INVENTORY MANAGEMENT OF A FLIGHT CATERER: DEVELOPING AN ACCEPTABLE RE-ORDER QUANTITY CALCULATION METHOD

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INVENTORY MANAGEMENT OF A

FLIGHT CATERER: DEVELOPING

AN ACCEPTABLE RE-ORDER

QUANTITY CALCULATION METHOD

EVA MARIA BOWE

University of Groningen

Faculty of Economics and Business

Master Thesis – Operations and Supply Chains

November 2011

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Abstract

This paper deals with the determination of the most appropriate re-order quantity calculation process for a flight caterer‟s „buy on board‟ products with the aim of keeping the inventory level and costs as low as possible. In order to obtain the most suitable approach for improving the current process causing problems of inventory imbalances at the flight caterer, first the demand is forecasted in a more precise way and then based on that value the re-order quantity is calculated incorporating additional quantity influencing factors. Before the new suggested approach is determined, the current uncontrolled re-order quantity calculation process and the factors influencing the re-order quantity are outlined. Regarding the demand forecasting, the most common traditional forecasting methods are compared and the „linear exponential smoothing methods‟, more specifically Brown‟s „One parameter exponential smoothing method‟ is found to be the most appropriate. Using the forecasted demand as a basis the different combinations of influencing parameters depending on the product are applied to step-by-step calculate the forecasted re-order quantity, the preliminary re-order quantity and the final re-order quantity. This final re-order quantity is the suggested quantity to be ordered in order to avoid inventory imbalances and reduce inventory costs.

Keywords: re-order quantity, demand forecasting, Brown‟s One parameter exponential

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1. Introduction

Cost reduction is a major issue in all areas of a company and this is also the case at the particular flight caterer dealt with in this paper. The caterer is particularly interested in reducing costs in its „buy on board‟ section since this department requires large quantities of relatively expensive products and the storage capacity is limited. When looking at the total inventory value at this particular basis, the „buy on board‟ products of only one particular low-cost airline make up about 30 percent of the total inventory value. The inventory value is money the company has tied-up in the form of goods and which is not available for operations such as investments and hence considered as a cost. This means that by reducing the total inventory value the company has more freed-up money on hand for other operations. Therefore, it is in the interest of the flight caterer to have as little money tied-up in inventory as possible. Thus, the goal of the company is to have as low inventory value as possible, while still having the minimum required amounts on stock, particularly in the „buy on board‟ section of the particular airline making up one third of total inventory.

The inventory value of this airlines „buy on board‟ products is determined by the existing inventory policy and more specifically by the demand forecasting process, because the timing and size of the orders influences the inventory level and consequently the inventory value. The main issue in the „buy on board‟ department is that the inventory of the mentioned airline has a large amount of money, 30 percent, tied up while on the other hand usually not all products are available in stock. This means that some products are not in stock while others are over-stocked. Such inventory imbalance causes problems in daily operations as well as unnecessary tied-up money for the over-stock products. Hence, a more appropriate demand forecasting process is believed to help avoid inventory imbalances and thus reducing the tied-up capital to a minimum.

According to Philips and Dawson (1962) the exactness of inventory control is necessary for reaching maximum profit. Thus, demand forecasting is a vital part in order to increase this required inventory control exactness. Demand forecasting determines which amount of products is needed at what point in time. The advantages of demand forecasting are that products are available when they are required, mistakes in planning can be countered and good customer service can be provided (www.champlainrac.com, 2011).

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5 forecasting is the driving force behind all planning activities as it enables management to approximate the future with some reasonable accuracy” (Korpcla and Tuominen, 1996, p. 2). By calculating the demand used for determining the re-order quantity more appropriately, the inventory levels are reduced to the required minimum. This in turn reduces the amount of tied-up capital in inventory value and consequently the costs of inventory, as only handling and storage costs for the minimum required demanded inventory levels occurs. Therefore, this paper has the goal of determining the most appropriate forecasting method in order to provide re-order quantities for the various products at the flight caterer‟s „buy on board‟ department that avoid inventory imbalances and keep tied-up money in inventory as low as possible.

2. The company

The company dealt with is a caterer which provides services in the air, sea and rail segment. It has operations in 44 countries worldwide with more than 14000 employees. In the different companies the company has various bases which operate in all or less of the three catering segments. The bases dealt with in this paper, provides only services in the in-flight segment. At this basis the operations are divided into the three departments „duty free‟, „buy on board‟ and „steward‟. In this work, the „buy on board‟ department is looked at, because the company wants to reduce the inventory imbalances and the resulting inventory costs. The „buy on board‟ department is made up of the services for three low cost airlines. One of these airlines requires the flight caterer not only to assemble the trolley but also to order and manage the

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3. The research approach

In order to get a good understanding of the inventory management of this flight caterer and more specifically of the „buy on board‟ products, the current practices were observed. This observation was conducted partly by means of asking superiors and peers what they are doing with the products and why they are doing it in this certain way, like for instance during storage, counting and assembly.

Next, to the interviewing personal involvement allowed to get a better feeling and understanding of the product handling. During this course the following tasks were carried out: count and record the weekly inventory, receive and allocate products in the warehouse as well as in the assembly area, assemble and revise trolleys with „buy on board‟ products, make a weekly consumption forecast and place orders with suppliers, estimate the consumption of new products and place orders in advance, prepare the return shipment of de-listed products. These various tasks lead to insights into what the flight caterer‟s part of the supply chain entails and how the inventory is managed. Hence, it could be experience firsthand which factors have an impact on the „buy on board‟ inventory at the flight caterer and the way it is managed and controlled. These factors and stakeholders, which are listed in section 5, are highly interrelated, for instance through suppliers requiring orders placed per case therefore many times the company either needs to order more or less units then actually needed. Thus, these interrelations cause a great complexity for inventory management at flight caterers, because when determining the amount to be ordered, not only the mere consumption amounts need to calculated, but also the effects of the interrelations on the order quantity need to be considered.

As the aim of this thesis is to determine an approach for reducing the inventory value of the „buy on board‟ products of the company, it will be elaborated on these influencing factors and their interrelation and based on these findings determine an approach to reduce inventory to the minimum required amount and therewith the tied-up money in inventory. Consequently, determining the appropriate forecasting method of demand is essential in order to determine a satisfying (Simon, 1962) re-order quantity, reducing as much unnecessary inventory as possible.

