International O.R.: Customized inventory management

How a small Greek manufacturing company solved its big, complex procurement problem.

International Operations Research

By George Nenes, Sofia Panagiotidou and George Tagaras

RODA s.a. is a small company based in Thessaloniki, Greece. It was established in 1948 as a family business that has evolved into the largest distributor and sole manufacturer of castors and wheels in Greece. It currently employs 29 people in two business units: institutional castors manufacturing and commercial.

RODA’s commercial business unit procures approximately 3,000 components and intermediate and final products from 28 European and Chinese suppliers, including RODA’s own production plant. The components and intermediate products are assembled in-house, producing thousands of variations of the main product types. In total, RODA procures, stores, assembles, sells and distributes nearly 10,000 stock keeping units (SKUs), ranging in complexity from small and inexpensive bolts to large heavy-duty wheels for industrial applications.

The ordering policy of the procurement department is supplier-dependent. In early 2007, the procurement department was placing orders on a continuous basis following empirical rules, knowing that these orders would be delivered periodically, once a minimum order size was accumulated. For example, a certain German supplier would send off an order to Greece by truck on a Thursday or Friday if the total weight exceeded 300 kgs. This occurred practically every other week with a few exceptions. The truck would arrive at RODA’s warehouse after five or six days, containing only the items that were available for delivery at the time that the order was assembled at the supplier, namely one or two days before the truck was actually loaded. Thus, the effective lead time ranged from eight days for some fast-moving items to a few weeks for slow-moving items that the supplier would manufacture to order.

The ordering and receiving process was further complicated by the substantial differences among suppliers in terms of delivery frequency and transportation time. A major Chinese supplier ships an order once a month, and it takes about two months for the shipment to arrive in Greece, clear customs and become available for sale, while suppliers of low-volume make-to-order specialized items may make as few as only two shipments per year. A natural consequence of the unpredictability and large variations of the order lead times was that RODA’s customers were experiencing similar uncertainty in the fulfillment of their own demand requests.

Realizing the complexities of the procurement process and feeling the need to have a better understanding of the service provided to its customers in terms of product availability, the company asked for our collaboration. The objective was to create a computerized decision support system, which would help the company not only systematize but also improve the operation and performance of its entire inventory management system.

Cleaning the Data and Modeling Demand

The customer base of RODA includes many small customers placing small orders and expecting immediate availability, along with a few large “institutional” customers (hospitals, super markets, large manufacturers) that place much larger orders but usually allow a reasonably long delivery time (“planned” orders).

The combination of many small orders with exceptionally large sporadic demands from large customers renders demand modeling a nightmare as the usual demand distributions fail to capture such irregularities. Fortunately, the problem is greatly simplified once we observe that the large “planned” orders do not pose a problem to the inventory system as long as the time window between order placement and requested delivery time exceeds the maximum effective lead time for the specific item, as is usually the case. This type of demand is satisfied by placing special orders to the respective supplier with sufficient advance notice, thus making sure that the desired quantity will be available exactly when needed. Consequently, such “planned” demand can and must be excluded from the regular (unplanned) demand time series.

However, cleaning the demand data proved to be one of the biggest challenges of the project, as it required a lot of work on the part of the company. A team including the procurement manager, the information systems manager and even the owner and CEO of the company scrutinized the raw data set of the 2005-2006 period, examining the detailed records of every single unusually large demand entry to find out whether the demand was “planned” or simply an unexpected large order. The good news was that this exercise not only removed many extreme data points, it also led to the complete exclusion of many SKUs that were examined first as “A” items (in terms of annual value) because their entire demand was planned and consequently they could be managed without keeping any inventory at all. RODA’s warehouse simply serves as a cross-docking facility for these items. The bad news was that even after that careful filtering, the demand for the vast majority of the remaining “A” items remains highly variable and irregular, thus defying the usual textbook assumption that demand may be modeled as a normal or Poisson random variable. Furthermore, the picture was even bleaker for the “B” and “C” items.

Thus, since the goal was to develop a universal system capable of managing the total stock of the company, the second big challenge was to address the problem of modeling the irregular unplanned demand of all SKUs from all suppliers in a way that would be realistic, scientifically sound and computationally feasible. To this end, the project team, which included the co-authors, first decided to allow the time unit of analysis to depend on the suitable time scale of the respective supplier. The time unit would be a month for the Chinese suppliers using maritime transportation and a week for European suppliers using trucks every one or two weeks. A second more important distinction had to do with the demand volume. We classified the SKUs in three categories: “faster-moving,” “slower-moving” and “very-slow-moving” items.

