Master Thesis, MSc Techology and Operations Management
Analysis of total production costs:
simulation-based optimization
Author: Koen Herps S-2534126 k.herps@student.rug.nl First supervisor: Dr. X. Zhu Co-Assessor:Prof. dr. ir. G.J.C. Gaalman
Faculty of Economics and Business
University of Groningen
September 2, 2016
2
Preface
This is the final report “Analysis of total production costs: simulation-based optimization”. This research is part of the master program “Technology and Operations Management” at the University of Groningen (RUG). I have been working on this project from April to September 2016 at KMWE / DutchAero located in Eindhoven and I would like to take this opportunity to thank several people that contributed to this project.
First of all I would like to thank all employees at KMWE / DutchAero for the possibility to participate in their project and to feed me with the necessary information when asked upon. From the university I would like to mention the critical feedback, knowledge, and support from both my first supervisor Dr. Zhu as my second supervisor Prof. dr. ir. Gaalman. I would not have been able to finish this project without all of you.
This whole project has been an enormous challenge for me and in the end I’m grateful for the development it has brought me. Personal growth can only be achieved when facing big challenges like this one. I have always been interested in the way different planning strategies work out and therefore I would like to thank the university once again for this project. It is because of this that I was able to keep going on.
Last but not least I would like to thank my parents, family, and friends for the support during this whole project. In the end the mental support, sincere interest, and advice are indispensable to finish a project like this one. Thanks to you all!
With kind regards,
Koen Herps
3
Management summary
The majority of this research has been conducted with the software program “Technomatix Plant Simulation”. To ensure the validity of its outcome, empirical data was retrieved from a company located in the south of the Netherlands, KMWE / DutchAero. The main objective of this research was to investigate the effect of several planning decision variables among other planning decision variables and their effect on the total production costs. The total production costs consists of interest over invested financial resources and the operational costs of applying surface treatment at an international supplier. From the perspective of KMWE, the objective was to find the most optimal settings of the individual planning decision variables that would minimize total production costs and do not neglect appointments that were made with the customer about delivery performance.
During this research, four planning decision variables were defined that would eventually influence total production costs; lot size, safety stock, dispatch rule, and order release strategy. Each planning decision variables has their own possible settings. The settings of both lot size and safety stock consist of an integer. A starting point on behalf of these settings was provided by KMWE. The other possible settings were arbitrarily chosen and set on – (1/3 of the initial setting) and + (1/3 of the initial setting). The possible settings of dispatch rules and order release strategy came from a literature review. The dispatch rule possesses five possible settings; first come - first serve, lowest stock level first, most expensive first, shortest setup time first, and weighted shortest processing time first. The order release strategy has two possible options; continuous and periodic. The periodic option was furtherly divided into two time intervals; one week and two weeks.
The results showed that both the safety stock levels as the order release strategy do have an optimal setting regardless of the other planning decision variables. This indicates that a more optimal setting will always lead to a more preferable outcome. The lot size and dispatch rule did not have a direct effect on the total production costs. These planning decision variables are dependable on the settings of other planning decision variables in order to achieve the desired outcome.
4
Table of Contents
Preface ... 2 Management summary ... 3 Table of Contents ... 4 1 Introduction ... 6 1.1 KMWE / DutchAero ... 6 1.2 Logistic challenges ... 7 1.3 Motivation research ... 9 2 Research design ... 9 2.1 Problem statement ... 10 2.2 Research objective ... 11 2.3 Research scope ... 11 2.4 Research approach ... 11 3 Literature review ... 12 4 Theoretical Framework ... 13 4.1 Hierarchical planning ... 13 4.2 Uncertainty ... 15 4.3 Overview ... 16 5 Simulation model ... 165.1 Overview simulation model ... 17
5.2 Input data ... 20 5.3 Practical problems ... 22 5.4 Verification ... 22 6 Experimental design ... 23 6.1 Lot size ... 23 6.2 Safety Stock ... 24 6.3 Dispatch rule... 24
6.4 Order release strategy ... 25
6.5 Performance... 26
7 Results and discussion ... 26
7.1 Descriptive statistics ... 27
7.2 Statistical analysis ... 28
7.2 Conclusions and discussion ... 30
5
Bibliography ... 33
Appendix A – Overview of all product families ... 36
Appendix B – Calculation unavailability operators ... 37
Appendix C – Overview of all experiments ... 38
6
1 Introduction
The logistic problems encountered at Klein Mechanisch Werkplaats Eindhoven / DutchAero (KMWE / DutchAero) will be the focus of this research. This chapter will elaborate on the specific characteristics of KMWE / DutchAero and how current events have led KMWE / DutchAero to search for solutions for their logistic problems. The first paragraph will give a brief introduction to KMWE / DutchAero and their operations. The second paragraph will zoom in on the department of KMWE / DutchAero that will act as center of this study. The third paragraph will discuss the before mentioned events that causes the current problems in detail. In conclusion the motivation for this research is given.