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7 determined which traditional forecasting methods are most appropriate either in their completeness or partially in the case of the flight caterer and then a method of forecasting is developed which combines the former methods with variables representing the specific needs of „buy on board‟ products at the company. The resulting forecasting method will thus be a combination of traditional methods adapted and modified for the influencing factors on hand at the flight caterer‟s „buy on board‟.

4. Stakeholders in the flight catering business

Before going into detail about the inventory management of the particular flight caterer, a brief overview about the air flight catering supply chain is given in order to illustrate the tasks and responsibilities of each major stakeholder as they all interact and thus influence the inventory management of the caterer.

Even though the air flight catering business is about supplying the airlines with food for their passengers, the business itself is not structured as a typical catering service mainly employing chefs. Rather, in the flight catering business logistics makes up a greater part than the actual cooking. Logistics is vital because delivering the right amount of trolleys containing the correct amount of products at the exact time and location is a typical complexity characteristic of the air flight catering industry (Jones, 2007). Therefore, the coordination and transport of the products and trolleys is of great importance. However, in order to ensure the accurate and timely delivery of the finished products, in this case the trolley, the flow of information, goods and money within the entire supply chain needs to flow smoothly. In terms of information flow, the stakeholders need to communicate the amount of trolleys or respectively products required, as well as when and where they are needed.

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8 and finally to the passenger while the flow of information for purchasing/ordering between the stakeholders goes reverse. The quality and availability of „buy on board‟ products adds to the travel experience of the passengers, which in turn affects their future purchase decisions. Only if suppliers, caterers and airlines communicate and interact well, the passengers have the desired products available.

5. Different product categories at the flight caterer

The logistics center of the flight caterer is currently assembling and supplying several types of products for the various airlines. These products are assembled in three different departments: „duty-free‟, „buy on board‟ and „stewards‟. The focus of this paper is on the „buy on board‟ department where trolleys are assembled for three airlines using this type of service. The concept of „buy on board‟ is offered by the low-cost airlines, which instead of providing free food and drinks offer their passengers an assortment of purchasable products. According to Jones (2007) these „buy on board‟ products are considered and treated as retail products. In the case of this flight caterer, the products for two airlines are all being purchased by the companies themselves. The flight caterer merely receives stores and assembles the products according to the order of the airline and thus charges handling. While for the remaining airline, which exclusively offers „buy on board‟ service, the flight caterer also has to order the products from the pre-determined suppliers as explained before in section 4 and is obliged to have sufficient inventory in stock for the total of ten days, including the products in circulation in the trolleys. Since the decisions about levels of inventory at the former two airlines are not at the liberty of the flight caterer, this paper will focus on the inventory management for the later airline as described in section 4.

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9 in mid-October and second of all as to determine forecasting methods for the products which necessitate more exact forecasting due to specific requirements for purchase. The main requirements are a minimum value or volume which has to be ordered from one supplier or the short expiration span. Thus, the products dealt with in this paper amount to 133 types of products from five different suppliers (see Appendix tables 1 through 5: Products to be analyzed).

Out of the five suppliers for the selected 133 products, three require a total minimum value amount to be purchased for each order, thus in this case the sum of the value of products for this supplier needs to be at least as high as this minimum value in order to be able to place an order. In case of suppliers A and B the minimum total values is € 2000 and € 1500 for supplier E. Also, for supplier C, which requires a total minimum volume, the sum of the products needs to amount to at least the minimum pallet volume if wanting to order from this supplier. The products to be ordered from the remaining supplier D do not need to fulfill a minimum criterion but because of the nature of the products their expiration span dictates a maximum amount of time the products can be ordered before being sold to the passengers.

Of the 133 different types of products to be analyzed, there is at least one of each product category, while the distribution is different for each supplier (table 1). Most of the 133 different products are of the categories perfumes and cosmetics with 32 percent and 20 percent respectively. Also ten percent of the products make up fresh foods. Since these products are either very expensive or have a short expiration span, having more accurate forecasts especially for these products can reduce inventory value to a good extent.

Table 1:Amount of products per product category per supplier

Product category Supplier A Supplier B Supplier C Supplier D Supplier E Percentage

Beverages and hot food 2 5 1 6%

Snacks and Sweets 11 16 19%

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10 In addition to using these minimum and maximum limiting requirements as criteria for selecting the most relevant products to be analyzed, these criteria also need to be included in the calculation of the re-order quantity as changes to the initially forecasted amount need to be made in order to meet these limiting requirements. Thus, section 12 deals with these specific requirements in more detail.

6. Current forecasting process

At this flight caterer the demand of „buy on board‟ products is based on historical data and subjective assumptions made by the person in charge of doing the forecast. However, since the demand is forecasted on a two week basis, this time horizon is rather short and demand can fluctuate highly. Therefore, the flight caterer in question takes the following steps for determining the re-order quantity of the „buy on board‟ products.

First, the current stock is counted. This has to be done because due to spoilage, damages, theft and losses, current inventory (Ik) is not simply the outcome of previous inventory (Ik-1) plus products received minus sales. Then the theoretical past consumption is determined, which is defined as the sum of products received (between Ik-1 and Ik) and the difference between previous inventory (Ik-1) and current inventory (Ik). However, as mentioned before since spoilage, damages and theft can occur on the plane these factors need to be considered as well because they increase the past consumption. Therefore, the real past consumption (RC) is calculated, which is defined as the sum of theoretical past consumption and products returned damaged or spoiled and products stolen. At the company the real past consumption is recorded for each flight each day in a Microsoft Excel sheet.

real past consumption (RC) = theoretical past consumption + products returned + products damaged + products spoiled

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11 incorrectly or the spoilage, damage and theft data was recorded falsely. The mistake needs to be corrected before the forecasting process can be continued. Once it is assured that the real past consumption data is correct, the theoretical re-order quantity is determined. The theoretical future re-order quantity is defined as the difference between current inventory (Ik) and the real past consumption. In case the current inventory (Ik) is zero the amount of real past consumption is the future re-order quantity.

