## 1 Introduction  
Over the past several decades, supply chain management (SCM) has emerged as an important topic and many operational research problems for the SCM have been attracted. Even though many researchers obtained local operational efficiency by optimizing the logistics flow of each entity (i.e., raw-material providers, manufacturing plants, whole-sale distributers, and customers) within supply chain (SC), they have become to recognize that the coordination between the entities in the SC is important to obtain global efficiency of logistics throughout the entities in the SC. Due to this reason, an integrated schedule of manufacturing and delivery has recently received great attention from the researchers. One review article by [PERSON] [1] introduced several single-period optimization models for integrating inbound-production and outbound-truck scheduling in the SC. The article introduced the integrated optimization models based on various objective function types using time, cost, and profit. For integrated scheduling problems between production and delivery, [PERSON] et al. [2] studied the integrated production with a single machine and delivery scheduling with batching. The limitation of the study was that they considered the batch delivery to only one customer. [PERSON] et al. [3,4] investigated a similar problem with [PERSON] et al. [2]. They extended the integrated scheduling problem to parallel machines in a production plant and multi-customers for batch delivery. However, they assumed that the delivery operation was processed using only a single truck. [PERSON] et al. [5] studied the coordination problem of the batching and delivery problem, where product-part batches were delivered between production sites by a 3 PL provider. Between the delivery process from upstream to downstream production sites, only the batch with all jobs completed at the upstream site can be delivered to the downstream site with two transportation modes. [PERSON] et al. [6] studied a coordination problem between the assembly manufacturing plant with parallel machines and multi-destination transportation with a constraint of make to order (MTO) inventory strategy. They decomposed the overall problem into a sub-problem of parallel machine scheduling and a sub-problem of 3 PL transportation and solved the problem. [PERSON] et al. [7] considered a coordination problem between a manufacturing plant with the unrelated parallel machines and multi-destination transportation with capacitated delivery trucks. Their problem minimizes biobjectives with the total distribution cost and the delivery time without batching and inventory strategies. [PERSON] et al. [8] considered a coordination problem of vehicle schedule and routing between the manufacturing plant with the parallel batch machines and multi-destination transportation with capacitated delivery trucks by the third-party logistics provider. The objective function of the article was to maximize the total profit of the company. Meanwhile, an integrated scheduling problem between two production processes had a structural similarity with the integrated scheduling problems between production and delivery in the SC. Several studies on the two-stage production and assembly scheduling problem were introduced [9; 10; 11]. In recent years, several meta-heuristic algorithms were proposed to optimally solve the integrated scheduling problem between production and delivery under different problem frameworks [12; 13; 14; 15; 16; 17; 18]. The fulfillment of due dates of customers is important to obtain a global logistics efficiency in the overall supply chain. Even though the tardiness factor is a significant factor on the integrated scheduling, to the best of our knowledge, a few meta-heuristic algorithms generate a near-optimal solution for the integrated scheduling problems. Furthermore, to the best of our knowledge, none of the research has an integrated scheduling problem, including a batching decision between the scheduling problems with a tardiness objective measure.