Yaman BARLAS                            Ayse AKSOGAN 
Bogazici University                     Altinyildiz Garment Group
Industrial Engineering Department       Koyalti Mevkii
Bebek, 80815 TURKIYE                    34530 Yenibosna
Fax: (90) (212) 265 18 00               Istanbul,TURKEY
E-Mail: ybarlas@boun.edu.tr

ABSTRACT

Quick Response is a new supply chain management system designed to meet the changing requirements of an increasingly more competitive market in the apparel sector. The main objective of this study is to build a System Dynamics simulation model of the portion of the textile and apparel pipeline including the retailing and wholesaling processes to search for inventory decisions and policies that yield reduced costs/increased revenues in terms of the retailer. More specifically, the purpose is to examine the effectiveness of the major Quick Response principles in achieving this goal. One such principle is the coordination of the order decisions made by the retailer, wholesaler, and manufacturer. In exploring the interrelationships between these decisions, order policies have had to be designed for 'hybrid' systems in which orders are discrete in time, whereas the processing of goods in the pipeline is continuous.The other purpose of the study is to examine the implications of diversification and the different assumptions about the effect of product diversity on customer demand, possible stockouts, and inventory levels. The model is built using the system dynamics methodology. The parameters are estimated using data from LEVI'S corporation. Model verification and validation tests are carried out, based on numeric data and other information obtained from LEVI'S. The effectiveness of inventory policies, in terms of inventory levels and adjustment times, are examined. The effects of delays on the performance and inventory control policies of the system are investigated. Next, the consequences of product diversification and different assumptions about the effect of diversification on customer demand are analyzed. Finally, the performance of the system under different demand pattern assumptions is explored.

1. INTRODUCTION AND PROBLEM BACKGROUND

New strategies are being adopted by a number of manufacturers and retailers in the textile and apparel industry to gain a competitive advantage in world markets [1]. Pressures from low-cost, global sources require companies to be more productive, react faster to market changes, and maintain smaller inventories. These developments in the operation of businesses entail significant changes in the traditional ways of managing manufacturing systems [2].

A new approach, methodology, and a set of tools, known as Quick Response, was born in order to address this problem.

'Quick Response is an operational philosophy and a set of procedures aimed at maximizing the profitability of the apparel pipeline. [It] depends on the integration of all the components -fiber, textile, manufacturing, and retail- into one consumer responsive whole. Quick Response is driven by comprehensive and rapid information transfer between the sectors of the pipeline from retail point-of-sale back upstream' [3].

The textile and apparel industry consists of several components and is characterized by its unusual length as displayed in Figure 1.1. Successful implementation of the Quick Response System requires changes in management mind-set and priorities, full use of the new technologies, and the realization that fiber making, textile manufacturing, apparel manufacturing, and retailing are not separate businesses, but must operate as parts of an integrated, consumer responsive supply system [3]. The objective of this study is to build a simulation model of the part of the textile pipeline including the wholesaling and retailing processes which link the end of the pipeline to the final consumer.

Producing a wider variety of goods, referred to as diversification, has a cost associated with it. It impacts all sectors of the industry, increasing work in process and inventory levels. Decreased equipment utilization, less efficient use of materials and reduced worker productivity are other cost penalties associated with diversification. A great deal of process research is needed to develop methods and technologies to minimize these cost penalties.

2. PROBLEM DEFINITION AND PURPOSE OF RESEARCH

Although most Quick Response literature consists of surveys and articles published in trade literature [5,6,7,8,9,10,11], there are some scientific and generic studies made by researchers. Major modeling work includes two studies by Nuttle, King, and Hunter(1991), King and Pointdexter(1991), another study by Nuttle, King and Hunter(1992), Fisher and Raman(1992). Also, Hunter(1990) and two studies by Fisher, Obermeyer, Hammand, and Raman(1994) provide comprehensive discussion of concepts, technologies, and tools of Quick Response.

The primary purpose of our study is to build a system dynamics simulation model of the portion of the pipeline including the retailing and wholesaling processes to search for inventory decisions and policies that yield reduced costs/increased revenues in terms of the retailer, in particular to examine the effect of some Quick Response principles for this purpose. In inventory systems where there are more than one independent decision points, the characteristic behaviour modes are oscillations and instability. In the system under study, the presence of periodic order decisions and flows while the processing of goods in the pipeline is continuous complicates the behaviour even more. The challenge is to formulate order policies for partially discrete and partially continuous inventory systems to smooth the oscillations as much as possible in order to reduce the costs of the retailer. The other major purpose of the study is to examine the effect of diversification and the different assumptions about the effect of product diversity on customer demand, possible stockouts, and inventory levels. The tradeoff between these positive and negative effects of diversification will be investigated.