1.1 KMWE / DutchAero
KMWE / DutchAero, henceforth called KMWE, is an enterprise which is located in the south of the Netherlands. Founded in 1955, KMWE started as a small company with the sole capability of milling small products primarily as an outsourcing partner for Philips N.V.. Over the years KMWE developed into an important partner for several markets with capabilities like machining, assembly, and thermal spraying. These markets are Aerospace & Defence, Semiconductor, Medical & Diagnostics, and Industrial Automation. With its headquarters located in the Netherlands, KMWE has transformed to an international supplier with plants in Malaysia, India, and a joint venture in Turkey. This has led to an impressive growth in the, now called, KMWE group. In 2016 KMWE employs 550 FTE’s across the world. The plants in the Netherlands are further separated by their capabilities. KMWE possesses plants for machining (KMWE Precision Components), assembly (KMWE Precision Systems), project management (KMWE Projects), 3D printing (KMWE 3DP), and one extra plant for special manufacturing processes (DutchAero). An overview of the KMWE group is given in figure 1. The focus of this research will be on the machining department of KMWE, KMWE Precision Components.
7
characteristic. Furthermore, the plant is divided into two main production areas; Manflex and Autoflex. The Autoflex possesses machines which can run automatically for 24 hours a day while the Manflex has machines that require an operator. However, in this study the work hours for both areas will be equalized to 12 hours a day. This will not affect the outcomes of this research, but leads to several advantages in executing this study. This will be explained in more detail in 5.1.4. It is important to note for this study that the whole KMWE Group has been certified for production processes according to ISO 9001, AS9100, and ISO 13485. Especially the AS9100 certification, a certificate that is required to work for the Aerospace & Defence market, plays an important role within this research. Chapter 1.2.2 will elaborate on this matter.
1.2 Logistic challenges
The logistic problems for KMWE that are dealt with in this paper have their origin in the Aerospace & Defence market. Since 2014, one big customer of KMWE, a large airplane manufacturer henceforth referred to as “OEM”, applied a strategic outsourcing strategy in order to redesign their own production activities. All products subject to this outsourcing strategy are referred to as QSF-B products. In the previous situation the OEM would buy their own materials, KMWE would subsequently process these materials into components, and the OEM further processes the components with additional surface treatment and ultimately assembly. The products that followed this production strategy are referred to as QSF-A products and their production process is visualized in figure 2. The company that is listed within the frames is the company that processes that activity.
Figure 2: Production process of the QSF-A products
8 1.2.1 Purchasing
Although the extra purchasing activity will only marginally be in the scope of this research, it is important to understand the consequences of this request for KMWE. One of the most discussed topics in building and managing a buyer-supplier relationship is supplier selection [Yu 2014]. KMWE does not have to face this challenge because it can take over the current supplier portfolio of the OEM. The fact that KMWE can take over the supplier portfolio does not mean that this extra activity is without negative consequences. First of all KMWE becomes accountable for the quality of the purchased material. Secondly, because KMWE has to buy the raw material themselves, a financial investment is required even before a work order is released onto the shop floor. In the previous situation, visualized in figure 2, first initial investment was required when a work order started. The purchasing activity will only be included through the value of the work-in-progress right as the work order is released. Issues like insufficient quality or shortage of raw material are not included.
1.2.2 Surface treatment
The extra activity related to applying surface treatment plays an important role within this research. Most important of all, because the extra surface treatment will surely lengthen KMWE’s order lead time [Al-Sayed 2016]. The expected increase in order lead time requires extra financial resource because of the costs of processing a work order (interest due to the purchase of raw material, machining, and surface treatment). This effect is expected to become even bigger due to another important characteristic of the Aerospace & Defence market, quality standards. A company is required to possess the AS9100 certificate to work in the Aerospace & Defence market for this OEM. KMWE does possess this certificate, but does not have the equipment to process the required surface treatment. After thorough analysis, KMWE perceived difficulties in finding local suppliers. Subsequently, this has led to international suppliers which are located further away than more local suppliers of other markets of KMWE (e.g. semiconductor, medical & diagnostics). This greater distance results in increased transportation time, which ultimately enlarges the order lead time. The increased order lead time will reduce operational competitiveness [de Treville 2014]. The new situation, for the QSF-B products, is displayed in figure 3.