Faster-moving items. Figure 1 shows the time series and the histogram of the weekly demand in 2005-2006 for a typical faster-moving item (W100). Note that the term “fast-moving” is very relative; in fact, its demand is intermittent as 57 of the 104 weeks exhibit zero demand, while the histogram of the 47 nonzero weekly demands is clearly asymmetric. It turns out that this type of demand pattern, which repeats itself in the vast majority of “A” items, is described quite accurately using the gamma distribution with a probability mass at zero for the weekly demand. Moreover, the gamma distribution is very convenient because of its flexibility and its reproductive property, which facilitates the determination of the total demand distribution in any time interval of interest.

International Operations Research

Figure 1: Time series and histogram of weekly demand of W100 in 2005-2006.

Slower-moving items. Many SKUs exhibit so sporadic and low demand that the gamma distribution cannot provide a good fit with any choice of parameters. An additional peculiarity of those SKUs is that since they are castors and wheels, customers usually order them in pairs. We found that the demand of such items is expressed with sufficient accuracy through the package Poisson distribution, namely a Poisson distribution for demand expressed in packages (pairs).

Very-slow-moving items. Finally, a large number of SKUs are demanded so infrequently that the available data does not suffice for any reliable characterization of their demand. The inventory policy for those SKUs can only be based on simple heuristic rules.

The Proposed Inventory Management System

After extensive consultation with the top management of the company and taking into account current practices and constraints, the project team decided to adopt the common (R,S) periodic review system for all SKUs and all suppliers, so as to standardize the procurement function keeping it simple at the same time. The ordering policy for all SKUs would be of the usual order-up-to-S type but the review period R would be supplier specific.

Although in theory the review period is a decision variable, to attain smooth transition to the new system the company decided to maintain the same order/shipment frequencies as before. For each supplier the value of R was determined by the company’s management based on practical and economic considerations such as vehicle or ship itineraries, minimum economic shipment quantities and the structure of transportation costs.

Despite the fact that the frequencies of deliveries remained unchanged, the ordering system was streamlined considerably by specifying a cut-off time point for the placement of orders at each supplier, sufficiently ahead of the scheduled order shipment, to ensure that the standard lead times will not be exceeded. Consider, for example, the German supplier that sends off a shipment every other Thursday or Friday. By placing the orders not later than a week in advance of the truck departure and taking into account the five to six days transportation time, it is practically certain that all the ordered items will be received after a lead time L = 2 weeks, except for those specialized items that are manufactured to order and arrive with the next shipment two weeks later (L = 4 weeks).

The new system imposes more discipline in the ordering process and enforces explicit negotiation and agreement with the suppliers about the availability of the various SKUs, which in turn specifies the realistic lead times that will be used in the analysis and determination of the base stock levels S. In addition, it provides a window of flexibility and a cushion against shortages at the supplier by still allowing orders to be placed before the designated order time so as to give the supplier a better chance to respond without delay.

Determination of Base Stocks. The remaining element for the full specification of the system was the determination of the base stock S for every single item, which would provide the desired level of service to the company’s customers. The service level is expressed by the fill rate ß, that is, the expected long-term fraction of demand that is satisfied immediately from available stock.

Given the characterization of the weekly or monthly demand either by means of the gamma distribution with a probability mass at zero or through the package Poisson distribution, it is possible to determine the base stock value S that provides the required fill rate using mathematical expressions that we developed in the context of this project.

When the available data is not sufficient to characterize the demand (very-slow-moving items), then simple rules were devised for the choice of S using information from SKUs with sufficient data [1].

Finally, with respect to base stock determination, there are two more special categories of items: (a) special-purpose SKUs, which RODA manages on an order-by-order basis, and (b) SKUs that have been stocked in the past but their demand has been extremely infrequent (no more than two demand instances in two years). The base stock for all those SKUs is set equal to zero.

The Decision Support System

To facilitate the implementation of the new system, the project team developed a computer program for the efficient computation of S values taking into account the required fill rates, prescribed by RODA’s top management according to the relative importance of each item, and the characteristics of the respective suppliers (order frequencies and lead times). In addition, the program makes recommendations when it detects irregularities in the demand data or excessive service requirements. The final result is a simple but flexible decision support system (DSS), which is described briefly below.

0. Data input: For every SKU, the program reads its code number, review period, lead time, target fill rate, and the historical “clean” demand string of up to 104 weeks or 24 months.

1. Check for sufficiency of demand data: For every SKU the program checks whether the available demand data is sufficient for statistical analysis. If it is not, it issues a warning and uses a simple rule of the form S=Aµ R+LB. to compute the base stock S for the given fill rate ß. If the target fill rate exceeds 0.80, the program also computes S for ß=0.80 and recommends that base stock, with the rationale that a higher service level is unnecessary. If there exist less than three nonzero demand periods, the program suggests S=0.

2. Demand analysis: A statistical test of the available data determines goodness-of-fit to the gamma and Poisson distributions. In the rare cases where the data does not fit any of these distributions, the gamma distribution is used for the items with average annual demand of at least 50 units and a Poisson distribution is used for the remaining items.