The primary purpose of our study is to build a system dynamics simulation model of the portion of the pipeline including the retailing and wholesaling processes to search for inventory decisions and policies that yield reduced costs/increased revenues in terms of the retailer, in particular to examine the effect of some Quick Response principles for this purpose. In inventory systems where there are more than one independent decision points, the characteristic behaviour modes are oscillations and instability. In the system under study, the presence of periodic order decisions and flows while the processing of goods in the pipeline is continuous complicates the behaviour even more. The challenge is to formulate order policies for partially discrete and partially continuous inventory systems to smooth the oscillations as much as possible in order to reduce the costs of the retailer. The other major purpose of the study is to examine the effect of diversification and the different assumptions about the effect of product diversity on customer demand, possible stockouts, and inventory levels. The tradeoff between these positive and negative effects of diversification will be investigated.

3. THE MODEL OVERVIEW

The model is mainly composed of the order decision and pipeline inventories of the retailer, the aggregated production decision of the manufacturer and its pipeline inventories, a consumer section where the relations between the final consumer and the retailer is represented, and a cost computation section where the costs and profit of the retailer are calculated. The STELLA II software is used to build and analyze the Quick Response model [21].

The pipeline inventories included in the model are the retail store inventory, the goods being transferred from the apparel manufacturer to the retail store, the apparel manufacturer inventory, and the goods in production at the apparel shop floor as displayed in Figure 3.1. The retail store places orders to the manufacturer according to the desired levels of its pipeline inventories, the actual levels of these inventories, and the amount of sales. The parameters that influence the order decision are the Store Inventory Adjustment Time and the Transfer Adjustment Time which represent the speed with which the discrepancies between the relevant inventories and their desired levels are corrected. The order is not realized by the manufacturer immediately. There is an order processing delay represented by Delayed Order Rate. The goods are shipped from the Apparel Manufacturing Inventory according to the Delayed Order Rate. They spend some time on the way, being represented by the stock "Goods Transferred", and finally reach the Store Inventory. The difference between the order rate and shipments gives the Manufacturing Backlog. The manufacturer places shop orders according to the desired levels of its pipeline inventories, the actual levels of these inventories, and the orders placed by the retailer. The parameters that influence the order decision are the Manufacturing Inventory Adjustment Time and the Production Adjustment Time which again represent the speed with which the discrepancies between the relevant inventories and their desired levels are corrected. The Manufacturing Order Rate is limited by the Maximum Capacity. The goods spend time in production, represented by the stock "Goods in Production". The goods that come out of production enter the Apparel Manufacturing Inventory.

The Potential Customer Demand is the volume of demand that enters the store. The Product Diversity is the number of SKUs, in terms of style/color, that the store offers as a line of apparel items. The Available Product Diversity is the Product Diversity of the store at a point in time. The probability that any of the product types will match the tastes and preferences of the Potential Customer Demand, F, is a function of the Available Product Diversity. The Actual Customer Demand is the volume of demand that matches a product type being offered in the store. The Lost Demand is the volume of demand that is lost because none of the product types in the store match the preferences of the Potential Customer Demand. The Size is the number of different sizes of each style/color combination that is offered in the product line. The Number of SKU represents the variety of products, in terms of style/color/size. The Typesupply is the average number of apparel items of each SKU that the store has in stock. The Ratio of Typesupply/Actual Customer Demand determines, by a graphical function, the Percentage of Demand Lost, which expresses the percentage of the Actual Customer Demand that is lost because an SKU is not in stock. The Stockout represents the incidence when the Actual Customer Demand can not be met because of certain items being out of stock. Lost Sales is the lost demand because of low diversity, added together with the demand lost because of Stockouts.

Research of production and inventory literature indicates that the costs relevant in an inventory system are the procurement costs, costs associated with the existence of inventories, and costs associated with stockouts (lost sales) [22,4]. The costs of the retail store consists of Transportation and Inventory Costs. The cost of lost sales is embedded in the Profit calculation. The difference between the Revenues and the Costs make up the Profit of the retailer.

The stock-flow diagram is given in Figure 3.1. The time unit of the model is one day. The retail store and the manufacturer both place orders once a week. This causes the related flows of the model to be discrete accordingly. Meanwhile, the processing of goods in the pipeline is continuous. The system under study is a partially discrete, partially continuous inventory system. In inventory systems, where there are more than one independent decision points, the characteristic behavior modes are oscillations and instability. In our model the behavior is complicated even more by the partial discreteness of the system. Our aim is to formulate order policies for this partially discrete, partially continuos inventory system.