9 1.2.3 Ordering policy
Besides these changes, the airplane manufacturer also decides to change their ordering policy. In the past, QSF-A orders were placed at KMWE with a predefined order lead time of 8 weeks. In the future the airplane manufacturer demands delivery four weeks after their order submission. The order lead time for QSF-B products of KMWE are surely longer than four weeks. Consequently, KMWE has to switch from a make-to-order to make-to-stock planning policy to deliver the orders on time.
1.3 Motivation research
KMWE discovered that the new situation will eventually drain their financial resources due to the amount of money they have to invest to process the products before they will eventually yield turnover. Also, the expected longer lead time results in a longer time interval before initial investment generates turnover. During this period, KMWE has to pay interest over the invested financial resources. KMWE currently does not possess the required financial resources to allow this new situation to last. Together with the requirement of the OEM to deliver within a four weeks’ notice, which forces KMWE to have a certain amount of safety stock, the new situation of the QSF-B products asks for a redesign of their own production strategy.
KMWE currently sees no direct opportunity to manage the surface treatment activity differently. Consequently KMWE starts by redesigning the way they manage their own machining process. The management of the machining process can be divided into the choice of settings of several planning parameters, a more elaborate view on that in the literature review in chapter 3. Eventually KMWE strives to reduce the costs of production in terms of interest over the invested financial resources to produce products by applying an optimal production strategy. This production strategy is a setting of different planning parameters. Subsequently this will lead to the following research question:
What is the effect of different planning strategies on the total production costs of a production process?
2 Research design
10
2.1 Problem statement
In order to fully understand the core of the problem of this research we will first specify the problems of the different stakeholders which are KMWE and the OEM.
2.1.1 KMWE
The OEM is currently responsible for roughly 10% (€ 5.000.000) of the total annual turnover (€ 50.000.000) of KMWE and makes them one of the biggest customers. This explains the desire of KMWE to keep them as their customer. The current requirement of the OEM to deliver within four weeks of their sales order submission, and their current order lead time which is expected to exceed these four weeks, forces KMWE to build a safety stock. Of course this safety stock can consist both work-in-progress as finished goods inventory. The total costs of this stock, in terms of interest, are currently not acceptable for KMWE.
KMWE already discussed with the OEM a starting point for certain planning decision variables like lot size and safety stock for the QSF-B products. KMWE is starting with a fixed lead time of 16 weeks, in other words required work-in-progress, and four weeks of demand on safety stock. The QSF-B product portfolio consists of 311 products. With an average value of € 170,00 and lot size of 24, the total value in the total stock is equal to just above € 1.250.000,00. That is 25% of the total annual turnover. From the very start it became KMWE crystal clear that they need to reduce this total value to not waste too much financial resources.
2.1.2 OEM
Since 2014 the OEM started with downsizing their supplier portfolio. The current supplier base of 100 suppliers needed to be reduced to 10. KMWE belonged to one of the 10 and were selected to expand their current product portfolio with QSF-B products. One of the main reasons for the OEM to reduce their supplier base was to work with less strategic partners rather than a lot distant suppliers. A strategic buyer-supplier relationship possesses four main advantages; (1) economic-based, (2) behavior-based, (3) resource-based, and (4) bridging-based [Tanskanen 2015]. This paper will not take up all these advantages, but one advantage for the buyer is important within this research; economic-based. One of the aspects of the economic-based advantage is delivery. “Delivery relates to all factors related to the timely and accurate fulfillment of buyer’s needs [Tanskanen 2015]”.
11
2.2 Research objective
The main research objective can be derived from the combination of the problem statements of both stakeholders. On the one hand KMWE wants to produce all QSF-B products for the OEM with the least possible production costs as possible, in terms of interest that has to be paid over invested financial resources. On the other hand the OEM, that emerged in a strategic buyer-supplier relationship with KMWE, wants to be ensured of timely delivery of ordered products. Therefore the objective of this research can be summarized in the following sentence:
Advice KMWE on how to reduce their total production expenses, in terms of interest that has to be paid over invested financial resources, without neglecting the delivery requirements of the OEM.
