Academic journal article Iranian Journal of Management Studies

# Optimization of the Inflationary Inventory Control Model under Stochastic Conditions with Simpson Approximation: Particle Swarm Optimization Approach

Academic journal article Iranian Journal of Management Studies

# Optimization of the Inflationary Inventory Control Model under Stochastic Conditions with Simpson Approximation: Particle Swarm Optimization Approach

## Article excerpt

(ProQuest: ... denotes formulae omitted.)

Introduction

In recent years, a large number of studies have focused on inventory management systems. For the majority of these studies, one of two procedures have been used. The first procedure determines the optimal values of the decision system variables by minimizing the average annual cost. The second (and, in theory, more correct) procedure determines the optimal ordering policy by minimizing the discounted value of all future costs (Mirzazadeh, 2007, pp. 658-666). Thus, each model has a different scope, parameter and method for solving. The problem is finding the time performance of the proposed method for solving the complex inventory models in order to determine the optimal decision parameter. In this study, we used an inflationary inventory model under stochastic condition with two unknown parameters. These parameters were (k) proportion of time in any given inventory cycle and (T) replenishment time inventory.

Figure 1 shows the scope and parameters of the inventory models with the most deteriorating items (Li & Mawhinney, 2010). In this study, we considered these models with the inflation rate. It is important to note that the rate can be deterministic or stochastic. After describing the resulting models, we considered the methods to solve them. We proposed a combination method using Simpson's rules- particle swarm optimization.

Since 1975, studies have considered the effects of inflation on the inventory system. For the deterministic situation, Buzacott (1975) dealt with an economic order quantity model, with the inflation rate subject to different types of pricing policies. Misra (1979) developed a discounted cost model and included the internal (company) and external (general economy) inflation rates for various costs associated with an inventory system. Sarker and Pan (1994) surveyed the effects of inflation and time value of money on the order quantity with finite replenishment rate. Other studies considered variable demands, such as Vrat and Padmanabhan (1990), Datta and Pal (1991), Hariga and Ben-Daya (1996) and Chung (2003).

In most real-life situations, inflation is uncertain and unstable. Horowitz (2000) discussed an EOQ model with a normal distribution for the inflation rate. Furthermore, Mirzazadeh and Sarfaraz (1997) presented a multiple item inventory system with a budget constraint and a uniform distribution function for the external inflation rate. Additionally, Mirzazadeh presented the impact of uncertain inflationary conditions on inventory models using the average annual cost and the discounted cost (Mirzazadeh, 2007, pp. 658-666). In more recent research, Yang and Chang (2013) investigated a two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation. Moreover, Lubik and Teo (2012) checked inventories, inflation dynamics and the New Keynesian Phillips curve. At the same time, Yang (2012) presented two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation. Meanwhile, Neetu and Tomer (2012) presented a deteriorating inventory model under variable inflation where the supplier credits were linked to order quantity.

Previous studies of inventory systems have used the classical numerical method. In this paper, to minimize the discount cost method in the inflationary inventory model, we proposed a combined method. This involved Simpson's rules and the particle swarm optimization.

Particle swarm optimization (PSO) is a population-based stochastic optimization technique. It is based on the social behaviours observed in animals or insects, e.g., bird flocking, fish schooling and animal herding (Blum & Merkle, 2011). It was originally proposed by James Kennedy and Russell Eberhart (1995). In PSO, individual particles of a swarm represent potential solutions which move through the problem search space, seeking an optimal or satisfactory solution. …

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