3. Search for spurious demand data: The purpose of this check is to identify any demand outliers, possibly corresponding to large planned orders, which have not been removed from the demand string. Specific conditions for characterizing a demand string as suspect have been derived empirically through extensive demand data analysis (e.g., a single weekly demand exceeds 30 percent of the total two-year demand). If at least one such condition is met, the program issues a warning and recommends a base stock that corresponds to ß=0.80.

4. Computation of base stock and other characteristics: The program computes the lowest S that achieves the target fill rate, as well as the values of the following demand and operating characteristics of interest:

  • E(D): average demand per time unit;
  • CV: coefficient of variation of demand per time unit;
  • P(D>0): proportion of time units with non-zero demand; and
  • E(OH): average stock on-hand; not computed when S is derived by the simple rules.

5. Output: A sample output is shown in Figure 2. The information printed for every SKU consists of:

  • input data: code, time unit (week or month), review period and lead time;
  • demand characteristics: the distribution that best fits the demand data, the distribution that was eventually used, E(D), CV and P(D>0); and
  • results: base stock S, average stock on hand, and actual fill rate, which may be higher than the target due to upward rounding of S.
International Operations Research

Figure 2: Sample program output; Poisson2 stands for package Poisson.

Results and Conclusions

The DSS is currently in full operation. It cooperates smoothly with the ERP system that the company installed in 2007; the ERP system feeds the DSS with demand information and the DSS returns the recommended base stock values S. These values are updated every six months, using the most current two-year demand data in a rolling-horizon fashion. At each review instance the ERP uses the S values to derive the appropriate order quantities, which may be adjusted upwards to take advantage of quantity discounts. Each order consists on average of 10 line items; 30 percent of those correspond to planned orders by RODA’s customers, which are inserted to the ERP outside and independently of the DSS, while the remaining 70 percent of the line items concerns SKUs managed to stock through the DSS.

According to Gabriel H. Saatsoglou, president and CEO of RODA, “This work has helped our commercial business unit to rationalize its procurement procedures and manage its stock in a more systematic and objective way. It has also contributed to an enhanced understanding of the distinct characteristics of the different types of SKUs, to an explicit examination of their relative importance and to the identification of many obsolete SKUs. The most concrete economic benefit of the new system is that it has resulted in substantial reduction of our inventories without compromising the provided service level to our customers, by identifying and removing excess safety stock from many SKUs.”

In addition to an inventory reduction of close to 10 percent, RODA reports a 26 percent reduction in transportation cost and a 22 percent reduction in the number of emergency orders to its suppliers. Furthermore, according to the yearly customer satisfaction surveys, the average rating of the order response speed improved significantly after the DSS implementation.

George Nenes (gnenes@uowm.gr) is a lecturer in the Department of Mechanical Engineering at the University of Western Macedonia in Greece. Sofia Panagiotidou (span@auth.gr) is a research associate in the Department of Mechanical Engineering at the Aristotle University of Thessaloniki. George Tagaras (tagaras@auth.gr) is the director of the Laboratory of Business Administration at the Department of Mechanical Engineering of the Aristotle University of Thessaloniki. Professor Tagaras has also held faculty positions at the Wharton School of Business and at INSEAD in France. He holds a Ph.D. in Industrial Engineering from Stanford University.

Reference

  1. 1. Nenes, G., Panagiotidou, S. and G. Tagaras, 2010, “Inventory management of multiple items with irregular demand: A case study,” European Journal of Operational Research, Vol. 205, No. 2, pp. 313-324.

Theory vs. Practice

Three reasons why standard inventory theory is often inadequate in practice:

  1. The standard textbook material on inventory control is based on the assumption that lead time demand follows a normal or Poisson distribution. This is often not the case in practice. Using the standard textbook models as approximations in cases where the departures from the assumed normal or Poisson distribution are serious leads to very unsatisfactory results.
  2. A usual assumption behind the mathematical formulas computing operating characteristics of inventory systems is that shortages are small, infrequent and don’t last long. However, when demand is extremely variable and intermittent, large and long shortages are inevitable unless the system holds excessive safety stock. Explicitly taking into account the high probabilities and magnitudes of stockouts is imperative in developing an accurate mathematical representation of an inventory system facing highly irregular demand.
  3. The standard textbook treatment of inventory management either completely ignores or provides very vague guidelines about the issues and complications that typically arise in practice due to the large number of suppliers and items that must be coordinated, incomplete or suspicious data, lead time variability, possibility of late order placement or emergency replenishment, etc.

Main Elements of the DSS

  • models lumpy demand both for fast and slow moving items
  • determines appropriate base stocks
  • calculates useful operating characteristics (e.g. service level, average stock on hand)
  • issues warnings and suggestions when it detects demand irregularities or excessive service level requirements

About the Project

  • The duration was five months.
  • Its cost was offset by the inventory and transportation cost savings in less than a year.
  • The president and CEO of the company attended most of the 12 common meetings of the project team (authors) with the directors of procurement and information systems.