2.3 Research scope
A proper definition of the scope of the research prevents that the research becomes too extensive. Therefore it is important to get a clear understanding of the parties and aspects that need to be included. At the highest abstraction level, three involved parties can be defined; KMWE, the OEM, and the international supplier that performs the surface treatment. For KMWE their own shop floor and corresponding planning strategy play an important role. The OEM is not involved within the production process, but their ordering policy is a weighty aspect in order to test the validity of the tested production processes. After all, if a production process cannot satisfy the four weeks delivery requirement, the production process becomes useless. The surface treatment consists of two factors; lead time of surface treatment and back and forth transportation.
2.4 Research approach
12
and executing of the simulation model. The last steps contains the analysis of simulation model outcomes.
The structure of this paper is as follows. The next chapter will provide a literature review on current events on the field of optimizing planning decision variables. Chapter 4 will elaborate on the choice of the different planning decision variables and the uncertainty in the production process. Chapter five extensively discusses the design and operation of the simulation model.The sixth chapter shows the experimental design. The results of the simulation study, conclusions and directions for further research will be discussed in chapter 7. The last chapter explains the assumptions and limitations of this research.
3 Literature review
The increasing competitiveness of the global industrial environment has led to the offspring of all kinds of strategic concepts. The do-or-buy decision is one of the most fundamental purchasing and supply strategy issues [Slack 2011:152]. Within this do-or-buy decision, one important strategic concepts is currently applied by OEM’s in the aerospace industry; strategic outsourcing [Mintzberg 1996; Rossetti 2005]. The concept of strategic outsourcing relocates every value-added task that does not fit the company’s core competence to another company [Kumar 2005]. Currently little investigation is conducted about the effect of such an outsource decisions on the supplier [Baraldi 2014]. However, when suppliers are required to perform multiple supply chain activities such as; surface treatment, assembly or testing, their total lead time will increase [Al-Sayed 2016]. Longer lead times will subsequently yield higher operational costs [de Treville 2014] and therefore reduce operational competitiveness.
13
Enough evidence exists about the benefits on waste reduction by optimizing separate planning parameters like lot size [Chang 1994], order release strategies [Land 2014], and dispatching rules [Heger 2015]. Moreover, multiple studies elaborate on the methodology in order to improve these separate planning decision variables [Pattloch 2001; Yang 2002; Boulaksil 2009; Thürer 2012; Sana 2010; Chiou 2013]. Renna [2015] investigated the influence of different order release strategies on due date performance (average lateness and percentage of orders in delay). A proper order release strategy lead to improved due date performance [Renna 2015]. Research on a holistic optimization of separate planning decision variables is scarce [Gansterer 2014]. Therefore, Gansterer [2014] conducted a research that investigated the possibility to optimize planning decision variables like safety stock, planned leadtimes and lot size. Within the same year, Land [2014] studied the effect generated from a holistic approach on order release strategies and dispatching rules. Land [2014] proved that an holistic approach can generate a positive effect on operational performance. In conclusion, an holistic view on the optimization of several planning decision variables is stressed by Molinder [1997].
This paper investigates to what extent different settings of planning decision variables can contribute to lead time reduction and ultimately reduce total production costs. The theoretical contribution of this paper exists on the holistic view on multiple planning decision variables. This study embodies the planning decision variables of both Gansterer [2014] and Land [2014]; lot size, safety stock, order release strategy, and dispatching rules. One setting of the four planning decision variables is referred to as one planning strategy. This holistic view provides insights in how to optimally cope with the uncertainty caused by long, imperishable supply chain lead times.
4 Theoretical Framework
The first section of this theoretical framework describes the different hierarchical planning levels of KMWE that will be included in this study. This section is divided in two subsections; medium-length and short term planning. The second part describes the uncertainty that has a negative effect on the total lead time. The last part provides a brief overview of the complete theoretical framework.
4.1 Hierarchical planning
14
rules [Albey 2011; Land 2014]. The different settings that each of the planning decision variables can take are discussed in the remainder of this chapter.
4.1.1 Medium-length
The choice for lot size depend on a trade-off between setup costs and holding costs. A Larger lot size result in higher holding costs but lower setup costs and vice versa. The determination of the most optimal lot size is referred to as the Economic Lot Scheduling Problem (ELSP) [Pinedo 2009:144]. The Economic Order Quantity (EOQ) model incorporates both setup costs and holding costs to calculate the most preferable lot size [Choi 2000]. The EOQ lot size will act as starting point within this study. Since this study investigates the holistic collaboration among planning variables, the optimization of one planning decision variable, the lot size, might be suboptimal. Therefore this study will also investigate lot size that are located close to the EOQ.
