Research on Zero-Wait Scheduling Problems in Multiproduct Processes with Due Dates - Intelligent Computing for Sustainable Energy and Environment - page 323

problems [4]. Ryu et al. developed a new multiproduct batch scheduling model with
penalty functions for earliness and tardiness [5]. Cafaro and Cerda developed a new
MILP continuous-time framework for periodically updating the work schedule of a
single unidirectional multiproduct pipeline over a multiperiod rolling horizon [6].
Subbiaha et al. discussed multi-product batch scheduling problems with intermediate
due dates [7]. The model formulation is extended to include release dates of the raw
materials and due dates of the production orders. And the meeting of due dates is
modeled by causing additional costs.
In the paper, the zero-wait scheduling problem in multiproduct processes with the
due-date window under uncertainty is discussed, and a newly evolutionary algorithm
named Improved Shuffled Fog-Leaping Algorithm (ISFLA) is proposed to solve it.
The remaining sections of this paper are organized as follows. In section 2, an NP-
hard problem, the earliness and tardiness multiproduct scheduling under zero-wait
strategy is presented. Section 3 proposes an improved shuffled frog-leaping algorithm
and section 4 summarizes experiments and results. The remaining section presents the
conclusion.

2 Problem Definition

In a multiproduct process, all products to be produced have the same production
route. Considering some assumptions regarding the multiproduct process, multi-
product batch processes scheduling problems can be described as the following.

2.1 Model Formulation

Parameters
N number of products,

( )

i  = 1 2 , , N

( )

M number of processing units, j  = 1 2 , , M

~ fuzzy processing time of product i on processing unit j , which includes the
transfer time, the set-up time and the clean-up time, etc.
[ ]

ij

i te due-date window of product i , the earliness due-date and the tardiness
due-date are denoted by e , t respectively.
h the weight of earliness,
w the weight of tardiness, normally

i

h < w

.

i i

Decision Variables
( )

~ starting (completion) time of the product i in the k th position of
processing sequence on unit j .

~

i j i j

k k