Substantial deviation from the optimal cost

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QUESTION

Problem 1

D = 100,000 per year, Ordering cost = S = $1000, H = $25/month. Assume a lead time of 1 day (365 days per year).

Fill in the following table.  Write out the formulas you are using.

Problem 1 Total Equation Used
Annual Demand (D)
Holding Cost ($/unit/yr) (H)
Ordering Cost (S per order)
Ordering Quantity (EOQ)
Number of Orders Per Year
Average Inventory
Q*, Maximum Inventory
Reorder Point (ROP)
Length of Order Cycle
Annual Holding Cost
Annual Ordering Cost
Holding Plus Ordering Costs

Problem 2

The data is D = 50,000/year, S = $500 per order, H = $0.25 per unit per year. Assume a lead time of 2 days.

(a) Repeat the calculations of problem 1.

Problem 2(a) Total Equation Used
Annual Demand (D)
Holding Cost ($/unit/yr) (H)
Ordering Cost (S per order)
Ordering Quantity (EOQ)
Number of Orders Per Year
Average Inventory
Maximum Inventory, Q*
Reorder Point (ROP)
Length of Order Cycle
Annual Holding Cost
Annual Ordering Cost
Holding Plus Ordering Costs

(b) It was determined that a mistake was made in the data and the correct data is D = 60,000 per year, S = $400 per order, H = $0.20 per unit per year. Calculate the correct EOQ and inventory cost.

(c) Now suppose we used the incorrect EOQ (based on the first set of data) instead of the correct EOQ. Calculate the inventory cost. (Find total holding cost plus ordering cost using EOQ from a with data from b.)

(d) Compute the percentage error in the EOQ and in the inventory cost. (Calculate total holding plus ordering costs for b. Find difference from cost found in c.)

(e) Moral of the story is that incorrect estimation of costs or demand (does or does not) result in substantial deviation from the optimal cost (circle the right answer).

Problem 3

The mean demand is 5000/week, standard deviation of demand = 1500 per week, H = 0.50 $/unit/year, S = $20,000/order. L = 2 weeks if they ship by air. Suppose we have the following extra information: if they ship by sea instead of air, L = 3 weeks. It saves $500 per year in transportation cost. Assume service level needed is 95%.

(a) Note that if lead time increases safety stock will increase. Compute by how much.

(b) Should they ship by sea?  (Hint: compute the change in safety stock if they ship by sea. Then see if the cost of carrying this additional stock is worth the savings in transportation cost.)

Problem 4

A distributor is planning to consolidate his two warehouses into a single one. He sells widgets from the warehouse. Each widget costs $100. He estimates that each separate warehouse today faces a mean demand of 1200 per week with standard deviation of 200 per week. The lead time is two weeks. His ordering cost is $100 per order. He plans to build a new warehouse and sell his two old ones. The net cost for doing so is not clear, but he wishes to know what he can afford. His holding cost is 25% per year.

(a) Determine the EOQ and annual inventory cost for each warehouse.

(b) Determine EOQ and annual inventory cost for single warehouse.

(c) Compute difference in safety stock between the 2 systems. Note that combined demand will have a standard deviation = square root (2) x std deviation of demand at a single warehouse. Assume that the service level needed is 99%.

(d) Compute the cost saving in combining into a single warehouse.

Sample Solutions
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