5.12 DataStream currently uses one central DC to supply the entire northeast reg

Question

5.12 DataStream currently uses one central DC to supply the entire northeast region of the United States. In order to improve customer service, the company decides to open two more warehouses and distribute the total NE demand as follows: (i) 50% to the central DC (ii) 25% each to the two new DCs To examine the impact of this strategy on DataStream, derive the expressions for the following inventory measures:

(a) Total inventory in the supply chain

(b) Total number of orders in the supply chain

(c) Frequency of orders from the DCs

4.10 Let the power curve expression you developed in Exercise 4.7 given above be denoted by ro(x) Coxrbo, where ro is the estimated effective rate in $/cwt and x is the shipment weight in pounds (Ib). Following the steps listed in the chapter, convert this expression to an equiva- lent (undiscounted) function, n(wQ)=GQ', where r, is the estimated effective rate in $/unit, Q is the number of units shipped, and w is the per-unit weight in pounds. Explain how these steps ultimately convet . $/cwt to $/unit.

Explanation / Answer

To be calculated:

Expressions for the following inventory measures:

(a) Total inventory in the supply chain

(b) Total number of orders in the supply chain

(c) Frequency of orders from the DCs

Given values:

Demand is distributed as;

Central DC (CDC) = 50%

New DC1 = 25%

New DC2 = 25%

Solution:

(a) Total inventory in the supply chain is determined as;

Total inventory = Sum of Inventory at the central DC, Inventory at the two new DCs and Inventory in transit

Total Inventory in the Supply Chain = I-CDC + I-DC (1) + I-DC (2) + I-I-T

where,

I-CDC = Inventory at the central DC (including safety stock)

I-DC (1) = Inventory at the new DC (1)

I-DC (2) = Inventory at the new DC (2)

I-I-T = Inventory in transit

(b) Total number of orders in the supply chain is determined as;

Total number of orders, N = D / Q*

where,

D = Annual Demand

Q* = Optimal or Economic Order Quantity

(c) Frequency of orders, also known as time between the orders, from the DCs is determined as;

Frequency of orders = Number of working days in a year / N

where,

N = Number of orders

If the DC operates for 365 days in a year, frequency of orders will be,

Frequency of orders = 365 / N

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