Safety stock is a perfect tool to cope with unreliable demand information [van Kampen 2010]. The determination of a proper safety stock level can be challenging, especially when there are multiple variable parameters in play [Ruiz-Torres 2010]. To get a proper indication of a proper safety stock level, Ruiz-Torres [2010] proposes the traditional safety stock calculation model. This model incorporates the expected lead time and the expected demand during this lead time. By applying variability within both lead time as demand, a proper estimation can be calculated.
4.1.2 Short term
The order release decision of Renna [2015] consists of two possibilities; continuous and periodic. The continuous method receives information from the shop floor and uses this information to calculate optimal order release moments. The periodic method is far less complex and releases orders at a certain time interval [Renna 2015]. The latter method is implemented easier, but the continuous method yields more optimal business results in a complex production environment [Renna 2015]. This study will incorporate both order release policies.
15
first, longest processing time first, shortest setup time first, least flexible job first, largest number of successors first, and shortest queue at the next operation are compound into new composite dispatching rules [Pinedo 2009:445].
Planning decision variables Possible settings
Lot size Integer, optimal lot size determined by EOQ
Safety stock Integer, safety stock determined by traditional calculation model
Order release strategy Continuous
Periodic
Dispatching rule FCFS
Priority selection
Composite of multiple rules
Table 1: Overview of planning decision variables and their possible settings
4.2 Uncertainty
The uncertainty within this model is caused by different types of risk. Risk is classified in three different categories; (1) risks linked to technical performance; (2) risks linked to budget, and (3) risks linked to schedule [Couillard 1995; Sinha 2004]. This study will focus on the latter two because technical performance is not an issue for both KMWE and the suppliers due to their obtained AS9100 certificate. In the situation of KMWE, risks linked to schedule are primarily influenced by transportation to international suppliers. Therefore, the transportation modes become an important decision [Meixell 2008]. The determination of the choice of the transportation mode is usually heavily influenced by either costs of lead time [Meixell 2008]. Caramia [2009] established the existence of a trade-off between costs of lead time. Meaning risks linked to schedule can be reduced with additional costs.
16
4.3 Overview
Figure 4 provides a schematic overview of the scope of this study. As mentioned in 1.2.1, the purchasing activity will be excluded from this study. This implies the assumption of infinite availability of raw material. The planning decision variables are the independent variables. This means that the setting of the planning decision variables are predefined at the start of a simulation run. The, independent, planning decision variables focus on the machining activity of KMWE. The transportation mode depends on the current status of the system. If the stock levels of the products of that work order is below a certain threshold, the surface treatment and transportation will be rushed. If the stock levels are sufficient than the surface treatment activity will not be rushed. Every time the model needs to make use of the rush transportation mode, a penalty has to be paid to the production cost. The planning strategy (e.g. setting of the four independent planning decision variables) that yields the lowest production costs will be appointed as the most optimal.
Figure 4: Schematic overview of the planning decision variables and their position in the production process
5 Simulation model
17
5.1 Overview simulation model
This paragraph will give an elaborate explanation about the main elements of the simulation study. The first section covers the processing of both work orders and sales orders. The second part shows the shop floor of KMWE. The third part will explain how the simulation model deals with the surface treatment and transportation. The last part will provide an explanation about all kinds of methods, variables, and tables that were required for the model to run properly.
5.1.1 Processing of work orders and sales orders
The simulation model has to cope with two different streams. One for the processing of work orders and one for the processing of sales orders. The reason why these two streams were inevitable has its origin in the ordering policy of the OEM. This ordering policy, like mentioned in 1.2.3, force KMWE to switch from a make-to-order to a make-to-stock production process. One of the characteristics of a make-to-stock policy is that work orders are not directly linked to a sales order. Therefore the production process needs one stream for work orders to increase the stock and one stream for sales orders to denude the stock. That way work orders and sales orders are not linked to each other. Both streams are displayed in figure 4.
Figure 4: Two processing streams of the simulation model; one for work orders and one for sales orders The upper stream processes work orders from left to right. Within the left frame, “OrderReleaseWO”, work orders are generated and defined on the aspects; product type, work order number, lot size, value, routing, processing time, and setup time and subsequently released according to the predefined work order release strategy. Subsequently they will be processed by KMWE’s own shop floor in the frame “ShopfloorKMWE”, receive additional surface treatment from the international supplier within the frame “OutsideProcess”, and finally be closed.
