This post will be made of a lot of quotes and references, that is kind of the point, very little original content will come from me as I am not the creator of much data science, just a user of it, though i am sure i will add commentary especially in retail as i have some practical experience in a few areas.
The funny thing about solving a data science problem is that their are many ways to solve it, so i don’t expect this to be 100% comprehensive, i try to find what appears to be a canonical solution, though that does not mean you cannot stuff everything into a neural net and close your eyes, which is what everyone appears to be doing these days…
“Price optimization is the use of mathematical analysis by a company to determine how customers will respond to different prices for its products and services through different channels. It is also used to determine the prices that the company determines will best meet its objectives such as maximizing operating profit. The data used in price optimization includes operating costs, inventories and historic prices and sales.” 
Anecdotally, retailers have always been interested in price optimization to the degree that prices can change per minute based on supply demand, much like Ubers price surge, the more you need it or want it the ore you will pay to a point, that point is what the retailers search for. An eternal exercise in Weber’s Law.
“Forecast, Learn, Optimize” 
Location of New stores
This one seems pretty obvious, if you are wanting to open a second or one thousandth store, where might you put it? But, “Where are your customers, where are your best prospects, and where are your current stores and your competitors”
This is very much a GIS exercise as well as an economics and demographic exercise. Take a look at the ARC GIS  tutorial on location allocation to get an idea of what is involved. This is not a sales pitch for GIS, but it is worthy to explore. Also consider building a new location may also take sales away from another store, also know as a form of retail cannibalization.
Product Layout in Stores
Having worked with retailers on this, I will summarize.
Also known as planongrams. These are very much optimization exercises. Factors for each store include size and weight of item, shelving size and locations and central display kiosks. Every piece of merchandise in the store is targeted to be in a specific location in space on a shelf based on weight, size, popularity, and sales.
Heavy items are not typically up high, such as one-gallon jars of pickles, though, for some reason my two liter sodas are always on the top shelf. You may want to place children’s cereal at eyelevel of a child sitting in a shopping cart or walking for instance, while adult cereals are located in non-premium shelf space. Only so many boxes, bottles or containers can fit with x number of square inches of a shelf, so all this must be taken into consideration in planning. Additionally, volume of sales may be considered to allow for more of one product over a lower selling one, so volume of sales may influence how many and where a product is located.
“In the broadest sense, merchandising is any practice which contributes to the sale of products to a retail consumer. At a retail in-store level, merchandising refers to the variety of products available for sale and the display of those products in such a way that it stimulates interest and entices customers to make a purchase.”
In retail commerce, visual display merchandising means merchandise sales using product design, selection, packaging, pricing, and display that stimulates consumers to spend more. This includes disciplines and discounting, physical presentation of products and displays, and the decisions about which products should be presented to which customers at what time.” 
This combines marketing, product design, store or website location design, product Layout, price optimization as well as discount targeting.
“Inventory management is the management of inventory and stock. As an element of supply chain management, inventory management includes aspects such as controlling and overseeing ordering inventory, storage of inventory, and controlling the amount of product for sale.
… inventory management is all about having the right inventory at the right quantity, in the right place, at the right time, and at the right cost”
“Shrinkage is the loss of inventory that can be attributed to factors such as employee theft, shoplifting, administrative error, vendor fraud, damage in transit or in store, and cashier errors that benefit the customer. Shrinkage is the difference between recorded inventory on a company’s balance sheet and its actual inventory. This concept is a key real problem for retailers, as it results in the loss of inventory, which ultimately means lost money. “
“Inventory shrinkage is a growing concern in the retail industry, with U.S. companies suffering more than $52 billion annually in known product losses”
“The most common kind of warranty on goods is a warranty that the product is free from defects in materials and workmanship. This simply promises that the manufacturer properly constructed the product, out of proper materials. This implies that the product will perform as well as such products customarily do.” 
After a warranty is made, the next objective in the interest of profit is to reduce the amount paid on a defective product by the following;
“Recover the cost of warranty -related parts failures from suppliers
Detect and reduce fraudulent claims and related risks
Determine optimum durations and conditions for warranty coverage
Accurately estimate the cost of specific warranties and terms
Perform root cause analysis on warranty -eligible failures
Improve customer satisfaction
Reduce claim volume through improved product quality“ 
Market Basket Analysis
“Market Basket Analysis is one of the key techniques used by large retailers to uncover associations between items. It works by looking for combinations of items that occur together frequently in transactions. To put it another way, it allows retailers to identify relationships between the items that people buy.”
“There is no one generally accepted definition of cannibalization. Kerin et al. (1978) use Heskett’s (1976) definition: “the process by which a new product gains sales by diverting them from an existing product”. Mason and Milne (1994) use Copulsky’s (1976) definition and are less concerned with process than with magnitude. They define cannibalization as “the extent to which one product’s customers are at the expense of other products offered by the same firm.””
“In marketing strategy, cannibalization refers to a reduction in sales volume, sales revenue, or market share of one product as a result of the introduction of a new product by the same producer…. For example, when Apple introduced the iPad, it took sales away from the original Macintosh, but ultimately led to an expanded market for consumer computing hardware.”
Demand Forecasting and Price optimization 
Next Best Offer Analysis
or Targeted Recommendations
“Next best offer (also known as next best action) is a form of predictive analytics that helps marketers and their organizations better judge customer spending habits and guide marketing efforts toward connecting with customers to close a deal.”
“Consider Facebook, which maps consumer habits on a real-time basis, 24-7. Every time a Facebook member posts a comment, photo or event, or responds to a comment, photo or event, Facebook logs that data. In that manner, the social media giant is constantly building a user profile of each user that helps Facebook analysts determine in a millisecond what users want to see, and what they are interested in buying.”
In Store Traffic Patterns
This borders in creepy and frequently brings up ethics questions whether justified or not, the gist is, while in the store, where are your customers, where did they just come from. To derive patterns you must capture this data via edge devices, which can give you heat maps but not individual tracking. Individual tracking relies on a device such as cell phone with the wi-fi enabled whether connected or not.
Using wi-fi routers in the store you can track an individuals phone based on mac address of the device then monitor where they go throughout the store, how often they visit the store, which areas they spend a lot of time in etc… The benefit of this could be recommendations on where to go next based on what other customers have done in the past, or if the customer has a loyalty app on the device, incentivize them by providing coupon if you detect them lingering on one area of the store for a while. Ideally this data would be collected over time for all customers with compatible devices, wi-fi routers have the ability to triangulate so you can generate heat maps and traffic patterns.