Abstract
The mixing process of liquid products is a crucial activity in the industry of essential commodities like, medicine, pesticide, detergent, and so on. So, the mathematical study of the mixing problem is very much important to formulate a production inventory model of such type of items. In this work, the concept of the mixing problem is studied in the branch of production inventory. Here, a production model of mixed liquids with price-dependent demand and a stock-dependent production rate is formulated under preservation technology. In the formulation, first of all, the mixing process is presented mathematically with the help of simultaneous differential equations. Then, the mixed liquid produced in the mixing process is taken as a raw material of a manufacturing system. Then, all the cost components and average profit of the system are calculated. Now, the objective is to maximize the corresponding profit maximization problem along with the highly nonlinear objective function. Because of this, the mentioned maximization problem is solved numerically using MATHEMATICA software. In order to justify the validity of the model, two numerical examples are worked out. Finally, to show the impact of inventory parameters on the optimal policy, sensitivity analyses are performed and the obtained results are presented graphically.
Highlights
The mixing problem has a great impact on different sectors of business management, viz. the medicine industry (Gautam et al [1], Essi [2], Ploypetchara et al [3]), cosmetics industry (Bernardo and Saraiva [4], Kim et al [5], Zhang et al [6]), chemical industry (Funt [7], Wu et al [8], Jasikova et al [9]), and so on, to produce essential commodities in our daily life
A few years later, Sharmila and Uthayakumar [19] established the optimal policy of a production problem with three different production rates
The concept of the mixing problem is implemented in the production inventory model for a liquid product with selling-price-dependent demand and a variable production rate under preservation technology
Summary
The mixing problem has a great impact on different sectors of business management, viz. the medicine industry (Gautam et al [1], Essi [2], Ploypetchara et al [3]), cosmetics industry (Bernardo and Saraiva [4], Kim et al [5], Zhang et al [6]), chemical industry (Funt [7], Wu et al [8], Jasikova et al [9]), and so on, to produce essential commodities in our daily life. In the area of inventory control, investigation of the production inventory problem of a mixed product along with the mixing process is an intersecting research area. In this connection, Nienow et al [10], Cheng et al [11], Fitschen et al [12], and many others have had a valuable influence in this area. Several researchers developed different production models by taking various production rates and imperfect production processes. Su and Lin [14,15] investigated two production inventory models with a demand- as well as inventory-level-dependent production rate. Öztürk et al [24] studied an imperfect production process with random breakdowns, rework, and inspection costs and Khara et al [25]
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