While the previous steps have been purely mathematical, the final forecasting step involves subjective judgment. In this step, the person in charge considers the following factors and makes an estimated guess on which quantity to order in the end:

 products still due to arrive which were supposed to arrive in the period between Ik-1 and Ik (the amount of products still left to arrive is subtracted from the future re-order quantity)

 minimum amounts to order per product/supplier (in case the re-order quantity is below the minimum order quantity, depending on the expected consumption in the period between Ik and Ik+1 the flight caterer either places an order or postpones it for a future order)

 amount per case (if the re-order quantity does not equal the case size, the company either rounds up or down the amount of cases depending on what the person in charge expects for future demand)

 expiration date (perishable products or products with expirations spans of less than 6 weeks are order a little less at the current re-order point (Ok) and adjust more closely at the next re-order point (Ok+1) )

 special sales offers of the airline (as more sales are anticipated more products are ordered depending on what sales increase the person in charge expects)

 expected increase/decrease in demand due to current commercials, trend of sales and availability and completeness of the product in all trolleys (in case not all trolleys contain the required stock, the amount missing to stock all trolleys plus the amount expected to be consumed must be ordered additionally)

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12 amount used for assembly some products are over-stocked while others where under-stocked or even not available at all. Therefore, the main goal of this paper is to not only determine the most appropriate traditional forecasting method for the „buy on board‟ department at the flight caterer, but also to incorporate the factors dealt with in the final judgmental adjusting step in a more uniquely defined way as to avoid inventory imbalances and the otherwise resulting high inventory costs.

7. Data collection

The consumption data used in this paper is taken from the Microsoft Excel files, which for each flight per day of the month state the amount loaded, the amount returned (only those products which can be loaded again) and the difference is the real past consumption. This consumption data is then added first daily and then further summed into two periods of 1st till 15th of the month and 16th till last day of the month respectively. This 15 day period was chosen because it is equal to the average assumed lead time and also the orders are placed based on the data from the last day of the month and the 15th day of the month. Since only the consumption of a 15 day period is considered when placing orders, having vast amount of data per day or even individual flights is not necessary and therefore the data has been modified by means of summation so that the amount of data points is reduced to the required minimum. Hence, the amounts of the respective periods can be used for making forecasts twice a month.

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8. Factors influencing the re-order quantity at the flight caterer

The following is a list of the potential factors having an impact on the re-order quantity decisions to be made at the flight caterer regarding the „buy on board‟ products for supplying a customer who only offers „buy on board‟ products to its passengers. As mentioned in section 6, a mere calculation of future demand based on past consumption data is not sufficient as additional factors affect the amount of products to be ordered. Such an influencing factor is for instance the fixed units per case size. Since the company can usually only order entire cases, the originally calculated re-order quantity must be altered so that only entire cases are ordered. However, not all factors are valid for all product categories mentioned above, for instance some fresh food products do not need to be ordered per fixed quantities per case. Therefore, when specifying and defining these factors per activity/stakeholder below, it is also determined whether or not these factors in deed need to be incorporated in the re-order quantity calculation or not. The applicability of each factor is based on the criteria of necessity of re-order quantity altering measures. After dealing with each factor, in section 8.1 the applicable factors are matched to each of the six product categories. The combination of the most important factors impacting the re-order quantity of the individual product will result in a unique combination of interaction variables, which will be applied in section 12 by means of adjusting the suggested re-order quantity of the forecasting method.

1. Supplier

a) Lead times: The average lead time of all suppliers is 15 days and since determining the re-order point exceeds the scope of this paper, the lead time will be assumed with 15 days and this will also be the order interval. Usually, if lead time varies, the re-order quantities need to be adjusted for instance to make sure that enough products are in stock to cover for a longer lead time of the next expected delivery. Since, in this case lead time is assumed to be fixed, no such quantity altering measures are required and therefore this factor will not be included as interaction variables in the final re-order calculations.

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14 quantity of units of products might be, only entire cases can be ordered and thus the quantity usually needs to be changed to meet this requirement. This can either be done through determining a set rounding decision point or always rounding up or down. Since this factor clearly makes alterations in the re-order quantity necessary, it is included in the final re-order quantity calculations.

2. Customer (airline)

a) Minimum amount of inventory needed to satisfy working period: the airline requires the flight caterer to always have at least stock for eight days plus two days loaded in the trolleys. Currently the airline operates 14 daily flights. The units per case quantities are given in the Appendix tables 1 through 5 of products to be analyzed. In case the current inventory (Ik) plus the re-order quantity is below the minimum required inventory, the re-order quantity needs to be increased in order to satisfy this requirement. Since re-order quantity altering measures might be necessary, this factor is also applied in the final re-order quantity calculations.

b) Variation in consumption due to promotions: sometimes the airline tends to announce special offers and promotions due to unforeseen reasons with only a few days of anticipation. In these cases it is impossible to include this in the forecast for the period when the promotions start. However, if the airline informs the flight caterer at least 15 days (the assumed lead time) in advance, the forecasted re-order quantity needs to be increased by the expected sales increase, since the consumption of the period with the promotion will be higher. This factor only needs to be considered in the final re-order calculations if the start and duration of the promotion is known at least 15 days in advance to enable re-order quantity changes.

3. Storage

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15 changes in demand can be dealt with better, as no re-usage of products is allowed. Due to this re-order quantity modification nature, this factor is included in the final re-order calculations.

4. Control

a) Theft and loss: unfortunately the air catering business is not spared from theft of products either from its own or the airlines personnel. Especially the high value cosmetics and perfume products tend to be stolen. As the stolen or missing products need to be replaced, the re-order quantity has to be changed by this factor. However, theft and loss of products are already included in, respectively subtracted from, the actual stock count value and real past consumption. Thus, this factor does need not to be incorporated separately in the re-order quantity calculations as an additional factor.

5. Forecast and purchase

a) Minimum order quantities (pallets/value): as has been explained in section 5, there are limiting total minimum order requirements for the majority of the products to be analyzed. In case this requirement is not satisfied, the quantities of one or more products need to be increased as to reach the minimum amount. Therefore, this factor has to be included in the final re-order quantity calculations in case the total order amount for a supplier requires changes.

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16 c) New products: this factor is relevant for the re-order quantity because no historical data is available for new products and the forecast will have to be based on estimated demand data. These additions of products are due to changes in the catalogue and occur twice a year in mid-April and mid-October for this particular airline. Most of the product changes consist of newer or similar cosmetics and perfume products. It can be assumed that the demand for the new products is akin to the one of older or similar products. Therefore, the demand of the later products can be used as an estimated demand for the new products in the forecasting method. However, since this approach requires the subjective judgment of which other products demand to use and change, this influencing factor will not be included in the re-order quantity calculations as a separate variable.

d) Products to be discontinued: certain products are discontinued due to changes in the catalogue. In this case the company needs to coordinate the purchase of these products with the anticipation that total stock needs to run out up to a certain date. When the last sales day of the product is known, the amounts to be re-order need to be calculated backwards; meaning that current stock plus forecasted demand up until the cut-off date plus re-order quantity equals zero. Thus, due to its quantity decreasing effect this factor has to be applied in the final re-order quantity calculations only for a few products and not repeatedly.

