I have just about lost count of the things that have broke in my house since mid May. The biggest appliance failure was the washing machine. It’s hard to go without a washing machine with three youngsters in the house.
The bearings could have been replaced for about $500, but a ~12 year old washing machine has a limited lifespan. My husband and I decided to purchase a new washing machine. Luckily, we were shopping for the washing machine over the Memorial Day weekend, when just about every appliance store put their washing machines on sale. I started by grilling the washing machine repair person about what machines he would recommend. This was extremely useful in narrowing down our choices. After spending a couple hours reviewing reviews and prices, we narrowed our choices down to four:
- repair our existing machine
- a low end washing machine
- a mid-level washing machine
- a high end washing machine
My husband and I listed our criteria:
- Washing machine capacity (three kids = lots of laundry)
- Price
- Features (both for doing laundry and making my life easier)
The capacity varied from 3.5 cubic feet to 4.3 cubic feet.
The price captures the purchase price and the chance of a $500 repair in the next five years. The price of the existing machine captures the immediate $500 and the probability of having to replace the machine in the next five years (where it would be replaced b ya mid-level machine). Repairing the existing machine came out to be the most expensive option over the next five years. The costs varied from $451 -$1222. We didn’t consider operating cost, because the water and detergent costs were dwarfed by the purchase and repair costs.
The features is a constructed scale, which captures on a scale from 0 to 4 how useful I find the features. The low end washing machine didn’t offer anything about the bare minimum, whereas the high end washing machine just about does the laundry itself. The mid-level and my existing washing machines offered nice features that I would take advantage of, and I scored them at 3 and 2, respectively.
After looking at the machines, I fell in love with the high end washer, despite its hefty price tag. My husband preferred the mid level washer. The high end washer has a larger capacity and features to keep laundry fresh when a wet load of laundry sits in the washer overnight. I eventually sided with my husband, since buying a high end washer would make him less inclined to buy me a fancy range/oven for my birthday. A fancy oven would help me bake the best possible Christmas cookies, so I don’t think I can live without it for much longer.
When researching the new washer, I did a quick multi-objective decision analysis on the washing machine decision with the three criteria mentioned earlier. I estimated our swing weights to be 0.25 for capacity, 0.60 for price, and 0.15 for features.
The values for the four options are:
- repair our existing machine = 0.27
- a low end washing machine = 0.60
- a mid-level washing machine = 0.61
- a high end washing machine = 0.58
The highest value was for the washing machine my husband preferred, the washing machine that we ended up purchasing. Does that mean we made the right decision? Not so fast. Three options have similar values. The three machines have different capacities, and capacity is a proxy for my time (less capacity = more time doing laundry). A quick sensitivity analysis on the weight for capacity (illustrated below) suggests that if we weigh capacity slightly more heavily, we should have chosen the the high end washer, and if we weigh capacity slightly less heavily, we should have chosen the low end washer. This quick MODA analysis has only convinced me that any decision could have been OK, except keeping our washing machine.
MODA analysis of washing machine purchase
Punk Rock Operations Research 
August 13th, 2011 at 11:00 am
Where did power consumption come in? With increasing energy costs this would seem to be an interesting component of the problem.
August 14th, 2011 at 7:43 pm
That is a good point. I figured that doing the same amount of laundry would lead to *roughly* the same energy costs. We compared front loaders, which all use way less water than the top loaders. Energy costs over a year pale in comparison to the purchase prices. Over time, that might not be true. If I spent more time on this analysis, I would have taken energy into account.
August 14th, 2011 at 9:55 pm
Wow, that surprises me. I guess I’m used to European efficiency labels that make consumption very clear (and of course, higher energy costs in Europe).
August 15th, 2011 at 8:47 pm
Nice application of DA and sensitivity analysis. Will share this with my undergrad students this semester.
August 16th, 2011 at 7:27 am
Thanks, Chris. They should really improve upon this analysis! Let me know what they would do differently.
August 16th, 2011 at 8:33 am
Peter, check out this spreadsheet to see the energy costs per year. At five loads per week, the energy costs are $42 for an energy star washer vs. $85 for a conventional washer. I was only comparing front loading energy star washers, so the energy costs would average out to be roughly the same. Had I added a conventional washer to my comparison, I would have needed to add in energy costs. Thanks again for your feedback!
August 21st, 2012 at 9:39 am
Laura – I mentioned my stress over buying a washing machine to a grad student and he led me to your blog. This is great – what did you end up buying?
August 21st, 2012 at 12:36 pm
Karen, We ended up buying a Whirlpool, I think it was model WFW9151YW or maybe WFW9351YW.
December 12th, 2013 at 9:06 am
Hi Laura – thanks for the great example. I have 2 quick questions about the maths behind the exponential utility function in your spreadsheet, and I hope you can share a little time to help me understand it.
You used the maximum and minimum payoffs in order to calculate the value of the utility function. Then you state the value of rho (or R). (1) How did you derive this?
You use a sort of ‘middling’ value in the range between max and min payoffs. (2) Why did you do this, and how did you arrive at these values?
Many thanks! I’m hoping to build one of these myself soon to support a house-buying decision.
December 12th, 2013 at 11:29 am
Paul, Thanks for the comments. To be honest, I don’t remember a lot of the details. I used “Strategic Decision Making” by Craig Kirkwood as the text – the values of rho (or R) comes from that text. To answer your broader question about doing an analysis for buying a house, I recommend “Smart Choices” by Hammond, Keeney, and Raiffa as a gentle introduction to building models to help with buying a house. I may do that this year too!
December 12th, 2013 at 11:59 am
Great, cheers 🙂