The Effects of Modelling Strategies on Responses of Inventory Models

The Effects of Modelling Strategies on Responses of Inventory Models

Anthony S. White (Middlesex University, London, UK) and Michael Censlive (Middlesex University, London, UK)
Copyright: © 2017 |Pages: 25
DOI: 10.4018/IJAIE.2017010102


This paper describes methods to model inventories from the APVIOBPCS family. It aims to examine the limits of modelling approaches within control-theoretic models using the Simulink package. Discrete and continuous time models were considered together with a finite pipeline delay and the Forrester exponential delay, in continuous and sampled data representation. The main effect of using a finite delay is to deepen the stock-out and increase the required order rate compared with the same response observed with an exponential form delay. Total time for recovery is similar with all models. The discrete performances are close to the continuous representation for a smaller review period. Results presented here illustrate that the various forms of control-theoretic models present similar step response results irrespective of simulation technique used provided they have the same delay type. However, the gains required for minimum cost are substantially different for each delay form and modelling technique used.
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1. Introduction

In the years since the Second World War many researchers have examined the problems of balancing production and inventory levels against costs. Many different analytical techniques have been used with no one technique being wholly satisfactory, these include classical Q, R inventory policy (Simchi-Levi et al., 2008), Discrete Event simulators such as Witness, the use of Systems Dynamics(SD) simulation (Forrester, 1961) and control-theoretic analysis (Disney & Towill, 2002a). Classical inventory analysis assumes random sales and ignores the dynamics and time delays inherent in the supply chain. The other techniques can handle random demand as well as deterministic inputs. Discrete Event simulators are capable of handling individual items or examining production lines and batch processes whereas both SD and control-theoretic viewpoints are best suited to macro policy descriptions (Pidd, 1998). Control-theoretic models can use either continuous time or discrete time modes. Both SD and control-theoretic methods cater for the delays inherent in supply chains and the embodied dynamics.

Since the 1980’s there has been a move away from “push” manufacturing towards Just-In-Time (JIT) production. This approach is entirely suited to a continuous ordering system, especially using Electronic Point of Sale (EPOS) information, whereas some processes are still operated in batches, for example in paper production where continuous processes are limited by the size of the plant available. Bliss (2001) has used a discrete event simulation of batch processes and push production to investigate the relationship between Work In Progress (WIP) batch size and plant utilization. The analysis presented here uses simulation of control-theoretic models with both continuous information and regular time discrete information decisions to examine overall inventory policy.

New e-manufacturing environments were optimised for rapid response (Gordon, 2002) and are generally concerned with Factory-to-Business (F2B). Pines (2002) states that using Lean and agile manufacturing processes requires greater efficiency in the Supply Chain.

The fundamental purpose of any company ordering policy is to match supply to demand by controlling production or distribution. Excess inventory levels must be maintained within acceptable costs and capacity requirements. However, the “bullwhip effect” of higher orders through the chain, the nearer to the manufacturer, may result (Lee, Padmanabhan and Whang, 1997). Chen and Disney (2003) report estimates that the economic penalty of the bullwhip effect can be 30% of factory gate profits.

Bullwhip can produce:

  • Excessive inventory throughout the supply chain;

  • Reduced customer service;

  • Lost revenues due to stock outs;

  • Reduced productivity of capital;

  • Inefficient use of transport;

  • Frequently missed production deadlines.

Disney & Towill (2002a), Lalwani (2006) at Cardiff University have analysed an Automatic Pipeline, Variable Inventory and Order Based Production Control Systems (APVIOBPCS) (Figure 1) extensively, to determine its’ stability and optimisation (Disney & Towill, 2002b). Analysis of the causal diagram in Figure 1 shows the actual inventory at the retailer is compared with the agreed re-order point. This decision point, the reorder level, is arrived at by the retailer, balancing his Customer Service Levels (CSL) against building up excessive inventory stocks.

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