6. Product

a) Spoilage and damages: the products which have been damaged or passed the expiration date in the trolleys are already included in the real past consumption data because they are set to be consumed on board. However, if the products are damaged or spoiled while in storage in the „buy on board‟ department, they are included in the stock count in the way that they are not available and thus cannot be counted. Therefore, even though spoilage and damages influence the re-order quantity, this factor is already included in the forecasting method and does not need to be applied as a separate factor in the final re-order calculations.

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17 bases daily. Since these false or expired products are considered as consumed products, this factor is already included in the real past consumption data value in the forecasting method and does not require separate incorporation in the final re-order calculations.

From the influencing factors listed above, based on the criteria of necessity of re-order quantity altering measures, the following factors have been determined as applicable interaction variables in the final re-order quantity calculations:

 Fixed amount of units of products per case

 Minimum amount of inventory needed to satisfy working period

 Variation in consumption due to promotions (with 15 day anticipation)

 Limited freezer storage capacity

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Minimum order quantities (pallets/value)

 Different order pattern in case of vacations

 Products to be discontinued

8.1 Applicable re-order quantity influencing factors per product category

In this paragraph the application of the seven influencing factors is presented for each of the six product categories: Beverages and hot food, Snacks and Sweets, Perfumes, Cosmetics, Miscellaneous and Fresh food.

With the exception of three products within the fresh food category (which are ordered in individual units), the first factor of „Fixed amount of units of products per case‟ is relevant to all six product categories as orders can only be placed as multiples of the quantity per case and hence the forecasted re-order quantities need to be adjusted for this factor. Therefore this factor needs to be included with a specific parameter in the final calculations (section 12) for all products, excluding the former mentioned three exceptions.

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18 hand of all of the products. Each product has to be put into the trolleys with a fixed amount, mandated by the airline. The company is obliged to have at least sufficient units on stock as inventory (on stock + in the trolleys) for ten days. However, the airline varies the amounts of the fresh products per day and trolley, so that this factor is not applicable for this product category. Thus, this factor needs to be included as a parameter in section 12 for the remaining five categories.

As promotions and special offers can take place for any of the 133 products and consequently the factor „Variation in consumption due to promotions‟ has to be applied in the final calculations to all product categories in case the flight caterer is informed about the promotion at least 15 days in advance.

„Limited freezer storage capacity‟ only affects the category of fresh products in the „buy on board‟ department, as these perishable goods need to be stored in a freezer before they enter the defrosting process one day prior to assembly. For this reason, this particular influencing factor needs to be applied merely for the fresh foods and not all products to calculate the final re-order quantity.

In section 5 the influencing factor „Minimum order quantities (pallets/value)‟ has been dealt with in form of the limiting requirements. As mentioned four of the five suppliers demand such minimum quantities per order and therefore, this factor has to be used in the end termination for all product categories except fresh food.

The factor „Different order pattern in case of vacations‟ is also applicable to all products of all product categories because the five suppliers all require the orders to be made prior to the start of their vacation period, if the flight caterer wishes to receive the order on time. Hence, this influencing factor is represented as a parameter for all products in the re-order quantity formula in section eleven.

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9. Overview of traditional inventory control methods

According to Ferbar (2010), in order to minimize total costs companies should consider the optimization of forecasting methods in light of the inventory control policy used by the company. Such cost minimization can be achieved through determination of initial and smoothing factors in the forecasting method. However, since the field of traditional forecasting methods covers a wide range of possible methods, the most appropriate forecasting method for the flight caterer needs to be determined first. This is done by evaluating the various methods and then determine which traditional forecasting method fits the situation of this flight caterer best and then in section 12 adjust this method by the previously selected influencing factors (see section 8).

Since there are so many factors which need to be considered, it is believed that incorporating subjective „personal probabilities‟ as done in the Bayesian approach described by Philips and Dawson (1968) for each factor in the forecasting calculation and then smoothing them as done with the safety factor by Howe (1974) might be a possible solution. However, this step will be taken after the appropriate traditional method has been determined by means of including the limiting requirements of section 5 and the influencing factors mentioned in section 8.

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9.1 Qualitative forecasting methods

In addition to historical data these methods also use judgmental processes and managerial experience to obtain forecasts. Demand forecasting with these methods involves predictions of the continuity of existing conditions and also determining turning points in the business cycle. These methods are used for situations with no historical data available and making long-term forecasts. However, for the „buy on board‟ products of the company, sufficient historical data is on hand and the forecasts are needed for a short period of two weeks or one month. Furthermore, qualitative forecasting methods require insights of experts in the field of forecasting and that these experts have sufficient time on hand for making decisions on a two week basis. The decision making process of judgmental processes is rather long due to for instance the usage of group decision making. Therefore, the time effort needed for this method would not pay off for making decisions every two weeks for 133 individual products. Hence, the appropriate conditions of ease of use and forecast horizon are not met and therefore the application of qualitative forecasting methods in this case is not appropriate.

9.2 Quantitative forecasting methods

The most common quantitative methods are time series and causal methods (Makridakis and Wheelwright, 1978). In time series methods forecasts are based on the past values and errors of a variable, because it is assumed that the past pattern will continue in the future (Armstrong and Green, 2006). Therefore, the underlying demand pattern needs to be identified and transferred into the future. Causal methods on the other hand try to determine the causal relationships of the forecasting variable with various independent variables and based on this make forecasts for the dependent variable (Korpcla and Tuominen, 1996).

9.2.1 Causal (explanatory) methods

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21 today‟s decision) needs some time to occur. Therefore these methods are more appropriate for forecasts of at least three months to two years (Mentzer and Cox, 1984). This makes these methods more appropriate for medium- to long-term forecasting, whereas at the flight caterer the forecast horizon with two weeks or one month is rather short-term. Furthermore, in case of using multiple independent variables a multiple regression program is required (Makridakis and Wheelwright, 1978). Since the flight caterer does not possess a sophisticated program for doing these complex calculations and management is not willing to buy such, the cost and non-conformity of the forecast horizon cause the causal methods not to be the most appropriate for the „buy on board‟ products at the company . Additionally, the method is only accurate if the relationship between independent variable(s) and dependent variable is consistent (Chase, 1997). However, as at the flight caterer‟s „buy on board‟ department no precise knowledge and estimate of the independent variable(s) exists, accuracy of the method cannot be guaranteed. Hence, regarding the appropriateness conditions listed in section 7, causal forecasting methods do not appear to be appropriate for the company‟s „buy on board‟ situation.

