Production Lot Size - Optimization long and difficult

[htoor9]

Homework Statement

Non-Slip Tile Company has been using production runs of 100,000 tiles, 10 times per year, to meet the demand of 100,000 tiles annually. The set-up cost is $5,000 per run and (annual) holding cost is estimated at 10% of manufacturing cost of $1 per tile. Production capacity of the machine is 500,000 tiles per month. Factory is open 365 days per year.

D = 1,000,000...Demand
r = 6,000,000...annual production rate
Q = 100,000...production lot quantity
C₀= $5,000...setup cost per cycle
C_h= $0.10...inventory holding cost per unit per time period
p = $1...production cost

1. During each cycle, what is the average amount of inventory? Should be in terms of parameters D,r,C0,Ch,p,Q (not necessarily all of them).
Find the holding cost over the entire year.
2. Sum up the 3 parts of total cost. Find the value of Q(in terms of D,r,c0,ch,p) that minimizes total cost.
3. Figure out how much to produce in each cycle(answer won't be an integer). What is total optimal cost? How does this cost compare with their current implementation?
4. For each integer within 6 of Q(Q-6 Q+6) find the total cost and plot this function. What do you see? Can we do the same thing we did with the EOQ?
5. Now find the optimal production quantity for the following problem. Be sure to label each parameter you use.

Homework Equations

The Attempt at a Solution

1. I think 1/2(r/10)...1/2(6,000,000/10) = $300,000
2. Total cost = cost to produce + setup + holding cost
Not sure where to go after this

 

[lippyka]

. 3. Not sure how to do this one either. 4. Not sure how to answer this one as well. 5. D = 1,000,000...Demandr = 6,000,000...annual production rateC0= $5,000...setup cost per cycleCh= $0.10...inventory holding cost per unit per time periodp = $1...production costQ = Optimal Production Quantity that minimizes total cost