K.P. Abdul Nazar & V. Madhusudanan Pillai (2015) A bit-wise mutation algorithm for mixed-model sequencing in JIT production systems, International Journal of Production Research, 53:19, 5931–5947, doi:10.1080/00207543.2015.1032438.
The description for the variable xi,k was provided in the notations part of Sections 3.1 and 4.1 of the above article (Abdul Nazar and Madhusudanan Pillai Citation2015). This description gives its relation with the decision variable yik. However, stating it as an equation is necessary for the completeness of the models. Hence, the equation given below is to be included in the constraint part of the model in those sections.
(1)
We apologise for this error.
It may be noted that while developing and solving the model, the above equation was used and while reporting the model in the original paper, an omission was happened in writing this relationship as an equation in the model. The use of this equation may be verified from the solutions reported in the original paper. For example, consider problem A of set 1 given in Table A1 of the original article. It is a 5-product sequencing problem with 16, 1, 1, 1, 1 as the demand for products 1 to 5, respectively. The solution obtained using LINGO 15.0 solver is given in Table B1 of the original article. The optimal sequence for this problem is 1 1 1 3 1 1 1 1 2 1 1 5 1 1 1 4 1 1 1 1 and its Production Rates Variation (PRV) value is 13.50. In fact, it is not possible to solve the model using the solver without Equation (Equation1(1) ), which relates the variable in the objective function (xi,k) to the decision variable (yik). When we try to solve the model without this equation using LINGO 15.0 solver, it gives an irrational value for the objective function even though it gives some random sequence as solution. For example, for the above problem the sequence generated for the model without using the Equation is 5 1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1 4, which actually has a PRV value of 24. Without the above equation, the model does not try to optimise the objective function, and just gives a random sequence satisfying the other constraints. Hence, it can be concluded that Equation (1) was incorporated in the model when it was solved, even though the relationship was given only as a description in the notation part of the model in the original article.
This corrigendum article is written to make it clear that the correct model was used in solving the problems of the original paper.