Abstract Number:003-0324

Optimization of a Production Plan Using Taguchi Robust Design

Sixteenth Annual Conference of POMS, Chicago, IL, April 29 - May 2, 2005

John F. Kros

East Carolina University

Department of Decision Sciences

3206B Harold Bate Building

Greenville, NC 27858

(252) 328-6364

Abstract

This paper describes and demonstrates a method to design a multi-response robust planning system using computer simulation. The structure of the research simulates production schedules while incorporating Taguchi design philosophy with multi-response surface methodology. The results of the experimental design are used to create a manufacturing planning system that is robust to uncertainties in a business environment. A Master Production Schedule (MPS) will be the planning system vehicle for experimentation. We illustrate the method by considering the design of a planning system for a make-to-stock manufacturing situation.

Purpose of the Paper

The purpose of this paper is to describe and demonstrate a method to design a robust planning system in a manufacturing setting using the techniques of Genichi Taguchi and simulation experiments. The structure of the research simulates production schedules while incorporating Taguchi design philosophy with multi-response surface methodology.

Background

The planning process for any company is most often a complex, dynamic environment. As a company grows, so does the overall complexity of the planning process itself. In addition, factors outside the sphere of the company’s reach can often erode the efficacy of a planning system. To combat this problem, two techniques have been introduced: Robust Design and computer simulation. Although each of these techniques has been widely written on (see Taguchi for Robust Design and Welch for simulation), Mayer and Benjamin were one of the first to combine simulation experiments and the Taguchi paradigm.

A number of articles followed involving Robust Design and simulation experiments. Dooley and Mahmood examined the concept of robust scheduling heuristics using experimental design and simulation. In 1995, Benjamin, Erraguntla, and Mayer researched using simulation for robust system design and Lim, Kim, Yum, and Hwang investigated the operational aspect of a direct-input-output manufacturing using the Taguchi method and computer simulation. A framework for designing, analyzing, and improving systems and processes via discrete event simulation and Robust design was presented in Sanchez, Sanchez, Ramberg, and Moeeni. Moeeni, Sanchez, and Vakharia applied Robust design and simulation to Kanban systems.

For instance, MPS materials generally have different lead times, delivery dates, and often compete for machine time when actual production commences. These noise factors, all of which have inherent uncertainties and are subject to frequent change, combine to destroy the validity of the MPS. Robustness to these noise factors is a necessity for the MPS to provide control over the manufacturing process. Large amounts of resources are expended managing the validity of the MPS. The literature suggests that creating a MPS that is more robust to noise factors is highly desired (see Ebert and Lee, Lin and Krajewski, and Lewis, Sweigart, and Markland). This research proposes the application of Taguchi’s design methodology to develop a MPS that is more robust to these noise factors.

Introduction

Make-to-stock companies typically produce end-items where each product is assembled from purchased and/or manufactured basic parts and subassemblies. Along with the control of the production and inventory system, companies wish to minimize inventory costs, maximize machine utilization, and provide on time delivery of product to the customer. Control of the production system and these objectives are accomplished through the use of a master production schedule (MPS). MPS is the process that specifies the products to be manufactured, the quantity to be produced, and the delivery date to the customer. Based on the MPS, individual components and subassemblies that make up each product are also planned. The MPS process is a complex, dynamic environment. The structure of the MPS reflects a firm’s basic manufacturing environment: make-to-stock, make-to-order, or assemble-to-order. The authority to manufacture a product is translated into the MPS from an aggregate business plan. The MPS processes inputs from forecasts of independent demand, the overall business plan, sales order due dates, component lead times, and end inventory numbers. The MPS communicates with the planning bills of materials (the actual list of components and the construction hierarchy), the materials requirements plan (MRP), and the rough-cut capacity plan.

Based on the MPS, individual components and subassemblies that make up each product are planned. Raw materials and subassemblies are ordered to make various components, those components are then scheduled to be processed through the factory. Often those materials have different lead times, delivery dates, and often compete for machine time when actual production commences. In addition to these factors, parts become defective during processing, lead times for raw materials change, and forecasts expand and contract. All these factors destroy the validity of the MPS and require large amounts of resources to manage all the exceptions and changes that occur.

Robustness to these exceptions and changes is a necessity for the MPS to provide control over the manufacturing process. However, the sheer volume of possible end-items to be manufactured makes actual customer demand difficult to accurately forecast and in reality the MPS is not robust to these exceptions and changes. Many companies attempt to hedge against these uncertainties by maintaining safety stockpiles of raw materials, work-in-process, and finished goods inventory. Although this type of hedge buffers against stock outs and missed delivery dates, it also leads to inflated inventory levels and costs. In addition, managers may attempt to hedge against changes in demand forecasts by building in safety lead times. Whybark and William concluded that safety stockpiles are a better hedge when dealing with quantity uncertainty while safety lead-time is a better hedge for timing uncertainties. In another study, Grasso and Taylor determined that safety stockpiles are a better hedge with supply-timing uncertainties than does safety lead-time. However, in general, companies must deal with a myriad of factors that destroy the validity of the MPS.