9.2.2 Time series methods

Before dealing with the various types of time series methods, the demand pattern of the „buy on board‟ products at the flight caterer will be analyzed. This is necessary, because the nature of the pattern is important for making a decision for the most appropriate time series forecasting method, which can either be smoothing, decomposition or autoregressive methods (Makridakis and Wheelwright, 1978).

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22 autocorrelations for a time lag variable and based on this randomness, stationary and seasonality can be determined (Makridakis and Wheelwright, 1978). From the autocorrelation for each product (see Appendix graphs 1 through 6), no seasonal pattern is apparent; therefore, ARMA will be applied as to confirm or disconfirm this finding. This is done by computing the autocorrelations of 24 time lags because the data is taken in half month steps, and 24 time lags correspond to the step of the same period one year later. Graph 7 shows that none of the autocorrelations with 24 time lags are significantly different from zero (the highest amount is only 0.36) and according to Makridakis and Wheelwright (1978) this means that no seasonality is present and the finding of the individual graphs is confirmed. Thus, these findings show that the demand pattern of the „buy on board‟ products at the flight caterer is non-stationary and not seasonal.

In comparison with causal methods, time series forecasting methods are easy to understand and use, especially for many products with a short-term forecast horizon (Chase, 1997).

9.2.2.1 Decomposition

Decomposition methods attempt to break down the demand pattern into three components (seasonal factors, cycle and trend) and after eliminating one after the other of these components step-by-step, the resulting new data pattern can be used for future forecasts. Decomposition methods require complex and time-consuming calculations. Furthermore, the flight caterer‟s „buy on board‟ department does not have appropriate software, which might aid making the calculations for many products faster. As a consequence, due to the extensive amount of time required for the calculations, the decomposition methods are appropriate for forecasting few items, unlike smoothing. Also, these methods are not so relevant for the data of the flight caterer, because no seasonality pattern is evident, as explained in the previous paragraph. Thus, in addition to the difficult usage of the method there is no need to determine and separate seasonality from other components, which makes the decomposition methods inappropriate for this case.

9.2.2.2 Autoregressive methods

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23 have any database for storing data but rather has to use Microsoft Excel sheets. Also the complexity of the method will make it difficult if not even impossible to make adjustments to the method in form of the influencing factors on re-order quantity (see section 8). Thus, the autoregressive methods are not methods to use in this case.

9.2.2.3 Exponential smoothing

In exponential smoothing methods the past values are smoothed as to eliminate randomness and this pattern is then transferred into the future (Makridakis and Wheelwright, 1978). Due to its simplicity in calculation and low cost in application but yet the fit of forecast horizon, smoothing methods are the most appropriate forecasting methods for the „buy on board‟ demand forecast of the flight caterer.

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10. Linear exponential smoothing methods in depth

Several different methods belong to this forecasting methods category. In exponential smoothing methods, one or more parameters are set to smooth out the differences between predicted and actual demand. The parameter has the function of damping abnormal fluctuations of actual demand (Ferbar et al., 2009). In this way the data pattern is corrected for the trend and can be used as a relatively accurate future forecast (Billah et al., 2006). The simple exponential smoothing model uses one parameter and gives more weight to recent observations then older ones causing the later to decrease exponentially (Makridakis and Wheelright, 1978). However, the more complex linear exponential smoothing methods are better at smoothing out randomness, because in contrast to the simple method they can correct for trends and hence are more appropriate for this case (Billah et al., 2006).

For purpose of flexibility in usage and improved decisions based on forecasts, more than one method should be used (Makridakis and Winkler, 1983). Therefore two methods will be used for forecasting in this paper. Among the linear exponential smoothing methods Brown‟s one parameter Linear Exponential smoothing and Holt‟s two parameter linear exponential smoothing are the most appropriate considering the situation of this flight caterer, because no quadratic pattern (Brown‟s Quadratic exponential smoothing) or seasonality (Winter‟s Linear and Seasonal exponential smoothing) is evident. The chosen forecasting methods will be applied separately for forecasting the future demand of the 133 selected „buy on board‟ products, and then the most appropriate one is chosen in section 10.3.

10.1 Brown’s ‘One parameter linear exponential smoothing’

The basis of this method is that a single and a double smoothed value are determined and adjusted for the trend. This is done by adding the difference between the single and double smoothed values to the single smoothed value and this sum is then adjusted for the trend. This summation is based on the rational that the single and the double smoothed values both lag the actual data when a trend exists (Makridakis and Wheelright, 1978).

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25 suggest to set the parameter to 0.2 because, the smaller the value for α, the larger the smoothing effect is. For this reason α is also set to 0.2 in order to make sure that the fluctuations in the data of „buy on board‟ products are smoothed out pretty well.

In this section the detailed calculations of the traditional demand forecast method are shown for only one product, namely product 1 of supplier A (see Appendix table 6). The equations for the different parts of the method, shown as columns in table 2, are as follows:

 Column A: Inventory demand for product

X = the actual historical demand data, in this case the real past consumption data

 Column B: Single exponential smoothing value S‟t = αXt + (1 – α) S‟t-1

 Column C: Double exponential smoothing value S‟‟t = αS‟t + (1 – α) S‟‟t-1

 Column D: Error difference of first smoothed value

= Inventory demand for product - Single exponential smoothing value

 Column E: Error difference of second smoothed value

= Single exponential smoothing value - Double exponential smoothing value

 Column F: Value of a

at = S‟t + (S‟t - S‟‟t) = 2 S‟t - S‟‟t

 Column G: Value of b bt = (S‟t - S‟‟t)

 Column H: Value of a +b (lagged one month)

Ft + m = at + btm where m is the number of periods ahead to be forecasted

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Table 2: Forecast with Brown‟s One parameter Linear Exponential smoothing

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The inventory demand (real past consumption) and the forecast demand value (F) are expressed as full (rounded) numbers, because the unit of a product cannot be split and therefore must be given in its entirety. From these forecasted demand values (F), it can be seen that for period 33 the demand is forecasted with 35 units. The flight caterer can continue these forecasting calculating by simply creating an Microsoft Excel spreadsheet with the corresponding formulas per column and then adding the actual inventory demand data for the next period in order to receive the forecasted demand for the period ahead.