The potential customer demand, expressed in the model as Pot Cust Dem, is the driving demand of the whole system. As stated previously, it is the volume of demand that enters the store per day. It is an input to the model. The product diversity, expressed in the model as Prod Diversity, is the variety of products, in terms of style/color, that the retail store offers as a line of apparel items. It is also an input to the model. The available product diversity, expressed as Available Prod Diversity, is the product diversity of the retail store at a specific time depending on theapparel items the store has in stock. The Available Prod Diversity is calculated as the minimum of Prod Diversity and Store Inventory as follows:

Available Prod Diversity = MIN(Prod Diversity, Store Inv)        (4.1)

Let      P  = the probability that a customer will prefer an SKU, 
              i.e. the probability that a customer will prefer 
              if there is one SKU in the store 


      (1-P) = the probability that a customer will not buy 
              if there is one SKU in the store

If there are two SKUs in the store the probability that a customer preference will match one is calculated by:

The calculation of the probabilities may go on for three SKUs, four SKUs, etc.

Tables 4.1. and 4.2. list the probabilities that a customer will decide to buy, for specific numbers of items for p=0.05 and p=0.25. Figures 4.3. and 4.4. show the associated graphs. Note that the shape of F changes meaningfully with changed p values.

Probability research is done to support the above findings. Existing statistical distributions are examined and the binomial distribution is found to express the above probabilities [23,24,25,26].

FIGURE 3.1. The Stock Flow Diagram of the Model

The probability function of the binomial distribution is given as:

If p is the probability that an event will happen in any single trial (called the probability of a success) and q = 1-p is the probability that it will fail to happen in any single trial (called the probability of a failure) then the probability that the event will happen exactly x times in N trials (i.e. x successes and N-x failures will occur) is given by p(x). Success may be defined as the situation when the customer prefers an SKU and failure as the situation when the customer dislikes an SKU and each trial refers to one SKU since all SKUs will be considered before the ultimate decision. The probability of success is obviously the above mentioned p, and the probability of failure 1-p.

Table 4.1. lists the binomial probabilities of success for p=0.25. The probabilities are the same as the probabilities calculated in Table 4.2. Table 4.1. can be continued for numbers up to 100.

The above results lead to the conclusion that the graphical relationship between the Available Prod Diversity and F can be obtained from the binomial distribution. P is initially assumed to be 0.25 and the graphical relationship between F and the Available Prod Diversity is given in Figure 4.4. Tests are done with various p values.

F' is calculated by:

                       F' = 1-F                                 (4.2)

        Actual Cust Dem = F x Pot Cust Dem                      (4.3)

         Lost Demand = F' x Pot Cust Dem                        (4.4)

         Number of SKU = Prod Diversity x Size                   (4.5)

         Typesupply = Store Inv / Number of SKU                  (4.6)

         Ratio = Typesupply / Actual Cust Dem                (4.7)

Extensive probabilistic and statistical study has been done to find the underlying distribution that determines the demand for each SKU and, as a result, the quantity of stockouts. A number of statistical distributions have been examined some of which are the hypergeometric distribution, the binomial distribution, the multinomial distribution, and the multivariate hypergeometric distribution [23,24,25,26]. The setting to which an underlying distribution is being searched for can be described with the following small example:

Let's assume that the actual customer demand is three and there are two SKUs in the store. There are four items in the store inventory. The actual customer demand may be distributed among the SKUs in a number of demand patterns:

The probability of the occurrence of each demand pattern and the number of stockouts associated with each demand pattern have to be known to calculate the expected number of stockouts. None of the known distributions examined fit the studied problem. The underlying distribution is designed as a modified version of the multinomial distribution.

The multinomial distribution is defined by

where xi is the number of items occurring in the ith class. The number pi is the probability of any item being assigned to the ith class, and it is the fraction of the total population belonging to that class.

If x1 through xk is interpreted as the demand for SKU1 through SKUk, n is the actual customer demand, and p1 through pk is equal to 1/SKU with the assumption that each SKU is equally likely of being preferred, the probability of each demand pattern occurring can be calculated by the probability function of the multinomial distribution.

In the previous example, the probabilities for the demand patterns may be calculated as:

Our example assumes that the store inventory is four with two items of each SKU. The stockout for each demand pattern may be found by taking the difference between the demand for each SKU and the supply of two. Then if the stockout and probabilities are multiplied and added up, the expected stockout may be calculated. For instance, in the above example, the expected stockout is given by:

since the only two possibilities of stockout are in the first and fourth demand patterns, where the demand for SKU1 and SKU2 are three for both.