The literature suggests that creating a MPS which is more robust to these uncertainties and changes (i.e., noise factors) is highly desired (see Ebert and Lee, Lin and Krajewski, and Lewis, Sweigart, and Markland.) This research proposes the application of Taguchi’s robust design methodology to the MPS problem. The next section will develop the MPS problem in the Taguchi framework.

Taguchi’s Methodology Applied to the MPS Problem

The make-to-stock manufacturing environment for an electronics maker is studied in this paper. The product being assembled consists of two prefabricated circuit boards, one single board and one board that is already attached to a metal shell. The shell is opened, the single board is interconnected to the existing board inside and secured to the shell, and then the shell is closed and transferred to test. As has been discussed, master production scheduling is complicated by demand uncertainty, changing lead times, and varying scrap rates. The areas affected by the noise factors include:

1. inventory - keeping too much in stock or not having enough to meet demand

2. machine utilization - difficulty in planning capacity, under/over loading

3. shortages - consequences from too much or not enough shippable product.

To cope with these problems, schedulers often form judgments about future forecasts and they adapt production schedules to reflect beliefs and opinions about forecast errors.

The research literature on scheduling has mainly investigated these informal procedures using one-at-a-time methods. However, as any experienced scheduler knows, any change in a forecast, lead time, or scrap rate has dynamic effects on the MPS, often multiplicative effects (i.e., one change my induce multiple often interrelated changes on many other factors). In turn, the noise factors also act in the same way, producing dynamic effects with regard to the MPS. The current research proposes the use of Taguchi’s design methodology to create an organized approach to investigating the effects of changes in MPS inputs and noise factors to the three affected by changes in the MPS. The next section will detail the parameters to be included and measured in the design.

MPS Design Parameters

This section will detail the response of interest, the factors that are controllable in the design, and the uncontrollable or noise factors in the design.

Response Parameters

For the MPS problem, three responses are of interest. These responses are as follows:

1. Total Inventory Cost - the total cost of carrying costs and shortage costs/period

2. Plant Utilization - the total cost of under and over capacity per period

3. Delivery Schedule - the total cost of missed deliveries and holding costs/period

Total inventory cost and plant utilization are characterized by the NTB case and have associated two-sided loss function. The delivery schedule response is characterized by the LTB case and has an associated one-sided loss function. The total inventory cost loss function illustrates that as per period inventory balance deviates from zero that losses increase. Holding costs are incurred when inventory balances are above zero and shortage costs are incurred when inventory balances are below zero. Distinct breakpoints appear on either side of zero. These break points show the level of inventory where loss per unit increase at a different rate. In this example, the loss per unit increase after those breakpoints for both excess and shortage cases. Management wishes to keep inventory balance at zero per period. In other words, no inventory shorts or excess inventory per period.

Utilization measures the number of units of capacity per period that were either excess or short. Overcapacity costs include overtime pay and the hiring of extra workers. Undercapacity costs include idle time of machines and workers. The loss associated with over capacity is symmetric with under capacity. The change is an increase in per unit capacity loss. Management wishes to balance the capacity per period. This means utilizing the machines at or near their intended capacity per period.

Shortages are measured as the number of units an order is short per period. The relationship is linear which corresponds to the flat rate shortage charge per unit. This rate was a standard rate in most of the customer contracts. Management’s goal was to minimize the shortage loss per period due to the high cost of missing scheduled deliveries.

Input Parameters

The MPS problem has six input parameters: MPS forecast bias, lot size technique, sub 1 purchase bias, sub 1 safety stock, sub 2 purchase bias, sub 2 safety stock, X1, X2, X3, X4, X5, and X6, respectively. The factors all affect the MPS in a manner in which a master scheduler can control (see Figure 15). The input parameters are:

X1 = MPS forecast bias -- bias introduced to the forecast numbers by a scheduler

X2 = Lot size technique -- technique used to determine # manufactured/period

X3 = Sub 1 purchase bias -- bias on the # of sub assembly 1 purchased/period

X4 = Sub 1 safety stock -- on hand inventory of sub assembly 1 at period 1

X5 = Sub 2 purchase bias -- bias on the # of sub assembly 2 purchased/period

X6 = Sub 2 safety stock -- on hand inventory of sub assembly 2 at period 1

All of these parameters are measured at three levels. A high level, a mid level, and a low level. The MPS forecast bias and Sub 1 and Sub 2 purchase bias’ will be varied from +50%, 0%, and -50% bias of the original forecasts or levels calculated by the initial MPS run. The safety stock values will be varied from 100% of total demand, +50% of total demand, and 0% of total demand. Table 5.1 summarizes this information.

