It’s all about the customer. It’s always about the customer, about being able to adapt to the marketplace to satisfy the customer,” says Robert L. Williams, Jr., assistant professor of marketing at Susquehanna University, in Selinsgrove, Pennsylvania.

Since 2005, when the U.S.’s biggest online retailer launched a membership scheme, with customers paying a monthly fee for services like streaming and for free two-day delivery—same-day delivery in certain markets—competitors have scrambled to keep up. Just between January 2014 and May 2016, shipping times fell 46% to 3.4 days from 6.3 days, according to an average of 238 merchants and online sellers surveyed by Slice Technologies Inc., a Palo Alto, California, shopping and package-tracking application. As a result of new technology making tracking easier, “Customers recognize they have that power, and they want to exercise it,” Prof. Williams notes.

A key objective, says Kenneth Cassar, Slice’s principal analyst, is “challenging consumers to think differently about the online channel. In the past, online was the place to go for low prices and broad selection. Increasingly, people are looking to the e-commerce channel for convenience. Convenience is creeping up on price and selection for importance.”

Any retailers aiming for same-day delivery face the same problems, according to a white paper published by Quintiq, a supply-chain optimization firm owned by Dassault Systèmes. The usual methods of assigning slots are unable to satisfy both cost savings and customer satisfaction. With regular rounds, customers don’t have enough choice for delivery time, but with dynamic slots, drivers waste time and fuel delivering a package at a certain time for one customer and then, hours later, a package next door for another customer. Quintiq uses forecasts to allocate delivery slots dynamically, updating in real time. That minimizes driving while giving customers maximum choice of delivery time.

Same-day delivery doesn’t apply to all of the millions of items for sale by online retailers, meaning even e-commerce behemoths must juggle convenience vs. selection. They must also invest in warehouses in order to get goods close enough to population centers for quick delivery, notes Daphne Carmeli, chief executive of Deliv. The Menlo Park, California, company works with retailers and businesses to provide same-day delivery in 17 U.S. markets using crowd-sourced drivers.

However, brick-and-mortar retailers already have vast inventory that’s conveniently close to customers—inside their stores. “Much of their inventory sits within a short drive of 90% of the population,” Ms. Carmeli says. “How do you leverage your stores to be the forward-fulfillment centers? Drivers leverage their GPS-enabled smart phones to respond to delivery requests. These technologies that power the supply and demand were not available 10 years ago.”

Retail chains and franchises are using “click and collect” or BOPIS (buy online, pick up in store) to give online shoppers the convenience of quick fulfillment from a store at no charge. Or they leverage the capabilities of BOPIS along with a service like Deliv to offer same-day delivery as an option at checkout. When customers select same-day delivery, Deliv is automatically notified of the order and dispatches a driver to pick up and deliver the order when it is ready, Ms. Carmeli says.

Retailers are “looking for opportunities to create a channel-integrated environment,” says Lars M. Bollweg, researcher at the Competence Center E-Commerce at the South Westphalia University of Applied Sciences in Soest, Germany.

Originally, retailers had a single channel, meaning a brick-and-mortar shop that people visited. That involved one database of customers in the background. With the arrival of the Internet, retailers had a physical shop and an online shop, each with a separate database. But both channels remained strictly separated. If someone ordered in the online shop, the sales clerks in the brick-and-mortar shop knew nothing about it, Mr. Bollweg says.

That improved with cross-channel management software, which let both databases talk to each other a little while remaining separated.

Then came omnichannel, or one big customer database. “Wherever the customer meets the company—by phone, online, in person—the retailer knows the whole history of shopping events,” such as whether the customer purchased frequently, or recently encountered a problem with a purchase, Mr. Bollweg says. “Omnichannel offers more opportunity to deliver more advanced services, but it’s tricky to do. It’s expensive. And it’s very challenging for small shops.” With apps and location services, for example, a store can send you a coupon for a discount just at the moment you’re in the neighborhood.

As a result, local shopping platforms sprang up to implement the strategy for groups of shops that would split the cost. Such shops, often run by individual entrepreneurs who lack technological skills, benefit from the platform’s e-commerce know-how, Mr. Bollweg says.

For example, a public-private initiative in a German city gives local small retailers an omnichannel framework, including centralized delivery of goods and returns. These platforms are a big trend in Germany, and also exist in the U.S. and Switzerland. However, some are only a year old and haven’t yet turned profitable, he says.

While more people are choosing same-day delivery for a bigger assortment of purchases, it’s still “very, very early days,” Mr. Cassar says. “I would be shocked if 20 years from now the majority of online sales were being delivered to consumers on the same day.”

The market has “room for everybody,” Dr. Williams concurs, “but with the customer in control, everybody has to step up their game. There’s no room for being complacent.”