The STELLA II language is not capable of modeling an algorithm that can make this calculation for any general SKU, demand, and supply values. A C program is built that calculates the expected stockout for any given SKU, demand, and supply values and is validated by hand-calculated results .(The code of the program is given in [29]). A series of runs are made with the C program. Detailed analysis of the results shows that the percent of demand lost by the stockouts is a function of the demand, the typesupply, and the number of SKU. The aim is to obtain a function that yields the percent of demand lost. Analysis shows that the relationship between the percent of demand lost and the Typesupply/Demand ratio is an exponentially decreasing function. As the number of SKU is increased the curve gets more convex. The SKU dimension prevents the exact plotting of the curve in two dimensions. Another complication is that, since the factorial of the demand is calculated, it becomes impossible to do the computations numerically above demand values of 30 and the computation starts to take too long above SKU values of 10. The curve can only change between a narrow range of values. The exact points on the curve can not be plotted, but an assumption can be made about its shape as suggested by numerous experiments done with the C program. Later simulation experiments will be done with a range of different shapes. The basic shape of the graphical relationship between Ratio and Percent Dem Lost is given in Figure 4.5.:

    Stockout = Actual Cust Dem x Percent Dem Lost            (4.8)

    Sales = Actual Cust Dem - Stockout                       (4.9)

Store Order Rate = ((Des Store Inv-Store Inv)/Store Inv Adj Time) 
                   + ((Des Transfers - Smth Goods Trans)
                   /Transfer Adj Time) + 7 x Estimated Sales  (4.10)

The desired store inventory, expressed as Des Store Inv, is the level of inventory that the store tries to keep on hand.

The store inventory adjustment time, expressed as Store Inv Adj Time, is the speed with which the discrepancy between the store inventory and its desired level is corrected.

The transfer adjustment time, expressed as Transfer Adj Time, is the speed with which the discrepancies between Des Transfers and the level of Goods Transferred are corrected. It is an input to the model.

The desired level of goods in transit, expressed as Des Transfers, represents the level of goods that must be kept in transit to assure the steady flow of goods in the pipeline. It depends on the sales and the amount of time that passes from the shipment of the goods from the manufacturing inventory until their exposure on retail store shelves, Ship and Rec Lead Time. It is calculated by the following equation:

      Des Transfers = Sales x Ship and Rec Lead Time        (4.11)

      Smth GoodsTransferred, 7)        (4.12)

      Est Sales = SMTH1(Sales, 7)                           (4.13)

Store Order Rate = ((Des Store Inv-Store Inv)/Store Inv Adj Time) 
                   + ((Des Transfers - Smth Goods Trans)
                   /Transfer Adj Time) + 7 x Estimated Sales

     Delayed Order Rate = SMTH1(Store Order Rate, 1)        (4.14)

      Ship from Man = MIN(Apparel Man Inv, 
                      (Man Backlog + Delayed Order Rate))   (4.15)

Store Receiving = Goods Transferred / Ship and Rec Lead Time (4.16)

Man Order Rate = ((Des Man Inv-Smth Eff Inv)/Man Inv Adj Time) 
                  + ((Des Goods in Prod - Smth Goods in Prod)
                  /Prod Adj Time) + Store Order Rate          (4.17)

The desired manufacturing inventory, expressed as Des Man Inv, is the level of inventory that the manufacturing plant tries to keep on hand. It is an input to the model.

The manufacturing inventory adjustment time, expressed as Man Inv Adj Time, is the speed by which the discrepancy between the apparel manufacturing inventory and its desired level are corrected. It is also an input to the model.

The manufacturing backlog, expressed as Man Backlog, is the part of the order that can not be met from inventory and is backordered. It is calculated as:

     Man Backlog = Delayed Order Rate - Ship from Man       (4.18)

     Eff Inv = Apparel Man Inv - Man Backlog                (4.19)

      Smth Goods in Prod = SMTH1(Goods in Prod, 7)          (4.20)

       Smth Shipments = SMTHN(Ship from Man, 14,2)           (4.21)

       Smth Eff Inv = SMTH1(Eff Inv, 3)                      (4.22)

       Des Goods in Prod = Ship from Man / Prod Lead Time    (4.23)

        Man Order Rate = ((Des Man Inv-Smth Eff Inv)/Man Inv Adj Time) 
                         + ((Des Goods in Prod - Smth Goods in Prod)
                         /Prod Adj Time) + Store Order Rate

        Prod Orders = MIN(Man Order Rate, Max Capacity)        (4.24)

         Prod Rate = Goods in Prod / Prod Lead Time            (4.25)

Let A = carrying cost of one unit of inventory for one unit of time

         Inv Costs = A x Store Inv                             (4.26)

Interviews with Levi's company indicated that the boxes are of three sizes, Small Size, Medium Size, and Large Size, in increasing order. Their prices are denoted by Small Box Price, Medium Box Price, and Large Box Price respectively.

