Food Production Enterprise Production Planning and Scheduling

As we all known, Production planning and scheduling is one of the important parts of food production production and management. Thus, the decision capacity of production planning will greatly and directly affect the economic benefits of companies and the development of operations. This study will describe the production scheduling problem of food production companies, by summarizing and review the previous studies, we specially introduce the use of programming optimization in food production production planning and scheduling and then analyze the instance son, build model using mathematics methods and finally solve the problem with software.


INTRODUCTION
The relationship between humans and the food production is very close, spreading to all aspects of life.
In modern life, we can't live without food production products anytime and anywhere, from the material life such as clothing, food, shelter to the spiritual life for example culture, arts and entertainment.Their production and use, even on behalf of a certain historical stage of human civilization.
Production scheduling problem of food production researches has attracted the attention of many scholars.Kiran and Smith (1984) summarized the research status in a dynamic environment based Job shop scheduling a simulation model of the pure (Montazeri and Van Wassehove, 1990).Rule bases scheduling method including the 20 common rules and for an actual FMS, analyzes the average waiting time of these rules, such as operations on the system performance, the machine the average utilization, the total processing time of the job impact.Wu et al. (2003) with a flexible PCB (printed circuit board) to install the system as an example, the scheduling method is proposed based on KBS knowledge (Knowledge one Based Scheduling).
Mathematical programming is one of the main methods of research and production scheduling.Voudouris and Grossman (1996) for Zero Wait for the next (ZW) operation the batch process scheduling problems have been studied and established a complex MILP model and proposed several simplified method for solving.Pinto and Grossman (1996) Presents a continuous time MILP model focuses on short-term scheduling problem of parallel devices.This model uses a pre-sorting (pre-ordering) strategy, with some simple arithmetic processing of pre-determined sequence of different batches, thereby reducing the number of binary variables in the model, accelerate the solving model.This study will use the mathematical programming method for a food production plant for production scheduling optimization.

METHODOLOGY
Example description: ZE daily food production plant is a professional production and sales of cleaning products business in southern China, the main products include special effects floor cleaning liquid, efficient dishwashing detergent, ZE hand washing gel, bleach, efficient toilet cleaner, air freshener.In addition to these six products sold outside alone, companies also packaged these products into a package promotions to market, including: a toilet kit numbered as one (two boxes effects floor cleaning liquid, two ZE hand washing gel, three air fresheners, two efficient cleaning toilet agent and an emulsifier), bedroom suit numbered as two (two effects floor cleaning liquid, an air freshener and a decoration), hall suit numbered as three (four effects floor cleaning liquid, an air freshener and a piece ashtray) and kitchen kits numbered as four (three effects floor cleaning liquid, two ZE hand washing gel, three efficient dishwashing detergent and one emulsifier).Among them, emulsifiers, ornaments and ashtrays are company's outsourcing products, as sales of packaged kits donated gifts.
There are large differences in different parts of the level of demand for these products as well.
The following gives the unit costs of different plants to produce these products (Table 1) and market retail price data (due to the production and sale of kits requiring additional packaging costs and procurement costs for emulsifiers, decorations and ashtrays, kit costs slightly higher than its total cost of each single piece).
Similarly, different plant machinery and equipment, as well as the level of quality of the staff, resulting in the production of the same product consumption per unit of labor is not the same, the time in which the package also includes the factory transmission time.Specific data are as follows (unit: hour).
In addition, the factory packaging kit also need to spend additional labor and different packaging kit consumed artificial plants is not the same (different kits consumption is basically the same).
According to data provided by the factory sales department, the next two months will be entered into the peak of this year's demand, the demand for different products in different regions roughly estimated as follows (Table 2 to 4).
It is known that the cost of production (Table 1 unit costs) will rise by 10% each month.For this reason and to consider the plant's production capacity, the plant production department will use inventory ways to resist inflation, which in the first month produce more products that will leave it to the first two months sales.However, such a production and inventory strategies will bring the plant's inventory costs by 5% (5% of production costs per unit of product).Also, due to the high cost of transportation products, factory will not use regional supplier of ways to meet the demand, that is, different regions of products for the needs of the region's markets.This study will be based on the actual situation currently facing, arranging the plant's production schedule for the past two months (2 months later, the plant is no longer left in finished goods inventory of these products) to obtain the maximum profit.

Symbol:
, , i j m X = "i" the name of products, "j" the production area, "m" the right month , i j p = Prices in the products "i" in region "j" , , i j m c = The unit cost of product "i" in the region "j" in the month "m" I i, j = The "i" product after the first month as the stock number in the region "j" t i, j = The district production time of the product "i" in the region "j" T j = The total regional production hours in the region "j" 0 , i j t = The total work time of packaging products "i" in the region "j" T 0 j = The total work time of packaging products in the region "j" , l i j t = The total packaging time of suit "i" (i>6) time in the region "j" l j T = The total work time of packaging suit in the region "j" DB i, j = The demand for the lower region of the "i" product in the region "j" UB i, j = The needs of the upper region of the "i" product in the region "j" Target equation: ).

Constraints:
Production hours:   Problem solving: Because of the complexity of the model, AMPL software is used to solve the model.The results are as follows (Fig. 1 and 2, Table 5 and 6).

CONCLUSION
Production planning and scheduling is an important process of the production process in business decisionmaking, the reasonable making or not directly affect the Economic benefits of companies, we take the food production industry as the main line of this study, using the linear programming theory describes the impact of linear programming function elements and each variable's change in analysis, which is made use of in the Examples.
Food production industry is one of the most successful areas in using applications of programming, we can see that programming optimization program has matured, it has created enormous economic benefits for the food production industry in the application of the world, China's food production industry should speed up plans to optimize the application itself speed, further narrowing the gap with foreign advanced application level.Programming technologies in the food production industry are getting more and more used program.The system to optimize with other applications are also being built to connect seamlessly from the application of these production operations management staff, laying with the plan to optimize the use of work-related foundation, which is to catch or exceed one of shortcuts in foreign advanced levels.

Table 1 :
Unit variable costs and benefits of different plant's products (unit: RMB)

Table 2 :
Labor consumption and maximum production capacity of different plant's products