18
ranks the sales order on their date of intake. If the current stock level is equal of higher than the sales order quantity the sales order is moved to the customer and the stock level is reduced with the same amount. If the stock level is not sufficient the sales order is stored for an extra day in the “DeliveryList” and checked again the next day.
5.1.2 Shop floor KMWE
The shop floor of KMWE in the simulation model consists of three important elements; allocation of the work order to the proper machine group, the actual machines that need to process the work order, and operators. For modelling purposes, the simulation model needs to distinguish machine groups with only a single machine and machine groups with multiple machines. A small subset of the complete shop floor model of KMWE is given in figure 5.
Figure 5: Small subset of the shop floor of KMWE The first, and most easy part, of the shop floor is the allocation of work orders to the proper machine group. A very straightforward process takes one work order that needs to be assigned and brings it to the right machine group. In figure 5, this process is modelled in the upper stream.
The actual machines needed the be modelled in two ways; machine groups with a single machine and machine groups with multiple machines. In figure 5, the objects “S1500D500” and “M1500D00” are an example of a machine group with only a single machine (1500D500). Work orders that need to be processed at the machine “1500D500” are stored in the buffer “S1500D500”. Every time a new work order enters the buffer, the complete set of work orders are sorted according to the dispatching rule that is predefined during a simulation
run. Once the machine “M1500D500” empties, the first work order in line gets processed. A machine group with multiple machines, figure 6, has a different appearance. The single machine needed to be changed into a frame
with multiple machines. Within the frame, the procedure of allocating work orders is quite similar. Figure 6: Machine group with multiple
19
Only the method that needed to be called per machine to process the next work order is slightly different.
The operators play an important role in the simulation itself. Each machine gets a dedicated operator as can be seen in figure 5 in the bottom left. When the operator for machine 1500D500 is free and ready to process a work order it is placed in the object “A1500D500”. If there is a work order, the operator itself is unavailable during the setup time and processing time of the work order while sitting in the object “U1500D500”. If there is no work order the operator simply waits until a new work order is present. More on the necessity of the operators in 5.3.
5.1.3 Surface treatment and transportation
The modelling of the surface treatment activity is more straightforward. An example of the surface treatment activity is given in figure 7.
Figure 7: Frame of the surface treatment process in the simulation model Once again work order are being processed from left to right. KMWE currently applies a hybrid procedure to determine when work orders are being shipped to the international supplier. All work orders are stored in the warehouse. When the amount of work orders is sufficient to fill up a complete truck, work orders are collected and prepared for transportation. In order to model this properly work orders enter the surface treatment activity and are placed in a buffer “WaitForTransport”. When the amount of work orders is sufficient all work orders are moved to “TransportOP”. After the work order have reached the supplier KMWE has to determine whether or not the work orders need to be rushed. If the work orders need to be rushed they are placed in the “SurfaceTreatmentRush”, otherwise in the “SurfaceTreatment”. After completion of the surface treatment the same procedure works for the transportation back. By processing a work order through the faster processes additional payment is required which is added to the total production costs of the whole system.
5.1.4 Methods, variables, and tables
20
Figure 8: Important methods, variables, and generators of the simulation model The stopwatch and two blue and red methods are primarily for resetting, initializing and running the simulation model. All blue methods have their own functionality. For example the methods “OfficeControl” and “WorkfloorControl” force the processes mentioned in 3.1.1 and 3.1.2 to stop working when out of working hours. The order intake and order release process stop working outside office hours (mon – fri 8:00 – 16:00, sat – sun closed). The machines at KMWE stop working outside of shop floor hours (mon – fri 6:00 – 18:00, sat – sun closed). The “check delivery” generates a new delivery list, mentioned in 3.1.1, for the expediting personnel every day. Subsequently the “prepare delivery” checks current stock and decides whether or not the sales order can proceed to the customer or should be sent back to the delivery list. Most of these methods are triggered by so-called “generators”. These five generators are displayed in figure 8 in the upper mid right section. The remaining methods are triggered by a sales order or work order entering or leaving a process.
The tables “Stocklevels” and “StockHelp” help the other methods to decide which action they should trigger. For example, the table “StockLevels” keeps the information of the current stock levels which ultimately help the method “PrepareDelivery” to decide whether or not the sales order can be shipped to the customer. Other important tables can be found in the frames “OrderReleaseWO” and OrderIntakeSO” for information on the product portfolio. These tables contain information like routings, quantities, and processing times. The order release strategy method is not in the overview displayed in figure 8. This method is in the fame “OrderReleaseWO”.
