Applications of Management Science

Kenneth D. Lawrence, Gary Kleinman, Kenneth D. Lawrence, Gary Kleinman

• Publisher: Emerald Publishing Limited
• Year: 2017
• Print ISBN: 9781787142831
• eBook ISBN: 9781787147324
• Topic: Business
• Subtopic: Management
• Index: Business

Applications of Management Science is a blind refereed refereed series. Each annual volume presents current studies in the application of management science to the solution of significant managerial decision-making problems. Authors investigate solutions to managerial decision-making problems using management science methodologies. In this volume, the first section is focused on multi-criteria decision applications, the second section on supply chain management and finally authors look at productivity analysis. Thus this volume will be of significant interest to those involved in the applications of these methods, in a realistic managerial problem solving environment through the use of state of the art management science modeling.

SUPPLY CHAIN MANAGEMENT

AN INTEGER PROGRAMMING SOLUTION TO THE FOLDING CARTON PRINTING PLATE LAYOUT PROBLEM

Robert J. Stawicki

ABSTRACT

Folding cartons are used in myriad consumer products. For some products, such as hair dye kits, a very high-resolution printing is required. This is typically done using a technology known as Gravure printing. Gravure printing utilizes engraved cylinders which are very expensive. As a result, the printer often combines multiple products on one set of cylinders to minimize the total number of cylinders used. Since the demand between products varies, this can result in overproduction of the low demand products. This chapter presents an integer programming formulation that assigns products across multiple sets of cylinders in order to minimize this overproduction. Sample problems, their solutions and solution times are presented.

Keywords: Integer programming; symmetry; printing plate layout; folding carton

INTRODUCTION

With the exception of canned and bottled goods, almost everything you see in a supermarket or many other retail outlets is packaged in what is known as a folding carton. The majority of these are printed using a relatively inexpensive printing technology known as offset printing. Offset printing uses inexpensive rubber printing plates which are glued to cylinders for printing. For each color printed on the carton, a separate plate is needed. For instance, if there are eight colors on the box, eight plates are used. For some products a higher resolution printing is required. For instance hair dye kits, the focus of this chapter, typically have a photograph of a model with her hair dyed the color of the kit. For this type product a different technology known as Gravure printing is often utilized. Gravure printing uses sets of engraved metal cylinders instead of rubber printing plates. These cylinders are very expensive (in excess of $100,000 per set). To minimize this cost, the printer will generally combine multiple different products together on one set of cylinders. In the example of hair dye kits, there might be 10–20 shades in a given product line. (For the remainder of this chapter the term “stock keeping unit” or SKU for short will be used to reference individual shades.) These 10–20 SKUs might be allocated across two or three sets of cylinders. It is also possible for other product lines to be less varied, but the work presented here is still applicable.

Note: While the actual example studied here used printing cylinders, unless you are intimately knowledgeable of printing technology it is probably easier to visualize this problem by thinking of flat printing plates. The terms cylinder and plate are used interchangeably. You may think of it as slicing a cylinder open and unrolling it into a flat plate.

The demand for each SKU varies significantly. For instance the demand for blonde hair dye, the most popular, might be 10 times the demand for dark black, the least popular. One strategy for assigning SKUs to individual sets of cylinders could be to rank order the demands and divide the SKUs across the sets based on where they fall in that rank ordering. There would be two problems with this type of approach.

First, even within a subset of SKUs the ratio of highest to lowest demand might still be two to one or more. Second, the number of SKUs might not be evenly divisible across the number of sets. Cylinder size is fixed by the design of the printing press. So the number of cartons that fit on a cylinder is dictated by the size of the carton and the size of the cylinder. For a product line with 21 SKUs, 12 cartons per set of cylinders and 2 sets of cylinders either there will be three wasted positions or overproduction of the products assigned to those positions. (It would be useful to note that when printing, the cardboard is one sheet for all cartons that fit on a cylinder. So, not assigning a carton to a position would result in the cardboard for that position being wasted.)

The problem presented here is to determine an optimal way of assigning SKUs to the surplus positions across the sets of cylinders. The overall objective is to match the production of each SKU as closely as possible to the demand for that SKU. All costs incurred by the printer are passed on to the consumer packaging company. Any excess production results in inventory carrying costs. Additionally since product re-designs are frequent this overproduction often becomes obsolete and has to be written off. “Background” section provides more background on the problem faced by the consumer packager. “Existing Literature” section reviews existing literature in this area. “Integer Linear Programming Formulation” section explains the integer programming formulation detailed in the appendix. “Results” section summarizes sample problems and results. “Conclusion and Future Work” section concludes and presents potential future extensions of th...

Table of contents

• Cover
• Title Page
• Multi-Criteria Optimization
• Applications of Optimization
• Supply Chain Management
• Index