If Ship from Man <=Small Size,

         Tranportation Costs = Small Box Price                 (4.27)

         Transportation Costs = Medium Box Price

         Transportation Costs = Large Box Price

        Remainder = Ship From man - [INT(Ship From Man /Large Size) 
                       x Large Size]                           (4.28)

        Transportation Costs = INT(Ship From Man /Large Size) 
                                x Large Box Price              (4.29)

        Transportation Costs = INT(Ship From Man /Large Size) 
                                x Large Box Price + Small Box Price

        Transportation Costs = INT(Ship From Man /Large Size) 
                                x Large Box Price + Medium Box Price

        Transportation Costs = INT(Ship From Man /Large Size) 
                                x Large Box Price      + Large Box Price

5. VERIFICATION AND VALIDATION OF THE MODEL

The model is validated by using information from a real system. After the tentative stock-flow diagram was built, a number of organizations were visited to find one that operates as a pull system as the Quick Response philosophy suggests. Levi's was found to operate as a pull system and to carry out restructuring activities implementing the Quick Response strategies.

Data were collected by talking to people in the customer service, logistics, and sales departments, and a retail store that sells Levi's products that was suggested by the customer service department.

The product line under study is the Bottoms product line which refers to the basic jean pants that are sold all year round. The maximum potential product line consists of 47 SKUs in terms of style/color combinations. In other words, the maximum Product Diversity is 47. Number of SKU is 668 with the addition of Size combinations. The Product Diversity is taken as 40 and the Number of SKU as 600, to represent the average numbers that a store keeps on hand.

One general difficulty stems from the fact that we are modeling a single retail store. Any data obtained from Levi's about manufacturing inventories, shipments, etc. reflect aggregates for all retail shops that sell Levi's items. Thus, we face the general problem of estimating the portions of aggregated data that corresponds to an individual store.

The parameters that have to be estimated in the manufacturing section of the model are the desired manufacturing inventory and the maximum capacity that the central manufacturing plant allocates to one store.

The manufacturing plant of the Levi's company has 50000 units/week capacity. On the average 20000 units/week is allocated to the production that is done for Belgium which is distributed to various parts of Europe. 30000 units/week is left for domestic production.

After examination of the finished goods inventory reports, Des Man Inv of the whole plant is found to be 270,000 on the average.

Des Man Inv and Max Capacity corresponding to the one store that we are studying is calculated by two different approaches and is verified. The first one is the sales ratio and the second, shipment ratio. It is assumed that these ratios can guide in the calculation of Des Man Inv and Max Capacity allocated to individual retail stores. The manufacturing plant ships 1,100,000 units/year shipment is done to original Levi's shops and to 'corners' (which are selling points where other brand names are also sold). Levi's sales are made at 350 selling points of which 80 are original Levi's shop, 50% of all shipments are made to original Levi's shops. The average shipments made to a Levi's store is calculated as:

This number represents the average of all stores among which are stores in small cities and towns where sales are quite rare compared to some other selling points. The customer service department estimated this number for our major retail store under study to be about 10,000 units/year.

The shipment ratio of the retail store may be calculated as:

The sales ratio represents the ratio of the sales made by the retail store to the sales made at all the selling points. Sales reports were examined to find that the sales ratio is yields 0.011. These ratios are used to calculate Des Man Inv and Max Capacity levels for the retail store. The values found by the sales and shipment ratios are quite close. Their average is used in the model, which is 0.010.

By this ratio,

Max Capacity = 30,000x0.010 = 300

Des Man Inv = 270,000x0.010 = 2700

Prod Lead Time is taken to be 12 days and Ship and Rec Lead Time two days as suggested by the logistics department.

The parameters that have to be estimated in the retail section are Des Store Inv, Ship and Rec Lead Time, inventory carrying cost, sizes and prices of the boxes used to transfer goods. Des Man Inv is taken as 4900 units on the store manager's suggestion and examining the available inventory data. Ship and Rec Lead Time is 2 days. The sizes and prices of the boxes are accepted as:

The inventory carrying cost is taken as 5000 T.L./day on the manager's suggestion.

The price is 1,900,000 which is the average price for the product line under study. The potential customer demand is taken 100 upon the store manager's suggestion

In System Dynamics studies, validation of structure is the most crucial component of validity [28]. It consists of direct structure testing and structure-oriented behaviour testing [28].

As mentioned earlier, the stock-flow diagram was tentative before contacts made with Levi's. The order decisions of the retail store and manufacturing plant were explored thoroughly to validate the structure and the order decisions of the Quick Response model.

