Running NPM scripts sequentially

You can prefix your scripts pre and post so they will execute automatically:

"scripts": {
  "prebuild": "echo \"Welcome\" && exit 1",
  "build": "start cmd.exe @cmd /k \"yo esri-appbuilder-js:widget && exit 1\"",
  "postbuild":  "start C:\\WebAppBuilderForArcGIS\\startupShortcut",
  "exit" : "start cmd.exe @cmd /k \"echo \"goodbye\" && exit 1\""
}

then run npm run build

Invoke these scripts via npm run and chain them with double ampersand &&:

npm run pre-build && npm run build_logic && npm run post_build && npm run exit

Explanation:

• Use && (double ampersand) for sequential execution.
• Use & (single ampersand) for parallel execution.

Following @Mobiletainment's great answer, you can also use npm-run-all to make the command much shorter and much more readable. In your case:

"scripts": {
    ...
    "build": "run-s pre-build build_logic post_build exit"
}

run-s is a shortcut npm-run-all provides, that runs all the given npm-scripts sequentially, hence the -s (run-s is a shorter version of npm-run-all -s).