5.2 Input data
21 5.2.1 Product portfolio
The product portfolio of QSF-B consist in total of 311 products. Due to simulation limitations this amount of 311 products had to be reduced otherwise modelling and running the simulation would be too time consuming. A good way to reduce the amount of products that need to be modelled, but still take into account all 311 products is by appointing product families. A product family refers to a group of products that might have the same production process, similar physical characteristics or similar pricing methods [Abdi 2012]. For this simulation study, the products that are placed in one product family need to have an identical routing and more or less similar processing times and setup times.
The data provided by KMWE already clusters the 311 products into product families based on processing time, setup times and dimensional characteristics. However, some product families still possesses different product that had a different routing. These product families had to be split up into different product families so all products within one product family had the same routing. This was necessary because the simulation model could only allocate one product family to one machine group. Eventually 44 product families remained that needed to be modelled. A complete overview of all product families is provided in appendix A.
5.2.2 Machinery
KMWE owns several machine groups. Each machine group has its own capabilities and therefore its own products it can process. The QSF-B products are located to 11 machine groups. An overview of these machine groups and their characteristics is provided in table 2. The last column
Machine group Number of machines in machine group % of capacity reserved for QSF-B
1200_105 4 34,17% 1200D70R 6 23,77% 1500D500 1 61,71% 1500GR55 2 11,57% 1500H4A 2 19,95% 1500HC40 1 22,13% 1500UL5 1 37,06% 1500UN35 1 86,47% 1500UN45 1 20,22% 2100UN35 1 16,17% GROB350 1 27,41%
22
gives the percentage of their total capacity that is required for the production of QSF-B products given their current lot size and annual demand.
5.2.3 Ordering policy OEM
The ordering policy of the OEM is the last special process that required input data from KMWE. Sales orders are submitted randomly through the week and not in a batch at a certain predetermined point. This means that sales orders are continuously created with a predefined inter-arrival time. This inter-inter-arrival time can be calculated by dividing the total amount of sales orders per year with the total simulation time. Within the case of KMWE, the OEM orders roughly 1200 sales order per year. With a total simulation time of 525600 seconds per year, the inter-arrival time of sales orders is equal to 26128 seconds.
5.3 Practical problems
The capacity of the machines was one of the biggest problems encountered during the modelling phase. This simulation study only incorporates the QSF-B products of KMWE, while KMWE also produces products of other markets on the machines. This means that without further modelling the machines will have overcapacity, as can be seen in table 2. Consequently, the overcapacity marginalizes the influence of the planning decision variables because queues will never arise. The total capacity of the machines must be increased to 100% to get a correct indication of the influence of the planning decision variables. This is the main reason for the inclusion of the operator mentioned in 5.1.2. After the completion of a work order, the operator will be transferred to, see figure 4 for the example, “U1500D500”. It remains in this buffer for a certain amount of time. Work orders that need to be processed on the machine of that operator need to wait until it is released. The time the operator remains unavailable is predefined at the beginning of a simulation run. Since the total required capacity of the machines and the required time for QSF-B orders are known, the calculation of the time an operator remains unavailable is straightforward. An overview of this calculation is provided in appendix B.
5.4 Verification
The verification of the simulation model is executed by two methods; modular simulation model design and in-process parameter checks. The first section will explain the working of the modular simulation model design. The second section provides an explanation about the in-process parameter checks.
5.4.1 Modular simulation model design
23
process and frame has been designed and built outside the real simulation model. This means that methods and processes were built in a less complicated environment before applying it to the main model. For example, the method that prioritizes work orders according to their current stock levels was built in another simulation model with only 2 products and predefined stock levels. 2 more products were added when this method works correctly. Subsequently, dynamic stock levels were implemented. After a complete check of the proper working of the method it was incorporated with the actual simulation model. Every method and frame within the main model was designed and build in a similar fashion.
5.4.2 In-process parameter checks
The second method of verification was executed by checking in-process parameters. After each simulation run, the program itself would give information per product family about their average processing time, waiting time, and failure time. When, for example, the failure times of a subset of product families were out of bounds, it meant that the machine the subset should be processed on was not working properly. This could indicate that the working hours method was not working properly. Also when the average waiting time of a certain subset of product families was too large in comparison with other product families, it meant that the methods that processes the operators were not working properly. Moreover, the final results of each simulation run also gives a preliminary indication that the model could not work properly. For example, if the total production cost would exceed the annual turnover, the model would of course not calculate the production costs properly.
