whole number. Do not round intermediate values.
   
   r =

Answer 1

Answer:

	Daily production rate, p	23500/250	94.00
	Daily demand/usage rate, d	D/o	29.20
	operation days, o=	Given	250
	Annual demand, D=	Given	7300
	Setup or cost per order, S	Given	$160.00
	item cost	Given	$15
	holding cost percent	Given	16.0%
	holding cost per year, H=	holding cost percent*item cost	$2.32
Answer a	Production order quantity, Q=	SQRT(2*S*D/(H*(1-d/p)))	1208.56
Answer d	length of production run in days, t	t= Q/p	12.86
Answer b	#orders per year or production runs per year=	Annual demand/ordered quantity, D/Q	6.04
Answer c	cycle time=	days per year/orders per year	41.39