Operation Management-QA268

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Question 1: (10 pts) True-False: (2 points per question) Answer each question True (T) or False (F).  You may, if you feel it is warranted, give a brief explanation of your response.
 

  • For a (s,Q) inventory control policy, the safety stock inventory will increase as the replenishment lead time increases.
  • In an EOQ exchange curve, both TCS and N increase as the ratio A/r increases.
  • The error incurred by a power-of-two policy is less than the error incurred by an integer policy.
  • The EOQ model is appropriate for determining the amount of safety stock needed for an item whose demand varies randomly over time.
  • In the power-of-two formulation of the joint replenishment problem, the reorder interval for each item in a family must be greater than or equal to the reorder interval for the family (major) setup.

 

Question 2: (10 pts) Multiple Choice: (2 pts per question) For each of the statements or questions below, write the letters of the correct responses in the blank provided.
 
The inventory that is carried to buffer or hedge against the uncertainty of demand or supply is called
 
(a) cycle stock

(b) pipeline stock

(c) congestion stock

(d) safety stock

 

Power-of-two reorder intervals are useful because they
 
(a) simplify the coordination of multi-item or multi-location replenishment problems

(b) have lower cost than the corresponding EOQ reorder intervals

(c) have lower cost than general integer reorder intervals

(d) (b) and (c)

 

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In a space constrained, multi-item EOQ problem, the optimal Lagrange multiplier increases as the amount of space available
 
(a) increases

(b) decreases

(c) sometimes increases, sometimes decreases

(d) none of it, it does not change

 

In an (R, S) inventory control policy, the order-up-to point, S, is determined by the probability distribution of the demand during a

(a) lead time

(b) single period

(c) review period

(d) lead time plus a review period.

 
Economies of scale in purchasing and ordering motivate a manager to

  1. increase the lot size and cycle inventory.
  2. decrease the lot size and cycle inventory.
  3. eliminate inventory.
  4. increase the lot size and reduce cycle inventory.
  5. none of the above

 

Question 3: (15 pts) Provide short answers for each question. Part d requires simple calculation. Be sure to show your work. (5 points per part)

  1. a) Why do we use deterministic inventory models, knowing that demand and supply are uncertain most of the time?
  2. b) Name three main pitfalls of managing inventories in supply chains and explain how we can convert them to opportunities.
  3. c) Lead time for a certain product has a mean of 6 days with a standard deviation of 3 days. Monthly demand for the product has mean of 300 with a variance of 900. Assume there are 30 days per month. i. (3 pts) What is the expected demand during lead time?
  4. (2 pts) What is the standard deviation of demand during lead time?

 

 

Question 4: (20 pts)
 
A company adopts an (s,Q) inventory policy where all the items meet a safety factor k=1.2.  The lead time from their suppliers is one month and interest rate r=20%. The other data for products are as follows:
 

Item i Demand, Di (units/year)

 

 vi ($/units)

 

 σi,1 (units)

 

 Ai ($)
1 1200 50.00 20 100.00
2 1800 30.00 50 100.00
3 1500 100.00 40 120.00
4 3000 150.00 75 150.00

 

a)Calculate the expected value of total safety stocks (TSS) and the expected total value short per year (ETVSPY) for the current policy.

  1. b) Using B2 cost criteria, determine a better ETVSPY for the same value of TSS. How much savings are realized?

 

Question 5: (15 pts)
 
Five DCs replenish their inventory from a cross-dock facility that operates on a breakbulk concept. Each time a DC places an order with the cross-dock; cross-dock places an order with the outside supplier for a fixed cost of $500 per order since the cross-dock does not keep any inventory. The operating costs and parameters of each DC are given below
 

 DCs Annual Demand

 

 Setup Cost Unit Item Cost

 

 Inv. Holding %
1 50 100 10 0.25
2 10 250 2 0.5
3 75 150 10 0.2
4 25 200 20 0.25
5 10 50 10 0.1

 

 

Using a power-of-two inventory policy,
 

  1. a) Determine the reorder points of each facility (cross-dock and DCs).
  2. b) Determine the total cost associated with the solution in part a.

 

Question 6: (20 pts)
 
The inventory of an item is reviewed once every 2 weeks and has a constant replenishment lead time of 4 weeks.  The average demand for this item is 15600 units per year with a standard deviation of 100 units per week.  The cost of each review is $50 and the item has a variable cost of $40 per unit purchased.  The inventory carrying cost is 26% per year (assume 52 weeks per year).  Assume that the demand is normally distributed.  The company uses a 98-percent fill rate (P2).

 

P 2 0.98 [%] Fill rate
v 40 [$/unit] Unit cost
r 0.26 [$/$/year] Carrying cost rate
D 15600 [units/year] Annual Demand  
σ1 100 [units/week] Standard deviation of weekly demand  
L 4 [weeks] Lead time
Year 52 [weeks]
k min 0 Minimum safety factor
A 50 [$] Setup Cost
R 2 [weeks]

 

  1. Calculate the optimal (R, S) base stock policy for this item.
  2. What is the imputed B2 penalty?

iii. Calculate the total relevant cost for this policy including average replenishment cost, average cycle stock, average safety stock, and average weekly cost for this policy.

 

Question 7: (15 pts)

forecast demand for a component at around 2500 units a year. They make the component internally and the production rate is 10,000 units a year. It costs $750 to setup each production run with a variable cost of $40 a unit.  Barring Ltd. uses a 20% of rate of return to estimate the holding cost.  It takes 15 days to setup the production.  Another manufacturing company offers to sell the component to Baring Ltd. for $50 a unit and $100 per order. The lead time to ship to product would be one month.

 

In house Other Source
D 2500 [units/year] v 50 [$/unit]
p 10000 A 400 [$]
r 0.2 [$/$/year]
v_p 40 [$/unit]
A_p 750 [$]

 

  1. What should the firm do (produce or procure) to minimize its total cost? What would be the firm’s inventory policy to attain this cost?
  2. The manufacturing company offers the following all-units quantity discount:
  • For orders of 400 units or more, it is offered a discount of 10% for every unit; and
  • For orders 750 or more, it is offered a 20% for every unit. How would your answers for part i change?

 

Product code: Operation management-QA268

 
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