Question

A distribution company is considering two locations for the construction of a new automated warehouse: Chicago and Dallas. Two types of automation are also being considered: bar coding and RF/ID (radio-frequency identification). The annual operating costs for each type of automation at the two locations are:

	Bar Coding		RF/ID
Location	Fixed Cost	Variable Cost per 1,000 units	Fixed Cost	Variable Cost per 1,000 units
Chicago	$1,800,000	$12.30	$2,700,00	$9.70
Dallas	1,500,000	13.10	2,300,000	9.40

For what range of annual product volume handled would each location and type of automation be preferred?

Notes:

The point of indifference between two alternatives is the point at which the total costs are equal: TC _A = TC _B. The total cost of each alternative is: TC = FC +( VC * Q), where FC are the fixed costs, VC are the variable costs, and Q is some volume/quantity/units. Then the point of indifference would be:

FC _A + (VC _A * Q) = FC _B + (VC _B * Q). Plug the appropriate fixed and variable costs into the formula and solve for Q.

At Q, you are truly indifferent to the two options, so other information must be used to make the decision and that information is typically expected demand. For volume or demand between zero and Q, the option with the lowest fixed cost typically yield the lowest total costs (see Figure 4.10). For volume or demand that is greater than Q, then the option with the lowest variable cost typically yields the lowest total cost (the investment begins to payoff).

For Figure 4.10, comparing Processes A and C, we are indifferent at 15,000 units. For the preferred ranges of volume, we would prefer Process C from 0 to 15,000 units; we would prefer Process A for volume of 15,000 or more.

Answer 1

As given in the question the total cost of each location and and automation type is:

,

where FC is the fixed cost for the location and automation type

VC is the the variable cost, for the location and automation type

Q is the annual product volume (in 1000s) handled at the location

Total cost for Chicago and automation type barcoding

Total cost for Chicago and automation type RFID ( Treating the RFID cost for Chicago as $2,700,000 based on the thousand separator)

Total cost for Dallas and automation type barcoding

Total cost for Dallas and automation type RFID

First we will draw the 4 total cost lines to get a sense of the total costs for different Q

We can see that the lowest total cost for product volume less than that corresponding to the dotted line is for location Dallas and automation type Bar code. And Dallas, Bar code indeed does have the lowest fixed cost of $1,500,000 of the 4 choices

For product volumes beyond the dotted line, we can see that Dallas with automation type RFID is the most cost effective. And Dallas, RFID indeed does have the lowest variable cost of $9.4 of the 4 choices

Now we solve the equations to find the indifferent volumes

We equate the total costs of Dallas - Bar code and Dallas RFID

T

That means the 2 costs are the same for annula product volume of units

For the product volumes less than Q= 216,216,216 units Dallas location with bar coding has the lowest total cost, for product volumes greater than Q=216,216,216 units, Dallas location with RFID has the lowest total cost.

There is no need to solve other equations as Dallas has the lowest fixed cost and variable costs and hence the total cost

The excel data for the graph is generated using

the table with data is

	Total Cost
Q - annual product volume (in 1000s)	Chicago - BarCode	Chicago - RFID	Dallas - BarCode	Dallas - RFID
100000	3,030,000	3,670,000	2,810,000	3,240,000
110000	3,153,000	3,767,000	2,941,000	3,334,000
120000	3,276,000	3,864,000	3,072,000	3,428,000
130000	3,399,000	3,961,000	3,203,000	3,522,000
140000	3,522,000	4,058,000	3,334,000	3,616,000
150000	3,645,000	4,155,000	3,465,000	3,710,000
160000	3,768,000	4,252,000	3,596,000	3,804,000
170000	3,891,000	4,349,000	3,727,000	3,898,000
180000	4,014,000	4,446,000	3,858,000	3,992,000
190000	4,137,000	4,543,000	3,989,000	4,086,000
200000	4,260,000	4,640,000	4,120,000	4,180,000
210000	4,383,000	4,737,000	4,251,000	4,274,000
220000	4,506,000	4,834,000	4,382,000	4,368,000
230000	4,629,000	4,931,000	4,513,000	4,462,000
240000	4,752,000	5,028,000	4,644,000	4,556,000
250000	4,875,000	5,125,000	4,775,000	4,650,000
260000	4,998,000	5,222,000	4,906,000	4,744,000
270000	5,121,000	5,319,000	5,037,000	4,838,000
280000	5,244,000	5,416,000	5,168,000	4,932,000
290000	5,367,000	5,513,000	5,299,000	5,026,000
300000	5,490,000	5,610,000	5,430,000	5,120,000
310000	5,613,000	5,707,000	5,561,000	5,214,000
320000	5,736,000	5,804,000	5,692,000	5,308,000
330000	5,859,000	5,901,000	5,823,000	5,402,000
340000	5,982,000	5,998,000	5,954,000	5,496,000
350000	6,105,000	6,095,000	6,085,000	5,590,000
360000	6,228,000	6,192,000	6,216,000	5,684,000
370000	6,351,000	6,289,000	6,347,000	5,778,000
380000	6,474,000	6,386,000	6,478,000	5,872,000
390000	6,597,000	6,483,000	6,609,000	5,966,000
400000	6,720,000	6,580,000	6,740,000	6,060,000