Supply Chain: Transportation and Logistics Management

Problem 1: Optimizing Service Performance (10 points)

Annual demand for a product is 5,000 units.  If the service level were to increase by 1%, the increase in revenue would be .25%.  Product costs are $35 per unit, margin is $4 per unit and carrying costs are 20% of product costs.  Lead time for replenishment of the product is 1 week and the standard deviation of demand over this lead time is 119 units.

1. What is ΔP (the change in profit for a 1% increase in service level)? ((4points)
2. What is ΔC (the cost to increase service level 1%)? (Leave your answer as a number times Δz) (4 points)
3. What is the optimal service level? (Use the highest whole percentage) (2 points)

Problem 2: Warehouse Sizing (10 points)

A private warehouse has an annual throughput of 20,000 items and an average material handling cost per item of $0.20/ft. The warehouse size is to be 500,000 sq. ft. Annual construction and maintenance costs are $300/ft. of perimeter.

1. If the loading and unloading dock is to be located at location X, a warehouse corner as shown in the figure, what are the best width and length of the warehouse? (4 points)

1. If the loading and unloading dock is to be located at location X, a warehouse corner as shown in the figure, what is the total cost for the optimal sized facility? (3 points)

1. If the loading and unloading dock is to be located at location Y, a warehouse side as shown in the figure, what is the total cost for the optimal sized facility? (3 points)

Problem 3: Facility Location – Center of Gravity Method (10 points)

A warehouse is to be built that will support three factories.  The (x,y) location of each factory, annual volume and transportation rate from each factory is given below.  Use a map scaling factor of k=500 miles.

1. Using the COG method, what is the optimal (x,y) location of a single warehouse? (5 points)

1. If the warehouse is located at an (x, y) of (6, 5), what would be the total transportation cost? (5 points)