However, since lead time is 15 days, it is necessary to order the required amounts one period in advance. In this case on 1st June, which is the beginning of period 33, the units forecasted to be consumed in the period 34, 16th till 30th June, have to be ordered. Therefore, it is necessary to know the demand of one period ahead, in this case of period 34, so that the corresponding orders can be placed on time. However, since no actual inventory demand data is known for period 33, the forecasted value for period 33 (F33), 1st till 15th June 2011, is used as the inventory demand data in period 33 to calculate the forecasted demand for period 34 (F34), 16th till 31st May, (see table 3). Thus, for the final re-order calculations, the value of 35 units for F34 has to be used.

Table 3: Addition of Brown‟s forecast to a second next period Period (t) Inventory demand Single exp. smoothed Double exp. smoothed Error dif. 1st smoothed Error dif. 2nd smoothed a b Forecast (t+1) 32 37 39,4 43,3 -2,4 -3,9 35,5 -1,0 35 33 35 38,5 42,4 -3,7 -3,8 34,7 -1,0 35

10.2 Holt’s two parameter linear exponential smoothing

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28 Again, the determination of the parameter values poses a difficulty, because one needs to assume the correct values for the given data. As has been explained for Brown‟s method, the larger the values for the parameters, the lower the smoothing effect. Therefore, for the case of this flight caterer it is assumed that the data should be smoothed slightly more than the trend. The corresponding parameter values used are α =0 .2 and γ = 0.3.

Another problem faced by this forecasting method is that for the first period not all required data is known, and hence, they are assumed to be zero, but will be equaled out throughout the process after around four periods (Makridakis and Wheelright, 1978).

In order to be able to better compare the results of Brown‟s and Holt‟s forecasting methods the data for the same product, namely product 1 of supplier A (see Appendix table 6), will be used in the forecasting calculations. Whereas Brown‟s method uses seven equations, Holt‟s method only requires three equations but one additional input variable (the γ). The equations in Holt‟s method of table 4 are as follows per column:

 Column A: inventory demand

X = the actual historical demand data, in this case the real past consumption data

 Column B: the smoothed data value St = α Xt + (1-α) (St-1 + bt-1)

 Column C: the smoothed trend value bt = γ (St – St-1) + (1 – γ) bt-1

 Column D: the forecast value

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Table 4: Forecast with Holt‟s two parameter linear exponential smoothing

Column A Column B Column C Column D

Period (t) Inventory demand Smoothed data Smoothed trend Forecast (t+1)

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30 According to table 4, the forecasted demand for period 33 (F33) is 34 units of the product. The full unit numbers are given for the same reason explained in the previous section.

For Holt‟s forecasting method it is also necessary to place orders in advance for period 34 at the beginning of period 33. The forecasted demand of period 34 (F34), is determined by using the forecasted demand for period 33 (F33) as the input inventory demand data in period 33, (see table 5). For Holt‟s method, the amount of 32 units as F34 would be used for further calculations.

Table 5: Addition to Holt‟s forecast for a second next period

Period (t) Inventory demand Smoothed data Smoothed trend Forecast (t+1)

32 37 36,1 -2,0 34

33 34 34,1 -2,0 32

10.3 The most appropriate forecasting method and forecasted re-order

quantity calculation

The difference in the forecast demand value for the period 33 (F33), between Brown‟s one parameter linear exponential smoothing method and Holt‟s two parameter linear exponential smoothing method, is only one unit and three units for F34. Brown‟s method forecasts one and three units respectively more than Holt‟s method. Thus, even though these differences might be small, they can influence the final re-order quantity (RQ) especially regarding the case size. In order to determine which of the two methods is more appropriate for the final re-order calculations, the shortcomings of both methods are compared. Brown‟s method requires more computation steps. However, in Holt‟s method difficult determinations of smoothing parameters, which increase vagueness, have to be done twice in contrast to only once in Brown‟s method. Furthermore, due to the lack of data for the two smoothing parameters in period one for Holt‟s method it is believed that Brown‟s method is more complete and exact and consequently, it is the most appropriate demand forecasting method for the flight caterer‟s „buy on board‟ department.

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31 the current inventory (Ik) is taken into consideration as well. Using the forecasted demand (F) and the current inventory (Ik) the company can determine which quantity actually needs to be ordered. The definition and calculation of the forecasted re-order quantity (FQ) is the difference between forecasted demand (F) and the current inventory (Ik). Since we have the situation that on 1st June the quantities for period 34, 16th till 30th June, need to be ordered, the forecasted demand for period 34 (F34) with 35 units and the current inventory stock of 194 units on 31st May (I33) are used to calculate the forecasted re-order quantity for period 34 (FQ34). In case the difference is zero or negative this means that it is not necessary to order any amounts of this product at the order point on 1st June (O33). When using the forecasted demand value (F34) of Brown‟s method for period 34, the forecasted re-order quantity (FQ34) is calculated as follows:

FQ = forecasted demand (F) – current inventory (Ik) FQ34 = F34 – I33

FQ34 = 35 – 194 = - 159

This result of the forecasted re-order quantity (FQ34) shows that without any adjustments of influencing factors, no units of this product should be ordered. The actual re-order quantity adjusted for these influencing factors is calculated in section 12.