The cost structure of the model is based on the transportation and inventory cost formation of the Levi's store. It is generalized to reflect the cost structure of a typical retail store. The transportation cost structure has been isolated from the complete model, verified, and appended afterwards.

The distribution center inventory is removed from the model, based on both the premise that in Quick Response Systems the distribution center inventory can be bypassed by replacing and simplifying its operations by the manufacturer and on the inventory structure of the Levi's company that does not include a distribution center.

As a result of the direct structure tests, the major components of the structure of the model are based on and validated by the Levi's inventory system. The next step is to test the validity of the model structure, by simulating the model under various conditions and assessing the validity of model structure by means of model behaviour, called structure-oriented behaviour testing.

One of the main objectives of this study is to formulate order policies for partially discrete, partially continuous systems. In the explanation of the equations the order policies for partially discrete systems have been given. They have been discovered through extensive study. The step by step modifications that have been done to discover these policies will be explained.

The model, when built with standard order policies of continuous dynamic inventory models, does not display meaningful behaviour. The inventory levels find equilibrium below or over desired levels. The results obtained are given in Figure A.1. The averages of Store Inv and Apparel Man Inv are 4925 and 2542, respectively, whereas their desired levels are 4900 and 2700.

The order policies of continuous inventory systems are clearly not adequate for partially discrete, partially continuous inventory systems. The reasons why the inventories do not reach the desired levels is the discreteness in the inventory levels and some flows, that originates from the discreteness in the order decisions. Smoothing is used in the inventories and flows that are used in the order decisions, to get rid of the discreteness to an extent, . In fact, the study shows that the discreteness can never be entirely rid of but the ranges in which the discrete variables change can be made smaller. Analysis has been done with generic representative models of the retailing and manufacturing sections of the pipeline. Adequate order policies for the two representative sub-models have been derived and then used in the complete model. Results show that these two sections display different characteristics in terms of inventory control. The retailing section is easier to control since only the incoming flow which is Ship from Man is discrete and the outgoing flow Sales is continuous. The manufacturing section is harder to control because both the incoming flow, Prod Orders and the outgoing flow, Ship from Man are discrete.

In the retailing section, the discreteness in the incoming flow Ship from Man is reflected in Goods Transferred stock. The discreteness in Goods Transferred stock, which is used in the order decision, disturbs the order decision. If Goods Transferred is smoothed before it becomes an input to the order decision the behaviour becomes meaningful and the store inventory reaches equilibrium at its desired level (Equation 4.12). The results are given in Figure A.2. The average Store Inv is 4910. Its desired level is 4900. Smoothing Goods Transferred with higher orders has only a slight effect on the behaviour of the system. Smoothing Store Inv has only a slight effect on the steady state behaviour while causing unstability in the transient behaviour.

In the manufacturing section, both the apparel manufacturing Inventory and the goods in production stocks have either an incoming or outgoing discrete flow. Desired Goods in Prod is also discrete since one of its inputs, Ship from Man, is discrete. When Goods in Prod is smoothed over seven days, the average Apparel Man Inv is 2517, whereas its desired level is 2700 (Equation 4.20). Since the order decision is still given according to some discrete variables, the behaviour is still not acceptable.

As stated above, Ship from Man causes the discreteness in Des Goods in Prod. The next step is to smooth Ship from Man over seven days. The behaviour of Apparel Man Inv improves but it still does not reach its desired level. Next, the order of smoothing is increased to two. The average Apparel Man Inv becomes 2631 (Equation 4.21). The next step is to smooth (Eff) Apparel Man Inv which is the only discrete variable left that is used in the order decision. The results obtained after smoothing (Eff) Apparel Man Inv over seven days are given in Figure A.3. The average Apparel Man Inv is 2707. More research has been done to discover if the order decision can be built without smoothing (Eff) App Man Inv by changing the orders of smoothing and the smoothing times of Ship from Man and Goods in Prod. Results show that the smoothing of the inventory is unavoidable.

Research has also been done to discover the effects of changes in the orders of smoothing and the smoothing times of the variables. Results show that smoothing the stocks ((Eff) App Man Inv and Goods in Prod) with orders greater than one causes oscillations in the inventories that grow with the order of smoothing. Changes in the smoothing times of Goods Transferred, Goods in Prod, and Ship from Man do not have a considerable effect on the system performance while decreasing the smoothing time of (Eff) Apparel Man Inv improves the system performance, by reducing the oscillations. The results obtained when (Eff) App Man Inv is smoothed over three days are given in Figure A.4. The average Apparel Man Inv is 2700 (Equation 4.22).

