Research Article Open Access

Modeling of Multi-Level Capacitated Lot-Size Scheduling Problem

Zuhaimy Ismail1, Diyana Abd Mahad1 and Tan Siew Ching1
  • 1 Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM, Skudai, Johor, Malaysia


Problem statement: Lot-size is the clustering of items for transportation or manufacturing processes occurring at the same time. The issue in lot-size problem is to design production processes so that the feasible production quantities are equal to customer demand quantities and the timing of production is such that inventory positions are almost zero. Approach: In this study, we explore the multi-level lot-size and scheduling problem. It is on a multi-level capacitated lot-size problem or known as the multi-level lot-size problem with bottlenecks. Two models were introduced to solve the multi-level lot-size problem namely the Billington model and Alf Kimms model. Using these models, a simple heuristic method was designed to solve a multi level capacitated lot sizing scheduling problem. Results: In this study, we showed that Alf Kimms model is more efficient than Billington model. The result given by Alf Kimms model is always feasible without further modification unlike the Billington model. This is due to the way the constraint is devised to ensure the inventory balance. The constraint used in Alf Kimms model ensures that inventory in hand is always sufficient to fulfill the demand occurred in each period. However, the use of this constraint in Billington model is to ensure that the total production for each item is always greater than or equal to the total external demand in the time horizon. Therefore, without some form of modification, the result given by Billington model will be infeasible production plan. Conclusion: A comparative study between these models shows that both models were successfully devised to solve capacitated multi-level lot sizing problem with the objective function to minimize the total holding costs and setup- cost. This study also shows that the production schedule will always start at the last period because this will give the lowest costs and it also shows that Alf Kimms model gives a set of feasible sub-optimal schedule compare to Billington model.

American Journal of Applied Sciences
Volume 8 No. 3, 2011, 290-296


Submitted On: 23 February 2011 Published On: 25 March 2011

How to Cite: Ismail, Z., Mahad, D. A. & Ching, T. S. (2011). Modeling of Multi-Level Capacitated Lot-Size Scheduling Problem. American Journal of Applied Sciences, 8(3), 290-296.

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  • Material Requirement Planning (MRP)
  • lot-sizing problem
  • scheduling problem
  • integer programming
  • multi-level capacitated
  • sub-optimal schedule
  • cumulative demand