Laravel5.4でマイグレーションファイルを生成しようと試みているのですが、外部キー周りの設定でエラーが出てしまっているようです。

mysqlの知識が疎いのですが、外部キーの設定方法が誤っているのでしょうか？

productsテーブルとcustomersテーブルにはそれぞれ、product_idカラムとcustomer_idカラムがあります(autoincrement)

ordersテーブルからそれらのカラムに外部キー制約を貼ろうとしているのですが。。。

[vagrant@localhost door]$ php artisan migrate
Migration table created successfully.

                                                                                                                                                                                                                 
  [Illuminate\Database\QueryException]                                                                                                                                                                           
  SQLSTATE[HY000]: General error: 1215 Cannot add foreign key constraint (SQL: alter table `orders` add constraint `orders_product_id_foreign` foreign key (`product_id`) references `products` (`product_id`))  
                                                                                                                                                                                                                 

                                                                          
  [PDOException]                                                          
  SQLSTATE[HY000]: General error: 1215 Cannot add foreign key constraint

CreateOrdersTable

<?php

use Illuminate\Support\Facades\Schema;
use Illuminate\Database\Schema\Blueprint;
use Illuminate\Database\Migrations\Migration;

class CreateOrdersTable extends Migration
{
    /**
     * Run the migrations.
     *
     * @return void
     */
    public function up()
    {
        Schema::create('orders', function (Blueprint $table) {

            $table->increments('order_id');

            $table->integer("product_id")->unsigned();
            $table->foreign('product_id')->references('product_id')->on('products');

            $table->integer("customer_id")->unsigned();
            $table->foreign('customer_id')->references('customer_id')->on('customers');

            $table->timestamps();
            $table->softDeletes();

            $table->engine = 'InnoDB';

        });
    }

    /**
     * Reverse the migrations.
     *
     * @return void
     */
    public function down()
    {
        Schema::dropIfExists('orders');
    }
}

#CreateProductsTable

<?php

use Illuminate\Support\Facades\Schema;
use Illuminate\Database\Schema\Blueprint;
use Illuminate\Database\Migrations\Migration;

class CreateProductsTable extends Migration
{
    /**
     * Run the migrations.
     *
     * @return void
     */
    public function up()
    {
        Schema::create('products', function (Blueprint $table) {
            $table->increments('product_id');
            $table->string('product_name')->unique("product_name");
            $table->timestamps();
            $table->softDeletes();

            $table->engine = 'InnoDB';




        });
    }

    /**
     * Reverse the migrations.
     *
     * @return void
     */
    public function down()
    {
        Schema::dropIfExists('products');
    }
}

#CreateCustomersTable

<?php

use Illuminate\Support\Facades\Schema;
use Illuminate\Database\Schema\Blueprint;
use Illuminate\Database\Migrations\Migration;

class CreateCustomersTable extends Migration
{
    /**
     * Run the migrations.
     *
     * @return void
     */
    public function up()
    {
        Schema::create('customers', function (Blueprint $table) {
            $table->increments('customer_id');

            $table->integer("building_id")->unsigned();
            $table->foreign('building_id')->references('building_id')->on('buildings');

            $table->integer("room_id")->unsigned();
            $table->foreign('room_id')->references('room_id')->on('rooms');

            $table->string("last_name")->nullable();
            $table->string("first_name")->nullable();

            $table->string("phone_number")->nullable();
            $table->enum("choices", ["male, female"]);
            $table->text('memo')->nullable();

            $table->timestamps();
            $table->softDeletes();

            $table->engine = 'InnoDB';


        });
    }

    /**
     * Reverse the migrations.
     *
     * @return void
     */
    public function down()
    {
        Schema::dropIfExists('customers');
    }
}