niques for planning and production scheduling. In
both texts, computational difﬁculties raised by these
problems are shown, because of its combinatorial
characteristics and, in general are classiﬁed as NP-
Hard.
With regard to production scheduling, including
sequence-dependent set-up is a thoroughly researched
topic, see (Allahverdi et al., 2008), where a review of
the literature that addresses this problem is presented.
In (R
´
ıos-Mercado and Bard, 1998), two models of in-
teger linear programming (MIP) with makespan min-
imization are presented for a ﬂow shop environment
with sequence-dependent set-up times, which are then
solved by Branch-and-Cut algorithms. These models
are used in (Kurz and Askin, 2004) and (Karmakar
and Mahanty, 2010), which are extended to Flexible
Flow Shop, with identical parallel machines at each
stage. (Rocha et al., 2008) propose two MIP models
for programming non-parallel machines, considering
sequence-dependent set-up times. In (Yilmaz Eroglu
and Ozmutlu, 2014) MIP programming models for
unrelated parallel machines with job splitting are pre-
sented, where a job can be divided between machines
available for processing separately. The solution of
these models is through hybrid heuristic methods be-
tween genetic algorithms and local search. (Hnaien
et al., 2015) tackle the two-machine ﬂowshop with an
availability constraint on the ﬁrst machine. Two MIP
models and a branch and bound (B&B) algorithm
based on a set of new lower bounds and heuristics are
presented. In (Jia et al., 2015), a makespan minimiza-
tion in parallel batch machines with non-identical ca-
pacities is solved, through two different heuristics.
The ﬁrst is based on the First-Fit-Decreasing (FFD)
rule and the second based on Max-Min Ant System
(MMAS).
All these papers have a continuous time MIP
models and the same function objective which is
makespan minimization. With regard to this study, the
method of solution is the same, but when applied to
the soft drink industry additional problems arise, such
as synchronization between production stages, which
will be explained in section 3.
The lot sizing and scheduling problem also pro-
vides solutions to the problem in matter, where a
lot sizing simultaneously exist with the production
scheduling. For more information, see (Drexl and
Kimms, 1997), which presents a survey on this issue
and a literature review. One of the most important
works in this area corresponds to (Fleischmann and
Meyr, 1997), where a model of planning and schedul-
ing with sequence dependent set-up and cost mini-
mization, called The General Lot-Sizing and Schedul-
ing Problem (GLSP), is presented. In that article,
the technique to simultaneously determine lot sizing
and scheduling corresponds to the use of a special
structure of time, which is divided into macro peri-
ods, where each macro period is subdivided into mi-
cro periods. In each macro period, elements that pro-
vide external information to the problem are caught,
such as demand and inventory costs. Micro periods
determine the order in which the products are pro-
duced since each micro period allows the production
of only one product. (Meyr, 2000) extends the GLSP
to include sequence-dependent set-up time, called
GLSPST, where the solution method of the model
corresponds to a dual re-optimization algorithm com-
bined with local search heuristics. In (Seeanner and
Meyr, 2013) a new extension is made, this time to a
multi stage environment and, in addition, properties
that allow better use of production lines are incor-
porated: quantity and splitting set-up, allowing split
quantities and set-up times in consecutive micro pe-
riods. Small instances are solved by standard solver
and relax-and-ﬁx heuristics, before being compared.
(Ferreira et al., 2009) use a model based on the
GLSP, but applied to the soft drink industry, in which
a two-stage model with parallel machines, sequence-
dependent times and synchronization between the two
stages is presented, what ﬁts quite well to the problem
to be solved in this study, except for the difference that
the objective of GLSP is a long-term plan to minimize
inventory costs and set-up. A relaxation approach
and several strategies of the relax-and-ﬁx heuristic are
proposed to solve the model. This same model is
solved in (Toledo et al., 2011), but using tabu search
algorithms. In (Ferreira et al., 2012), 4 formulations
are presented of only one stage to model the problem
of two stages of the soft drink industry addressed in
previous articles, two of them based on GLSP and the
other two on the asymmetric traveling salesman prob-
lem (ATSP). In (Toledo et al., 2014), the model pre-
sented in (Ferreira et al., 2009) is also solved, but in
this case the combination of a genetic algorithm with
mathematical programming techniques is used.
These articles related to the soft drink industry,
have lot sizing models in conjunction with produc-
tion scheduling, in order to minimize costs, which
differs from the model shown here. The main objec-
tive of this paper is to provide a production scheduling
for a short term period with makespan minimization.
Another difference with the previous articles is that
this paper allows the division of a lot to be processed
in different tanks, which reduces waiting time in the
packaging lines. Besides this, this paper incorporates
a solution strategy using the plan currently employed
by the ﬁrm as the upper limit for the model solution.
Short-term Production Scheduling in the Soft Drink Industry
417