###### Abstract  
Due to the shortage and high cost of shipping containers, manufacturers that distribute products for worldwide customers must optimize their delivery. Commonly, they complete their delivery schedule first before creating the production schedule. This article tries to address the scheduling problem arising in the process of creating the production schedule to meet the delivery schedule. The complexity of the situation is increased since there is concern about producing as few product types as possible in a single period and having a balance of production load over multiple periods. A mathematical programming model for addressing this production scheduling problem is proposed in the form of integer programming. This model can be solved using LINGO, a commercial mathematical programming software. Microsoft Excel(r) spreadsheets are used to store both the data input and the output of the mathematical programming model. The advantages of using Excel are its easy-to-read format and familiarity with most users in various companies. Computational experiments in several cases show that the proposed method is effective to create the production and delivery schedule in various problem settings as expected. production schedule; integrated production and delivery; mathematical programming; integer programming +
Footnote †: journal: Applied system  
Previous research has demonstrated that the production schedule can be prepared using a mathematical programming approach by considering a variety of settings, constraints, and objectives. [PERSON] and [PERSON] [23] discussed a scheduling problem for a multi-objective, multi-period, multi-product manufacturing operation in terms of four objectives: capacity utilization, delivery schedule compliance, cost minimization, and overtime minimization. They compared the approaches of mathematical programming and simulation to solve the problem. [PERSON] [24] proposed a mathematical model in which a manufacturer purchases raw materials, fabricates products, and distributes them on a regular basis to a single customer. The model's purchasing and production schedules are output decisions with the goal of minimizing total costs, with each production run divided into multiple shipments. [PERSON] et al. [25; 26] considered the situation in a factory that produces multiple products and faces cyclic demand, i.e., the delivery schedule is repeated in the long run. They proposed a production model for creating production sequences. [PERSON] et al. [27] discussed a manufacturing environment in which machines operate in parallel and require periodic maintenance. They proposed mathematical programming models for creating production schedules. [PERSON] et al. [28] proposed a novel mathematical programming model for scheduling production in the steel industry that takes energy consumption and carbon emissions into account in addition to traditional production performance indicators. As demonstrated in the preceding studies, the production schedule is inextricably linked to the delivery schedule. As a result, numerous researchers are also developing simultaneous or integrated planning between production and delivery schedules. [PERSON] et al. [29] examined several integrated production, inventory, and delivery problems where customers specify delivery dates. They proposed an integrated model with the goal of finding an integrated schedule for processing orders, keeping finished goods, and delivering them to customers that minimizes inventory and delivery costs. [PERSON] et al. [30] proposed an integrated production and delivery scheduling model, in which each job is occupied with release dates and deadlines. [PERSON] et al. [31] discussed integrated production and delivery planning in which parallel batching machines are available and orders are generic in size and processing time. [PERSON] et al. [32] proposed an integrated production and delivery scheduling model for manufacturers who produce many products and whose manufacturing setup is dependent on the production sequence.