A new approach for solving capacitated lot sizing and scheduling problem with sequence and period-dependent setup costs
Abstract: We aim to examine
the capacitated multi-item lot sizing problem which is a typical example of a
large bucket model, where many different items can be produced on the same
machine in one time period. We propose a new approach to determine the
production sequence and lot sizes that minimize the sum of start up and setup
costs, inventory and production costs over all periods.
Design/methodology/approach: The approach is composed of three steps.
First, we compute a lower bound on total cost. Then we propose a three
sub-steps iteration procedure. We solve optimally the lot sizing problem
without considering products sequencing and their cost. Then, we determine
products quantities to produce each period while minimizing the storage and
variable production costs. Given the products to manufacture each period, we
determine its correspondent optimal products sequencing, by using a Branch and
Bound algorithm. Given the sequences of products within each period, we
evaluate the total start up and setup cost. We compare then the total cost
obtained to the lower bound of the total cost. If this value riches a prefixed
value, we stop. Otherwise, we modify the results of lot sizing problem.
Findings and Originality/value: We show using an illustrative example,
that the difference between the total cost and its lower bound is only 10%.
This gap depends on the significance of the inventory and production costs and
the machine’s capacity. Comparing the approach we develop with a traditional
one, we show that we manage to reduce the total cost by 30%.
Research limitations/implications: Our model fits better to real-world
situations where production systems run continuously. This model is applied for
limited number of part types and periods.
Practical implications: Our approach determines the products to
manufacture each time period, their economic amounts, and their scheduling
within each period. This outcome should help decision makers bearing expensive
start up and setup costs, to reduce their Inventory and Production costs and
Start up and setup cots.
Originality/value: The main idea of the proposed approach is to
intelligibly reduce the number of products to manufacture within each period in
order to decrease the setup cost; since in case of limited machine’s capacity,
we show that setup costs could increase when reducing the total number of parts
manufactured over the entire planning horizon. In fact, the triangular
inequality in setup costs is proved to be not usually available.
Keywords: Multi-item
capacitated lot sizing; Sequence-dependent setup costs; Iterative approach;
Production planning; Scheduling
Author: Imen Chaieb Memmi,
Sondes Hammami Laaroussi
Journal Code: jptindustrigg130077