In System Dynamics, once the structure has been thoroughly validated and verified, the next step is behaviour validation [28]. The behaviour of the structurally validated and verified model is shown in Figure 5.1. The behaviour of the variables have a discrete nature. The discreteness originates from the discreteness of the orders. The basic dynamic behaviour pattern of the inventories are oscillations. The oscillations are apparent in the transient behaviour of the manufacturing section inventories. Since the orders are discrete, the inventories do not reach constant equilibrium levels, but the averages of these variables are at the equilibrium value. The average of Apparel Man Inv given in (5.1.2.) is 2700, exactly at its desired level. The retail section inventories have smoother behaviour patterns since the outgoing flow is continuous, as mentioned previously. They quickly reach steady-state as shown in (5.1.1.) and find equilibrium at their desired levels. The average of Store Inv is 4910. Ship from Man, given in (5.1.2.) is done once a week. Transportation Costs given in (5.1.4.) are calculated once a week accordingly. Inv Costs in (5.1.4.) are calculated according to the level of inventory. Transportation Costs and Inv Costs, together with Revenues make up Profit given in (5.1.5.). A portion of the Pot Cust Dem in (5.1.6.), determined by F, turns into Actual Cust Dem. Only a percent of Actual Cust Dem becomes Sales and the remaining is Stockout.

The behaviour of the variables have been validated by interviews and data from LEVI'S. Apparel Man Inv generated by the model given in (5.1.2.) displays similar behaviour patterns with the apparel manufacturing inventory of LEVI'S. The average Apparel Manufacturing Inventory of LEVI'S is approximately 270,000. The portion that corresponds to the LEVI'S shop under study is found to be approximately 2700, which is the average Apparel Man Inv. Sales given in (5.1.6.) are validated by the Sales Reports of the Levi's company. The average of the sales values in the Sales Report is 39.5 and the average sales in the model is approximately 38. Ship from Man values given in (5.1.2.) are validated by both the Headquarters and the LEVI'S shop. Store Inv given in (5.1.1.), Transportation Costs given in (5.1.4.) and Profit given in (5.1.5.) are validated by the LEVI'S shop. The verification and validation studies being completed, the model is ready for simulation experiments and analysis.

6. SIMULATION EXPERIMENTS AND ANALYSIS

If the assumption is made that Actual Cust Dem is not homogeneous while Store Inv is homogeneous, the structure of the model are as given in Figure 3.1. This is the final version on which all remaining experiments/analysis are carried out.

6.1. Product Diversity Analysis

In the original runs Prod Diversity is 40, The Size variety is 15, the Pot Cust Dem is 100, and p is 0.1. The results obtained with these values are given in Figure A.5. In order to examine the different effects of product diversity, we experiment with diversity=20 and 18 Fig A.6. and Fig A.7. As we decrease the diversity from 40 to 20, the probability of the store's product line matching customer preferences de&#141;reases, but this effect is offset by a decrease in 'percent demand lost due to type stockouts' (since type_supply/demand is higher). The result in this case is increased sales. (Compare Fig A.5.3 and A.6.1.) As we further decrease diversity from 20 to 18, lowered probability of customer preference matching this time dominates the effect of decreased percent demand lost due to stockouts; hence lower sales (Fig A.7). In this particular example, we see that a diversity of 20 is ÒoptimumÓ.

7. CONCLUSIONS

In this study, a System Dynamics simulation model was built for the portion of the textile and apparel pipeline including the retailing and wholesaling processes, in order to search for inventory decisions and policies that yield reduced costs/increased revenues in terms of the retailer. The model was verified and validated by using data from LEVI'S.

An important conclusion is that standard order policies of purely continuous inventory systems are not appropriate for partially continuous, partially discrete inventory systems, in which the orders are discrete, whereas the processing of goods in the pipeline is continuous. Order policies have been designed for partially discrete inventory systems with more than one order decision points. Experiments have been done to test the effect of increased delays on the behaviour of the system. Two different kinds of delays have been considered: (a) Information Processing Delays, (b) Material Delays. As the delays are increased, the behaviour of the system is disturbed. Increased delay requires closer control of the inventories. Experiments have also been done to discover policies that will increase sales. Research shows that the problem is two-dimensional. It depends on both the number of SKU and the level of inventories. Thus, diversification, which means the product diversity, also implies increased inventories. Therefore, whether and to what extent increased product diversity means increased profits is a subtle question, explored in detail through simulation experiments. This tradeoff implies that for a given system, there ought to be an optimal product diversity, shown to exist with simulation runs.

