HTML

vue select v-for

<select class="form-control" name="template" v-model="selected">
    <option v-for="item in inventory" v-bind:value="item">
       {{ item.name }}
    </option>
</select>

vue select

<select v-model="selected">
  <option v-for="option in options" v-bind:value="option.value">
    {{ option.text }}
  </option>
</select>
<span>Selected: {{ selected }}</span>

vue select option v-for selected

new Vue({
  el: '#app',
  data: function() {
    return {
      selectedFlavor: 'lime',
      flavors: ['blueberry', 'lime', 'strawberry']
    }
  },
  methods: {
    change: function() {
      this.selectedFlavor = 'strawberry';
    }
  }
})


<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.13/vue.min.js"></script>
<div id="app">
  <button @click="change()">Set Strawberry</button>
  <select v-model="selectedFlavor">
    <option v-for="flavor in flavors" :value="flavor">{{flavor}}</option>
  </select>
</div>