Question

Ashlee's Beach Chairs Company produces upscale beach chairs. Annual demand for the chairs is estimated at 1,000 units. The frames are made in batches before the final assembly process. Ashlee's final assembly department needs frames at a rate of 20 per week. Ashlee's frame department can produce 25 frames per week. The setup cost is $100/setup, the annual holding cost per frame is $4, and the cost of production $30 a frame. The company operates 50 weeks per year. Set up an optimum inventory system for Ashlee that would minimize the annual cost of the inventory system. Find the following:
a. Production quantity (Q)
b. Number of production runs
c. Length of production run (tp)
d. Peak inventory
e. Average inventory
f. Idle time (ti)
g. Cycle time
h. Number of cycles
i. Total annual inventory cost (T)
j. Total annual cost of the system (TS)

Answer 1

solution-

Set up cost K=$100

Holding cost h=$4 per frame

Production cost c = $30 per frame

Production rate of assembly r'=20 per week=1000 units per year

[ in 1 week they are producing 20 chairs so in 50 weeks they will produce 50*20=1000 chairs]

Production rate of frame r=25 per week = 1250 units per year

Demand a= 1000 units per year

Now , demand for chair = demand for frame =1000 units per year

Also, chair can be produced only if they have frame so we will consider the production of rate = production rate of frame = r (as r>r')

Q is the economic lot size.

In this model each production cycle time T consists of two parts t1 and t2. Where t1 is the period during which the stock is growing up at a constant rate r - a per unit time and t2 is the period during which no production but inventory is decreasing at a rate of a units per unit time.

S is the stock available at the end of time t1 which is expected to be consumed during the remaining period at the consumption rate a.

a