11. Conversion of influencing factors into parameters for the final re-order

quantity calculation

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Parameter 1: ‘Promotions’

If a promotion is known with at least 15 days anticipation, the factor “Variation in consumption due to promotions” applies for the product concerned. It is assumed that the sales of the product will increase with 20 percent for one period. Therefore, the forecasted re-order quantity (FQ) has to be increased by this amount. In case there is no promotion, the multiplication factor is set to zero, so that forecasted re-order quantity (FQ) is not increased. The parameter „Promotions‟ (P) is defined as the amount by which the re-order quantity needs to be adjusted if a 20 percent increase in sales due to promotions is assumed and the formula is as follows:

P = [Forecasted re-order quantity (FQ) * 1.2] - Forecasted re-order quantity (FQ)

Parameter 2: ‘Storage capacity’

For fresh frozen food the deep freezer storage room is limited to the demand of one month. Therefore, the factor “Limited freezer storage capacity” applies only to these products. Thus, by ordering the fresh products, the amount should be as close to the forecasted re-order quantity (FQ) as possible. However, due to the issue of spoilage, a few extra fresh products should be available. In order to make sure that the storage limits are not exceeded, it is assumed if an additional 10 percent is ordered, in the uneven periods (1st, 3rd, 5th etc.) but not in the even periods (2nd, 4th, 6th etc.), that these few spare fresh products are available. Therefore, in the even periods more precise adjustments are made. This parameter (S) „storage capacity‟ is defined as the quantity by which the forecasted re-order quantity is altered and is determined mathematically as follows:

S = [Forecasted re-order quantity (FQ) * 1.1 (uneven)] - Forecasted re-order quantity (FQ)

Parameter 3: ‘Discontinued’

Mainly due to changes in the product catalogue, certain products are not sold after a certain period and it is hence desirable that stock is only available up until the last sales date. In order to calculate the amount which is actually needed, the current inventory (Ik), which is the amount of units in the trolleys and on stock, is subtracted from the forecasted re-order quantity (FQ). Naturally, if the outcome is zero or negative, no order is placed. Therefore, parameter „Discontinued‟ (D) is defined as the amount by which the Forecasted re-order quantity (FQ) is changed due to the decreasing influence of discontinued products. It is expressed as the following formula:

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Parameter 4: ‘Vacations’

As has been stated before, vacations necessitate a change in the order points by usually leaving one order point out. This in turn requires the flight caterer to order the demand for one month and not only for one period at once at the order point (Ok). Hence, if such a change in the order pattern occurs, the factor needs to be applied for determining the re-order quantity. The parameter (V) „Vacations‟ is defined as the amount that alters the forecasted re-order quantity (FQ) due to omitting one order point and the corresponding formula is as follows:

V = [Forecasted re-order quantity (FQ) + Forecasted re-order quantity next period (FQt+1)] - Forecasted re-order quantity (FQ)

At this point, the preliminary re-order quantity (PQ) needs to be calculated because the last three parameters 5 through 7 are based on an already altered re-order quantity value. The preliminary re-order quantity is defined as the forecasted re-order quantity (FQ) adjusted for the increasing or decreasing amounts of the parameters 1 through 4. In mathematical terms it is calculated as follows:

PQ = FQ + P + S + D + V

Parameter 5: ‘Case size’

The influencing factor of “Fixed amount of units of products per case” is different for each product because the units per case differ. In mathematical terms the re-order quantity thus needs to be a multiple of the units per case. However, since the first four factors will influence, usually through an increase in units, the forecasted re-order quantity (FQ), this factor will be considered after factors 1 through 4 have been dealt with, as mentioned above. In order to make sure that not too many but also not too little amounts are ordered, this factor will be implemented as a rounding parameter. In case the amount of units is less than a multiple of 50 percent of the units per case, no additional case is ordered and vice versa. This factor applies to all products except the three fresh sandwich products because these three products do not need to be ordered in fixed case sizes. The parameter (C) „Case size‟ is defined as the rounding decision for ordering only entire cases of the product. This is expressed by the following mathematical term:

C = preliminary re-order quantity (PQ) / units per case

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Parameter 6: ‘Minimum quantity’

Section 5 describes the minimum requirements for certain suppliers. Since the factor “Minimum order quantities (pallets/value)” can influence up to 58 products at once (see Appendix table 1), this complexity can best be managed in form of a matrix. In this matrix the value sum or pallet sum of all products of the particular supplier need to equal at least the minimum requirement. It is suggested to create these matrices in Microsoft Excel spread sheets so that only the final case amounts need to be included and the total sum is calculated automatically. In case, the minimum requirement sum is not met, it should be checked if more cases can be added by omitting parameter 5 for particular products. Thus, in this case subjective judgment has to be applied. The parameter (M) „Minimum quantity‟ is defined as the decision amount at which, based on the sum of re-order quantities all products of a supplier meeting the minimum required amount, subjective judgment leads to more case orders or not. This parameter is expressed mathematically as follows:

M= ∑preliminary re-order quantities (PQ) of all products value/pallet amount ≥ minimum requirement amount

(if not satisfied, subjectively judge for which product more cases need to be ordered)

Parameter 7: ‘Working period’

Regarding the factor “Minimum amount of inventory needed to satisfy working period” this factor should automatically be met by having sufficient inventory on hand at all times. Nevertheless, to make sure that this criterion is satisfied, the sum of current inventory (Ik), which includes the products in stock and in the trolleys, and the preliminary re-order quantity (PQ) need to be at least as high as the amount required for 28 trolleys plus the demand of eight days. However, this is a factor which should be considered as a control mechanism to make sure that the quantity ordered is indeed sufficient for operations of 10 days. If this is not the case, it is necessary to decide subjectively if an additional case needs to be ordered. Therefore, this parameter will not be included in the calculations directly but rather used for checking at the end. Since the amount of fresh food products varies daily from trolley to trolley, the parameter cannot be applied for these particular products. The control parameter (W) „Working period‟ is defined as the control point determining if additional amounts of a product need to be ordered if the preliminary re-order quantity (PQ) does not meet the amount required for one working period. The corresponding formula is as follows:

W= current inventory (Ik) + preliminary re-order quantity (PQ) ≥ amount in 28 trolleys +

* 8

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12. Final future re-order quantity calculations

Kahn (2009) states, that the outcome of the forecast method should not be considered as the end point; rather it is the starting point for further calculations and forecasts. This is in accordance with the approach in this paper of using the outcome value (forecasted demand (FD) and forecasted re-order quantity (FQ)) of the linear exponential forecasting method as an input value in the final re-order quantity calculations including the parameters presented in the previous section. The company should use an inventory model which leads to the lowest level of inventory while making sure that sufficient stock is available for the working period as in this way the inventory value. Thus, by ordering the amounts determined as the final re-order quantity in this section, the inventory value and consequently, the inventory cost is kept as low as possible while the availability of all products is guaranteed.

As can be seen in table 7 in the Appendix, there are three categories describing different ways the parameters are applicable to the 133 products: „all but parameter 2‟, „all but parameters 5, 6 and 7‟ or „all but parameters 6 and 7‟. The category „all but parameter 2‟ makes up the majority with 119 products (see Appendix table 7), which amounts to 90 percent of the 133 total products. The other two categories make up 2 percent and 8 percent respectively. A complete re-order quantity calculation, including the forecasted demand with Brown‟s „One parameter linear exponential smoothing‟ will be provided for each of these three types with one product example.