Table 5.1: Summary of Input Parameter Factor Level Values

MPS Bias / Lot Size Technique / Sub 1
Purchase
Bias / Sub 1
Safety Stock / Sub 2 Purchase Bias / Sub 2 Safety
Stock
Level 1 / +50% / Lot 1 / +50% / 100% of demand / +50% / 100% of demand
Level 2 / 0% / Lot 2 / 0% / 50% of demand / 0% / 50% of demand
Level 3 / -50% / Lot 3 / -50% / 0% of demand / -50% / 0% of demand

Three different lot-sizing techniques were employed. The first technique is referred to as single period balancing. This technique calculates lot size (LS1) as follows:

LS1 = periodx original forecast - available inventory periodX-1 + shortages period X-1 (59)

This technique attempts to minimize inventory costs per period by looking at the current forecast and one period past inventories and shortages. In doing this, the technique tends to push higher amounts of production into later periods as the MPS becomes dynamic. It, however, does to the best job at minimizing per period inventory costs.

The second technique is referred to as multiple or cumulative period balancing. This technique calculates lot size (LS2) as follows assuming production should begin in period 0 and continue until period x:

LS2 = cumulative revised forecast period0 to x - cumulative manufactured period0 to x(60)

This technique attempts to minimize inventory and minimize shortages per period. Unlike LS1, it looks not only at the current period but all previous periods. The technique implicitly takes into account shortages due to the cumulative aspect of the method. Production tends to be higher in the earlier period for this technique as the MPS becomes dynamic and shortage costs per period tend to be lower.

The final technique is referred to as average order quantity (AOQ). This technique calculates lot size (LS3) as follows:

LS3 = (61)

This technique is the simplest of the three and attempts to even production out over the forecasted demand window. Overall, the technique tries to trade-off holding costs and shortage costs. Many also refer to LS3 as a fixed order quantity. The next section describes the noise factors included in the experiment.

Noise Parameters

The MPS problem has four noise parameters customer forecast bias, scrap rate, sub 1 lead time bias, sub 2 lead time bias, Z1, Z2, Z3, and Z4, respectively. The noise factors all affect the MPS in a manner that is uncontrollable by the master scheduler. The noise parameters are defined as follows:

Z1 = Customer forecast bias - bias introduced to the forecast by a customer

Z2 = Scrap rate - the rate that units are deemed unshippable or defective

Z3 = Sub 1 lead time bias - the number of periods difference from original quoted lead time to actual lead time for Sub 1

Z4 = Sub 2 lead time bias - the number of periods difference from original quoted lead time to actual lead time for Sub 2

All of these parameters are measured at two levels. A high level and a low level. The Customer forecast bias will be varied at +50% and 0% of the original forecasts given. The scrap rate will be varied at 5% and 0% of the manufactured units per period. The Sub 1 and 2 lead time bias’ will be varied at 4 and 0 periods each. Table 5.2 summarizes this information.

Table 5.2: Summary of Noise Parameter Factor Level Values

Z1 -Customer Forecast Bias / Z2 -Scrap Rate / Z3 - Sub 1 Lead Time Bias (periods) / Z4 - Sub 2 Lead Time Bias (periods)
Level 1 / +50% / 5% / 4 / 4
Level 2 / 0% / 0% / 0 / 0

Orthogonal Array Setup

With the responses, input parameters, and noise parameters defined, the orthogonal array can be created. This experiment contains six input factors at three levels each and four noise factors at two levels each. Using the general rules for choosing an orthogonal array, the alternatives are an L18 or and L27 for the inner array and an L8 for the outer array. The L18 was chosen for the inner array and the L8 for the outer array. The inner array will be described first.

Inner Array

The L18 was chosen because 7 three-levels factors can be studied and 1 two-level factor. Since the experiment contains 6 three level factors and at the most two interactions would be relevant, the L18 was feasible and more economical than the L27. Table 5.3 displays the inner orthogonal array. The safety stock bias for sub 1 and 2 are derived from demand based on 2400 original units forecasted.

The orthogonal array presented represents the order and method by which the experiment will be carried out. In a sense, it is an organized data collection process. According to this array there will be eighteen experimental runs, hence the L18 denotation. The array states what the level setting for each input parameter will be when each experimental run is completed.