Question

Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 6,900 copies. The cost of one copy of the book is $13. The holding cost is based on an 15% annual rate, and production setup costs are $155 per setup. The equipment on which the book is produced has an annual production volume of 21,500 copies. Wilson has 250 working days per year, and the lead time for a production run is 15 days. Use the production lot size model to compute the following values:

A. Minimum cost production lot size. Round your answer to the nearest whole number. Do not round intermediate values.

Q* =

B. Number of production runs per year. Round your answer to two decimal places. Do not round intermediate values.

Number of production runs per year =

C. Cycle time. Round your answer to two decimal places. Do not round intermediate values.

T = days

D. Length of a production run. Round your answer to two decimal places. Do not round intermediate values.

Production run length = days

E. Maximum inventory. Round your answer to the nearest whole number. Do not round intermediate values.

Maximum inventory =

F. Total annual cost. Round your answer to the nearest dollar. Do not round intermediate values.

Total annual cost = $

G. Reorder point. Round your answer to the nearest whole number. Do not round intermediate values.

r =

Answer 1

ANNUAL DEMAND = 6900
SETUP COST = 155
HOLDING COST = 1.95
DAILY PRODUCTION = 86
DAILY USAGE = 27.6
COST PER UNIT = 13

1. PRODUCTION EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST * (1 - (DAILY USAGE / DAILY PRODUCTION))) = SQRT(2 * 6900 * 155 / (1.95 * (1 - (27.6 / 86))) = 1271

2. NUMBER OF PRODUCTION RUNS = ANNUAL DEMAND / EPQ = 6900 / 1271 = 5.43

3. CYCLE TIME = EPQ / DAILY USAGE = 1271 / 27.6 = 46.05

4. RUN TIME = EPQ / DAILY PRODUCTION = 1271 / 86 = 14.78

5. MAXIMUM INVENTORY = POQ * (1 - (DAILY USAGE / DAILY PRODUCTION)) = 1271 * (1 - (27.6 / 86)) = 863

6. AVERAGE INVENTORY = (EPQ * (1 - (DAILY USAGE / DAILY PRODUCTION))) / 2 = ((1271 * (1 - (27.6 / 86))) / 2) * 1.95 = 431.55

ANNUAL HOLDING COST = AVERAGE INVENTORY / 2 HOLDING COST PER UNIT = (431.55 * 1.95) = 841.52
ANNUAL ORDERING COST = (ANNUAL DEMAND / POQ) * SETUP COST = (6900 / 1271) * 155 = 841.46
TOTAL PURCHASE COST = ANNUAL DEMAND * PER UNIT COST = 6900 * 13 = 89700
TOTAL ANNUAL COST OF INVENTORY = ANNUAL HOLDING COST + ANNUAL SETUP COST + ANNUAL PURCHASE COST = 91382.98 OR 91383

7. LEAD TIME = 15 DAYS
ROP = DAILY DEMAND * LT = 27.6 * 15 = 414

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