12.1 Re-order calculations for a product with all but parameter 2

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Parameter 1: ‘Promotions’

In order to show how the parameter P „Promotions‟ is applied, it is assumed that the particular product is supposed to be on promotion for period 34. However, since the value of FQ34 is negative with (-159) the original formula for this parameter needs to be changed as to make sure that a 20 percent increase is added and not a decrease of the order quantity. This leads to the following calculation:

P34 = [Forecasted re-order quantity (FQ34) + Forecasted re-order quantity (FQ34) * (-0.2)] - Forecasted re-order quantity (FQ34)

P34 = [(-159) + (-159) * (- 0.2)] – (-159) = 32

The result of the application of the „Promotions‟ parameter with 32 units shows that the amount to be ordered is increased by 32 units and will be included in the preliminary re-order quantity (PQ) later on.

Parameter 3: ‘Discontinued’

There is no discontinuation expected for this product as it will stay in the catalogue and the parameter D „Discontinued‟ is not calculated for this example leading to neither a decrease nor increase of the order quantity. Therefore, the current inventory (I33) is set to zero to guarantee the non-alteration on the re-order quantity. This is expressed in the following calculation:

D34 = [Forecasted re-order quantity (FQ34) – Current inventory (I33)] - Forecasted re-order quantity (FQ34)

D34 = [(-159) – 0] – (-159) = 0

The discontinuation factor decreases the order quantity by 0 units in the preliminary re-order quantity (PQ) calculations.

Parameter 4: ‘Vacations’

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Table 6: Forecasted demand with Brown‟s method for a third next period Period (t) Inventory demand Single exp. smoothed Double exp. smoothed Error dif 1st smoothed Error dif 2nd smoothed a B Forecast (t+1) 32 37 39,4 43,3 -2,4 -3,9 35,5 -1,0 35 33 35 38,5 42,4 -3,7 -3,8 34,7 -1,0 35 34 35 37,7 41,4 -3,1 -3,7 34,0 -0,9 34

As can be seen in table 6 the forecasted demand for period 35 (F35) is 34 units. For applying the formula of the forecasted re-order quantity (FQ), the current inventory (Ik) value is needed as well. As the order is placed on 1st July, the current inventory (I33) of 31st May with 194 units has to be used, same as in the calculation for period 34. The forecasted re-order quantity of period 35 (FQ35) is calculated as follows:

FQ = forecasted demand (F) – current inventory (Ik) FQ35 = F35 – I33

FQ35 = 34 – 194 = -160

The value for the forecasted re-order quantity of period 35 (FQ35) is (-160) units.

Once the values of FQ34 and FQ35 are known, they can be put into the formula for the „vacation‟ parameter. However, again due to the negative values for both forecasted re-order quantities, the formula has to be adjusted for the „Vacations‟ parameter in the following way to lead to the caused increasing alteration:

V35 = [Forecasted re-order quantity (FQ34) + Forecasted re-order quantity next period (FQ35)] - Forecasted re-order quantity (FQ34)

V35 = [(-159) + (+160)] – (-159) = 160

The variation in the order pattern due to the parameter „Vacations‟ increases the order quantity by 160 units.

In order to be able to apply the rounding decision parameter „Case size‟, the alteration outcomes of parameters 1, 3 and 4 have to be added to or subtracted respectively from the forecasted demand to reach the preliminary re-order quantity (PQ).

PQ34 = FQ34 + P34 + S34 + D34 + V35 PQ34 = (-159) + 32 – 0 + 160 = 33

This means that up to this point 33 units should be ordered.

Parameter 5: ‘Case size’

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38 product needs to be ordered in case sizes of 216 units (see Appendix table 1). The formula for determining the amount of cases to be ordered is as follows:

C34 = preliminary re-order quantity (PQ34) / units per case

(if the amount is not a complete number, round up if ≥ multiple of x.50,otherwise down)

C34 = 33 / 216 = 0.15

Since the decimals are not greater than 0.50 the amount is rounded down to 0 cases. Thus, the result of C34 is that zero cases of this product should be ordered.

Parameter 6: ‘Minimum quantity’

So far, after having applied parameters 1, 3, 4 and 5 the re-order quantity of product 1 from supplier A is 0 cases per 216 units. However, it still needs to be checked whether the requirements of parameters 6 and 7 are satisfied. Since the application of parameter 6 requires that the order quantities of all products of the supplier, in this case supplier A, are available, quantities for the remaining products in the matrix are assumed.

Table 7: Order matrix for supplier A

Product number Units per case Quantity of cases Case price Total volume

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40

57 56 0 £952,00 £238,00

58 54 1 £459,00 £612,00

Table 7 shows that the sum of all products of supplier A is 31,071.04 €. Using this value, the parameter M „Minimum quantities required‟ is applied for a minimum required total amount of 2000€ (see Appendix table 1) as follows:

M34 = ∑preliminary re-order quantities (PQ34) of all products value/pallet amount ≥ minimum requirement amount

(if not satisfied, subjectively judge for which product more cases need to be ordered) M34 = 31,071.04 € ≥ 2000 € (satisfied)

The application of this parameter indicates that the minimum requirement of 2000 € is met and thus the condition is satisfied and the order quantity of 0 cases, determined with parameter 5, for product 1 of supplier A does not need to be further adjusted.

Parameter 7: ‘Working period’

Finally, the check of parameter W „Working Period‟ is conducted based on the re-order quantity calculated with parameter 5. The current inventory (I34) for the particular product is 194 units and the amount demanded in trolleys is 5 units, thus 140 units for 28 trolleys (see Appendix table 1). In mathematical terms this parameter is applied as follows:

W34= current inventory (I34) + preliminary re-order quantity (PQ34) ≥ amount in 28 trolleys + * 8

(if not satisfied, determine subjectively whether an additional case is ordered or not)

W34 = 194 + 0 ≥ 140 +

*8 (satisfied)

After checking for parameter 7, the minimum amount per working period requirement is satisfied and hence, the re-order quantity can stay unchanged.

Since the requirements of parameters 6 and 7 are met, the final re-order quantity for period 34 (RQ34) of product 1 from supplier A is 0 cases.

INVENTORY MANAGEMENT OF A FLIGHT CATERER: DEVELOPING AN ACCEPTABLE RE-ORDER QUANTITY CALCULATION METHOD