Finally, the system is experimented with changing demand. The results show that coping with changing demand requires the coordination of the different sections of the pipeline. Assuming changing and unknown demand patterns increases the complexity of the problem significantly. Our findings in these cases are tentative, far from conclusive. More extensive research is needed on how to best cope with this problem, in terms of what demand forecasting tools to use, and how to share these forecasts with the rest of the pipeline. In a different direction, this research can be extended to include the costs and revenues of the manufacturer and wholesaler as well, so as to improve the profit of the whole system. The model can also be modified to be implemented in other pipeline configurations, such as single manufacturer-many retailers, many manufacturers-many retailers, many retailers-many distributors, etc.

REFERENCES

1. Kincade, D.H., N. Casill, and N. Williamson, "The Quick Response Management System: Components for the Apparel Industry," Journal of the Textile Institute, Vol. 84, No. 2, pp. 147-155, 1993.

2. Park, S., "Quick Response with Overseas Production," Production and Inventory Management Journal, pp. 11-14, Fourth Quarter 1994.

3. Hunter, N.A., Quick Response in Apparel Manufacturing: A survey of the American Scene, The Textile Institute, Manchester, Engla 1990.

4. Hax, A.C., D. Candea, Production and Inventory Management, Prentice-Hall, New Jersey, 1984.

5. Braithwaite, A.J., "Management of Quick Response," Textile Asia, pp. 134-137, May 1990.

6. "Special Report: Quick Response," Textile World, pp. 38-50, February 1987.

7. ÓSpecial Report: Du Paatch Meeting," Textile World, pp. 57-62, November 1987.

8. ÓSpecial Report: FASLINC," Textile World, p. 55, January 1988.

9. "Special Report: JIT and QR," Textile World, pp. 49-60, May 1988.

10. "Special Report: Quick Response," Textile World, p. 45, May 1989.

11. "ATME-1 89 Post-Show Report," Textile World, pp. 94-95, June 1989.

12. Nuttle, H.L.W., R.E. King, and N.A. Hunter, "A Stochastic Model of the Apparel Retailing Process for Seasonal Apparel," Journal of the Textile Institute, Vol. 82, No. 2, pp. 274-259, 1991.

13. Hunter, N.A., R.E. King, and H.L.W. Nuttle, "Evaluation of Traditional and Quick Response Retailing Procedures Using a Stochastic Simulation Model," Technical Report, 1991.

14. King, R.E., M.L. Pointdexter, "A Simulation Model for Retail Apparel Buying," Technical Report, 1991.

15. Hunter, N.A., R.E. King, and H.L.W. Nuttle, "An Apparel-supply System for QR Retailing," Journal of the Textile Institute, Vol. 83, No. 3, pp. 462-471, 1992.

16. Fisher, M., and A. Raman, "Reducing the Cost of Demand Uncertainty through Accurate Response to Early Sales," Working Paper, 1992.

17. Fisher, M., W. Obermeyer, J. Hammond, and A. Raman, "Accurate Response: The Key to Profiting from QR," Bobbin, pp. 48-62, February 1994.

18. Fisher, M.L., J.H. Hammond, W.R. Obermeyer, A. Raman, "Making Supply Meet Demand in an Uncertain World," Harvard Business Review, pp. 83-93, May-June 1994.

19. Forrester, J.W., Industrial Dynamics, The M.I.T. Press, Cambridge MA, 1961.

20. Low, W.C., and W.R. Fey, "Production, Orders, and Inventory: Modeling their Dynamic Interactions," Working Paper, 1968.

21. Richmond, B., and S. Peterson, An Introduction to Systems Thinking, STELLA II Software Manual, High Performance Systems, Hanover NH, 1990.

22. Hadley, G., and T.M. Whitin, Analysis of Inventory Systems, Prentice-Hall, New Jersey, 1963.

23. Freund, J.E., and R.E. Walpole, Mathematical Statistics, Prentice-Hall, New Jersey, 1980.

24. Hogg, R.V., and J. Ledolter, Engineering Statistics, Macmillan Publishing Company, New York, 1989.

25. Ostle, B., W.M. Richard, Statistics in Research, The Iowa State University Press, Iowa, 1975.

26. Spiegel, M.R., Statistics, Mc Graw-Hill, New York, 1961.

27. Sterman, J.D., "Modeling Managerial Behaviour: Misperceptions of Feedback in a Dynamic Decision Making Experiment," Management Science, Vol. 35, No. 3, pp. 321-339, March 1989.

28. Barlas, Y., "Model Validation in System Dynamics," Proceedings of the International System Dynamics Conference,Methodological Issues Vol.,pp.1-10, 1994.

29. Aksogan, A., M.S. Thesis, Bogazic&#141;i University, 1995.

APPENDIX