Inventory based Multi-Item Lot-Sizing problem in uncertain environment: BRKGA approach

In this paper, Multi-Item Capacitated Lot-Sizing Problem (MICLSP) has been taken into consideration. Demand for each item in each period is uncertain and it is known at the starting off first time period. This paper also addresses the backlogging and a high penalty cost occurred for backlogging. Simultaneously, the penalty cost for exceeding the resource capacity is also occurred. These both penalty costs are included in the main objective function. In this connection, the main objective is to achieve such a solution so that the total cost should be minimized. The ingredients of total cost are the setup cost, production cost, inventory holding cost, and aforementioned both the penalty cost. To solve this computationally complex problem, a less explored algorithm Biased Random Key Genetic Algorithm (BRKGA) has been applied. According to the authors’ knowledge, this paper presents the first study for the application of BRKGA in lot-sizing problem. The encouraging results proved that the proposed algorithm is an efficient algorithm to tackle such complex problems. A comparative study with other existing heuristics shows the supremacy of proposed algorithm on the basis of quality of the solution, number of generation and computational time.