Manufacturing Inventory and Supply Analysis

A Mathematical Modelling Approach

Sanjay Sharma

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000457780
• Edition: 1
• Topic: Technik & Maschinenbau
• Subtopic: Maschinen- und Anlagebau

This reference text discusses models and analyzes cases that are useful for material requirements planning (MRP), just-in-time (JIT) environments and supply chain environments, as well as traditional production-inventory systems.

It covers important concepts, including production-inventory systems, optimal purchase quantity, optimal production quantity, instantaneous procurement, multiple input items, sensitivity analysis, multiproduct manufacturing, determination of optimum cycle time, fractional backlogging, and incorporating input item procurement and flexibility in the production rate.

Aimed at senior undergraduate and graduate students, and professionals in the field of industrial engineering, production engineering and manufacturing science, this text:

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• Provides detailed models/analysis pertaining to various cases which are useful for material requirements planning and supply chain environments

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• Elaborates manufacturing rate flexibility, demand variation and production rate variation

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• Discusses the multi-item manufacturing environment and presents models with backorders, as well as fractional backlogging

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• Analyzes flexible production rates, along with upward and downward variations

1

Introduction

DOI: 10.1201/9781003213994-1

A manufacturing inventory system mainly consists of: (a) procurement of raw materials and components, and (b) manufacture of components, sub-assemblies and finished products. Inspection and quality control of the raw materials, components and finished goods also play a role in proper understanding of the manufacturing inventory system. The present work is focused on the mathematical modelling of such systems, primarily on procurement and production of items.

The present book is organized in the following chapters:

1. Introduction
2. Batch size
3. Batch size relevance for JIT
4. Price variation
5. Batch size for MRP
6. Multiproduct manufacturing
7. Manufacturing rate flexibility

Industrial or business organizations operate in the variety of systems with wide fluctuations from time to time. Challenges before the managers, as well as professionals, will be to deal with them effectively with some rationale in decision making. Formulation of the problem is a useful tool and often a prerequisite for the solution of different business complexities. In order to undertake in-depth studies, a clear idea of various functions of an industrial organization is essential. To serve this purpose, an industrial structure is discussed briefly in Section 1.1. This includes important functional divisions of an industry such as:

1. Production
2. Inspection and quality control
3. Marketing
4. Finance
5. Accounts

Their implication for production-inventory system optimization is explained since each views inventory in a different context.

Classical categories of production system i.e. job, batch and mass production are described in Section 1.2 for creating a suitable background. Further, just-in-time (JIT) environment and material requirements planning (MRP) systems are discussed due to their significance from application point of view. Two types of costs are significant. These are the costs, including:

1. Those pertaining to ordering of any material/components
2. Setting up of a machine for manufacture of any product

These two types of costs are related to different environments, but are mathematically similar. In addition these, inventory carrying costs are included in the models. Depending on the situation, shortage costs may also be incorporated in the inventory system. Shortages may result into either:

1. Complete backordering, or
2. Partial backordering

Partial backordering is also discussed briefly, as it will help in the modelling process to optimize the procurement or production lot size.

Mathematical models have been developed in Chapter 2 by incorporating different types of realistic features. In addition to ordering/setup costs and inventory holding costs, these features include:

1. Purchase/production costs
2. Quality defects
3. Shortages which are completely backordered
4. Partial backordering

An integrated production-inventory model is formulated considering partial backordering and quality defects, apart from various costs.

The concept of ‘nil inventory’ seems to be very appealing, but this approach is not always economically or practically feasible. However, firms should try to move closer to this goal. Relevance of lot sizing is always there, whether it is JIT or traditional approach. These issues, discussed in Chapter 3, are consistent with the JIT concept. The models are formulated which are also useful in meeting supply chain goals. Production of end items is considered, along with the replenishment of input items. The following aspects are covered:

1. Instantaneous procurement
2. Finite replenishment rate of input item
3. Multiple input items
4. Frequent delivery of produced item

Price discounts are often declared by the manufacturing or supplying firm in order to reduce their inventories or increase their market share. The purchasing firms try to take advantage of these situations in order to decrease their overall procurement costs, but it depends on the present stock position among other features of that particular inventory item at which price discounts are offered. Chapter 4 is concerned with the modelling procedures related to price discounts for replenishment with variety of stock positions, such as:

1. Positive stock status
2. Negative stock status
3. Negative stock equivalent to optimal maximum shortage quantity

Discussion is also presented for a declared price increase. This situation is also analyzed concerning the replenishment start at a variety of stock positions, as mentioned previously.

Various MRP lot sizing procedures have been explained in Chapter 5:

1. Economic ordering quantity
2. Period order quantity
3. Silver–Meal heuristic
4. Least total cost
5. Least unit cost
6. Lot for lot
7. Fixed period requirements

Shortages are generally not considered in an MRP environment. Although shortages are undesirable, as they result in loss of goodwill, these are sometimes unavoidable in the real world. The kind of insight provided in Chapter 5 can be useful for tradeoffs whenever it is not possible to avoid backordering due to one or another problem being faced by an organization. Another heuristic procedure is also introduced which has wide applications, as it does not allow shortages in the MRP environment and an important objective of MRP is achieved. Emphasis is on using it, if it gives lower costs in comparison with the other practical lot sizing rules. It can also be used effectively for the optimization of multilevel production-inventory systems.

Multi-item manufacturing environment is discussed in Chapter 6. Models are presented with backorders, as well as fractional backlogging. Shelf life of a product needs to be considered, because it affects certain production situation, and thus, the shelf life constraint is incorporated. This is related to the use/consumption of an item before a certain specified period known to the management. The following approaches are explained to evaluate the optimal results:

1. Common cycle time
2. Different cycle time

Input item procurement is also incorporated, along with multi-item production scenarios. Flexibility in the production rate is described briefly in the context of a family production environment.

It is always useful to have flexibility in operational systems. Production rate variation is sometimes necessary because of demand variation, among other reasons. In addition to the demand variation, a flexible production rate is analyzed in Chapter 7, along with upward and downward variations. Situations with and without shortages are incorporated, along with the total relevant costs. Upper and lower bounds have been obtained for facility setup costs, in order to ensure an economical variation concerning:

1. Upward demand variation
2. Downward demand variation
3. Upward production rate variation
4. Downward production rate variation

The manuscript provides the detailed models/analysis pertaining to various cases which are useful for MRP, JIT and supply chain environment, as well as traditional production-inventory systems. Interaction effects of various operational parameters on the relevant costs are discussed, along with the managerial implications wherever these are appropriate.

1.1 INDUSTRIAL STRUCTURE

An industrial organization is aimed at the conversion of raw materials into finished products. These products will be consumed by another industry or will be available in the open market through a distributing network. Figure 1.1 shows the industrial structure with major functions. The marketing division of the industrial organization is engaged in executing the sales of the products, as well as in forecasting the demands. The forecasts made will be useful in generating the production plans, which are targeted by the production division with the ...

Table of contents

• Cover Page
• Half Title Page
• Title Page
• Copyright Page
• Contents Page
• Preface Page
• About the Author Page
• Chapter 1 Introduction
• Chapter 2 Batch Size
• Chapter 3 Batch Size Relevance for Just-in-Time (JIT)
• Chapter 4 Price Variation
• Chapter 5 Batch Size for Material Requirements Planning
• Chapter 6 Multiproduct Manufacturing
• Chapter 7 Manufacturing Rate Flexibility
• Additional Reading
• Bibliography
• Index