Page 51 - IJOCTA-15-2

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D. Balpınarlı, M. Onal / IJOCTA, Vol.15, No.2, pp.245-263 (2025)
We aim to find a production plan to maximize as pricing, deterioration and perceived freshness
total profit over a finite planning horizon. of the items. For instance, 12–15 incorporate per-
ishability such that items deteriorate continuously
This is an extension of the single item version
of the same problem that has been analyzed in. 4 over time (i.e. deteriorate non-instantaneously),
whereas 16,17 incorporate the effect of pricing on
In particular, we propose the following approach. 18–22
demand rate. incorporate both pricing and
We find an initial solution using a Lagrangian re-
perishability. They assume non-instantaneous de-
laxation method. This solution is, in fact, a hy-
terioration, too. Some researchers incorporate
brid solution obtained by combining two distinct
freshness to account for cases where items do
solutions generated in the process of solving the
not deteriorate continuously but deteriorate in-
Lagrangian dual problem. Starting with this ini-
stantaneously when they reach their expiration
tial solution, we then implement a Tabu Search
date. 23–27 present examples of such models that
algorithm to find improved solutions.
incorporate pricing and freshness.
The remainder of this paper is organized as
follows. In Section 2, we present a review of the The economic lot sizing problems have been
related literature. In Section 3, we describe and studied in the literature since the 1950s when they
formulate the multiple item ELSIDD problem. In were first introduced by. 28 In the single item ELS
Section 4, we explain the details of our solution model of, 28 there are demands for an item over
approach. In Section 5, we show the effectiveness a discrete and finite planning horizon. There are
of our solution method by comparing its perfor- production, setup, and inventory carrying costs.
mance with the performance of a standard com- The aim is to find a minimum cost production
mercial solver. Finally, we conclude our paper plan to satisfy demands in each discrete time pe-
and discuss possible future research subjects in riod. To this day, this basic model has been ex-
29-31
Section 6. tended in several ways. For instance, ana-
lyze ELS problems with finite production capac-
2. Literature review ities. In particular, 29 proves that the ELS with
time-invariant (i.e. constant) production capac-
The related literature can be considered in two
ities can be solved in polynomial time when all
categories. In one, there are the Economic Order 31
the cost functions are concave. proposes an al-
Quantity (EOQ) type models, where the stocks
gorithm with an improved complexity for the case
change continuously over time (due to demand where holding cost is a linear function of inven-
and/or deterioration), and the planning horizon tory.
is (usually) infinite. Structure of optimal solu- 30
tions to this type of models usually consists of On the other hand, proves that several cases
repeating cycles of stocks. In the other one, there of the ELS with production capacities are NP-
are the ELS models where demand can occur in hard. In the literature, usually, an ELS problem
discrete time periods, and the planning horizon is is said to be capacitated if there are finite produc-
(usually) finite. tion capacities, and uncapacitated if there are no
production capacity restrictions or production ca-
EOQ literature is very rich in studies that con-
pacities are infinite. In this paper, we also adhere
sider models where the demand is not a given pa-
to this choice of words. For more recent work on
rameter but is a function of other decision vari- 32–36
ELS problem, see.
ables. Since the relation between price and de-
mand is obvious, many of these models natu- The majority of ELS problems in the litera-
rally consider the effect of pricing decisions on ture assume that demand is given as a parameter
demand (see e.g., 5–7 and. 8) There is extensive lit- and known in advance. However, as stated previ-
erature on EOQ models with stock-dependent de- ously, there are factors such as pricing and stock
mand as well. 9,10 presented EOQ models where level that might affect the demand. By controlling
the demand rate is a function of the inventory such factors, demand can be manipulated. As a
on hand such that the demand rate decreases result, demand might become a decision variable
as the stock level decreases. 11 considers an EOQ rather than a given parameter. Nonetheless, there
model where demand rate is a concave function is limited research on ELS models where demand
of the inventory level and holding cost is non- is a decision variable that depends on other deci-
linear on both the quantity and the time the sion variables. The work we present in this paper
items are stored. To this stock-dependent de- can be counted within this group of research.
mand model, researchers incorporated some com- For instance, 37 and 38 work on single item un-
bination of several other factors that might con- capacitated ELS problems where demand is a
tribute to the depletion rate of the stocks, such function of price. They propose algorithms that
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