An Aggregate Production Plan for a Biscuit Manufacturing Plant Using Integer Linear Programming - Open Access Library Journal

OALibJ > Vol.6 No.11, November 2019

An Aggregate Production Plan for a Biscuit Manufacturing Plant Using Integer Linear Programming ()

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DOI: 10.4236/oalib.1105743 752 Downloads 2,965 Views

Author(s)

Dilishiya Kalpani De Silva, Wasantha Bandara Daundasekara

Affiliation(s)

Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka.

ABSTRACT

Effective planning, scheduling, and synchronization of all production activ-ities are the key responsibilities of the management of a manufacturing plant. Therefore, it is necessary for the management of the plant to design the production process so that the total production cost is minimized, subject to the available resources that cannot be compromised. In this study, a biscuit manufacturing plant is selected and an integer linear programming (ILP) model is formulated to determine aggregate number of batches that the plant should produce from each product per month so that monthly demand is satisfied with available resources. The objective is to minimize the monthly production cost of the plant. The required data were collected from the production plant for a period of one month, and then, the objective function and constraints were formulated. The management has given a paramount importance in satisfying the demand so that there will not be any unsatisfied customer. According to the managerial requirement, any feasible solution obtained by the model must satisfy the demand. Therefore, demand constraint is considered as a hard constraint. The management is forced to adjust the labour and machine requirements more frequently according to the monthly demand. Thus, labour and machine hour constraints are considered as soft constraints. Formulated ILP model was implemented as a spreadsheet model in Excel and solved using Excel Solver which uses the simplex algorithm and incorporates the integer requirement of the model when finding the optimal solution. Total available labour and machine hours can be changed within a particular range until a feasible solution is found. The solved model determines the number of batches to be produced from each product and the corresponding minimum cost per month. By implementing this production plan, manufacturing excess of biscuits can be avoided and hence utilizes the physical and human resources to the optimum manner. Additionally, the machine and labour idle times and the needed overtime hours can be identified using the solution while the additional overtime cost will be added to the monthly production cost.

KEYWORDS

Integer Linear Programming, Soft Constraints, Hard Constraints, Spreadsheet Model, Excel Solver, Simplex Algorithm

Share and Cite:

De Silva, D. and Daundasekara, W. (2019) An Aggregate Production Plan for a Biscuit Manufacturing Plant Using Integer Linear Programming. Open Access Library Journal, 6, 1-16. doi: 10.4236/oalib.1105743.

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