The movie, Star Wars VII, is coming out Friday, Dec. 15th. Emagine Saline, a mov
ID: 383707 • Letter: T
Question
The movie, Star Wars VII, is coming out Friday, Dec. 15th. Emagine Saline, a movie theater south of Ann Arbor with ridiculously comfortable seats, is planning to sell an opening day poster that can be purchased only on Friday. It costs Emagine $1.50 to purchase each poster from their distributor, and they're planning to sell them for $10 each. Because they are required to recycle any unsold posters after Friday, there is no salvage value. They don't know what the demand for the posters will be so they have decided to assume it is uniformly distributed between 75 and 130 posters. The inverse of the Unif (a, b) distribution is F-1(t) a + t(b - a). (a) How many posters should Emagine Saline purchase? Note, they would like to purchase an integer quantity. One of your friends, Phillip, does stock-keeping for Emagine. He mentioned his boss asked him to figure out how many boxes of popcorn kernels to order and how often. He isn't sure what to do. Conveniently you took at IOE 202, and you tell him that you'lI help him out as long as he nabs you one of those sweet Star Wars VII posters. He rolls his eyes but agrees. xes of popcorn kernels. Each time an order is Phillip tells you each week, Emagine uses 235 bo placed, it costs $15, and orders take ½ week to arrive. The cost per box of popcorn varies based on how many boxes are ordered at the same time, see table below. The cost to hold a box per week is 5% of the value of the box. The cost per box is: Number of boxes 0-150 151-400 401-1000 1000 Cost per box $3 $2.4 $2.25 (b) How many boxes should Emagine order each time an order is placed? They would like to order an integer quantity. Show all work (c) How much will this order policy cost per week? (d) How often should Emagine place an order? (e) What is the re-order point? (f) If the lead time were to increase, would you expect the re-order point to increase or decrease? (g) If boxes of popcorn kernels are perishable (i.e., go bad after enough time has passed), how would this change how we model this problem?Explanation / Answer
(a) Cost of Understocking, Cu = selling price - cost = 10 - 1.5 = 8.5
Cost of Overstocking, C0 = cost - salvage value = 1.5 - 0 = 1.5
Optimal in-stock level, t = Cu / (Cu+Co) = 8.5/(8.5+1.5) = 0.85
Optimal stocking level (number of posters to purchase) = F-1(t) = a + t(b-a) = 75 + 0.85*(130-75) = 122
(b) Starting with initial price, P = $ 3
Holding cost per unit per week, H = 3*5% = 0.15
EOQ = SQRT(2*D*S/H) = SQRT(2*235*15/0.15) = 218
EOQ is in the range 151-400, so the applicable unit price is $ 2.7
Recalculate H = 2.7*5% = 0.135
EOQ = SQRT(2*235*15/0.135) = 229
Total weekly cost of EOQ policy = Ordering cost + Holding cost + Purchase cost
= (D/Q)*S + (Q/2)*H + D*P
= (235/229)*15 + (229/2)*0.135 + 235*2.7
= 665
For the next level P = 2.4, Q = 401,
Total weekly cost =(235/401)*15 + (401/2)*2.4*5% + 235*2.4 = 597
For the next level P = 2.25, Q = 1000,
Total weekly cost =(235/1000)*15 + (1000/2)*2.25*5% + 235*2.25 = 588
Total weekly cost is lowest for Q=1000
Therefore, optimal order quantity = 1000
(c) Total cost per week = 588 (as determined above)
(d) Order frequency = Q/D = 1000/235 = every 4.26 weeks
(e) Reorder point = D*L = 235*(1/2) = 118 (where L is the lead time)
(f) Reoder point would increase with increase in lead time.
(g) If popcorn kernels are perishable, then apply the newsvendor model