## 2 Literature Review
### Production Planning  
Production planning is one of the essential activities in supply chain management. Before the beginning of every financial year, many manufacturing companies prepare a production plan. The perfect production plan gives an idea of what quantities of goods are to be produced for each period over the financial year to full fill the demand for each period. The production plan can be executed weekly, monthly, quarterly, or even yearly depending upon the products of the company. Production scheduling is the allocation of available production resources over time to the best satisfy essential criteria, such as quality, delivery time, demand, and supply. A production problem includes a production scheduling problem, machine capacity planning problem, storage, and freight scheduling problems. In the past two decades, technological advancements, international competition, and market dynamics have had a significant impact on the manufacturing industry. Many researchers used different types of mathematical programming techniques for production planning models, such as linear programming [29], mixed integer linear programming [30; 31; 32], and goal programming [33; 34; 35], and others technique [36; 37; 38].  
Some notable work includes [39] which proposed a multi-objective model for production planning problem, in which demand and resource availability were specified in the form of grey fuzzy numbers. Reference [40] investigated several distinct types of fuzzy uncertainties in their multiproduct, multiperiod production planning model. Reference [41] established a fuzzy multi-objective model for aggregate production planning problem that contained multiple products and multiple periods in uncertain environments. The proposed model attempts to simultaneously minimize total production cost and minimize total workforce cost under some set of realistic constraints. Reference [42] studied a multi-objective aggregate production planning problem, in which they considered the four criteria, shortage and inventory, overtime and idle time, workforce level, and currency saving in a mid-term planning horizon, respectively. Reference [43] formulated multi-objective integrated production and distribution planning. In this modeling, they considered some of the inputs information about the parameters of the modeling vague. Reference [44] formulated a new model for the production distribution problem under uncertain environments and developed an efficient fuzzy goal programming model to get the optimal quantity.  
In this paper, we have formulated a production planning problem as a bi-level multi-objective programming problem with a multi-choice interval type parameter. The central purpose of this manuscript is to discuss the four different types of the scenario of multi-choices in objective functions as well as in the constraints. The equivalent crisp form of the multi-choice parameter [45] has been obtained using a general transformation technique of binary variables. The efficient compromise solution of the formulated problem has been obtained by using bi-level and fuzzy goal programming technique, respectively. The solutions obtained from both methods have been compared.  
The rest of the paper is planned as follows. Section 3 contains the model formulation of the discussed industrial production planning problem. Section 4 contains the general formulation of BLMOPP. Section 5 contains the formulation BLMOPP with multi-choice interval type. In Section 5, we discuss the transformation technique of multi-choice interval type parameter into their equivalent deterministic form. Section 6 contains the fuzzy goal programming formulation of BLMOPP with a multi-choice interval type parameter. Section 7 contains the numerical case study with the multi-choice decision-making problem solved using LINGO 16.0. Section 8 concludes the paper.