6 Experimental design
This chapter will elaborate on the choice of the planning decision variables. The different planning decision variables are; lot size, safety stock level, dispatching rule, and order release policy.
6.1 Lot size
At the start of the QSF-B project, KMWE made certain appointments on behalf of lot sizes of product families. These appointments will act as a starting point for this simulation study. The other possible settings of the lot size of product families are chosen arbitrarily since no data of possible settings is available. The different settings for lot size are therefore:
Lot size settings per product family Initial setting defined by KMWE
24
6.2 Safety Stock
KMWE made appointments with the OEM about the safety stock levels similar to the lot sizes. The current appointment obligates KMWE to have at least the demand of one whole month on store. Other possible settings are also arbitrarily chosen since this data is also not available.
In order to model the safety stock in the simulation model, first the practical implications need to be explained. The OEM requests KMWE to have the established safety stock in store at all time. Furthermore KMWE has its own predefined fixed lead time for a single work order. This is the amount of weeks it takes a work order to be processed. The total required stock, both work-in-progress as finished goods, of one product can hence be calculated with the following formula:
Total required stock (WIP and finished goods) = Fixed lead time + required stock finished goods Different settings of the safety stock will reduce the “required stock finished goods” part of the equation and thus reduce the total required stock. The possible settings for the safety stock are:
Safety stock settings per product family
Initial setting - (1/3)
Initial setting defined by KMWE
Initial setting + (1/3)
Table 4: Overview of the different settings of safety stock levels
6.3 Dispatch rule
25
orders are not directly linked to sales orders. Consequently work orders will not have a due date that is linked with a sales order. The first due-date first (FDD) dispatch rule is slightly altered so it could be applied in a make-to-stock policy as well. After alteration, the lowest stock first-rule (LSF) works in a similar way. When a machine is freed, it check the stock levels of the products that are in the waiting queue. The product family with the lowest stock gets the highest priority. An overview of the applied dispatch rules is provided in table 5.
Dispatch rule Goal
First come, first serve (FCFS) Variance in throughput times
Lowest stock first (LSF) Maximum Lateness
Weighted shortest processing time (WSPT) Weighted sum of completion times, WIP
Most expensive first (MEF) Reduce rush costs
Shortest setup time first (SST) Makespan and throughput
Table 5: Overview of the dispatch rules and their main purpose
6.4 Order release strategy
This study incorporates two different order release strategies; periodic and continuous. The periodic system releases all generated work orders after a certain, predefined, time interval. The continuous release strategy calculates the need for work orders to be released on production parameters elsewhere in the system. When these parameters reach a predefined threshold, work orders are released for production.
The most easily implemented order release strategy is the periodic order release strategy. The periodic release strategy has two possible settings which are discussed with KMWE: one week and two weeks. This means that generated work orders are stored for either one or two weeks and then released in the production process.
The purpose of continuous release strategies is mainly to control the WIP levels in the production system [Roderick 1992]. The continuous order release strategy evaluates the current stock levels for each of the product families and releases work orders of a certain product family when the required stock gets below the predefined threshold. Table 6 shows the different order release strategies and their possible settings.
Order release strategy Setting
Periodic 1 week
26
Continuous Below required threshold
Table 6: Different order release strategies and possible settings
6.5 Performance
Each run of the simulation needs to be evaluated on its performance. The objective of this research is to find out which setting of planning decision variables should be appointed as the most optimal, with respect to production costs. These costs can be increased in two ways; interest over invested financial resources and the costs of surface treatment. The costs of interest, currently 10% over three months, over invested financial resources are calculated with the average work-in-progress stock levels and finished goods stock levels of all product families. During each simulation run, the average stock levels of both work-in-progress as finished goods are recorded. The costs of interest over these stock levels of each individual product family can be calculated with the following formula:
Cost of interest = Average WIP level * value of WIP * interest rate + Average finished goods level * Value of finished goods * interest rate
It is important to note that work-in-progress products have a lower value, roughly 50%, than finished goods products. This is caused by the surface treatment activity. After machining, the work orders are shipped to the international supplier. Until the international supplier has to be paid the products are administrative work-in-progress products and contain the value of a work-in-progress product. After completion of the surface treatment activity the supplier has been paid. Consequently the products are evaluated as finished goods since the surface treatment activity is the last process in the total production process. Work orders are completed after the surface treatment activity and added to the finished goods stock.
The last step of evaluating a simulation run is the addition of the surface treatment costs. These costs are predefined and based on which transportation mode and surface treatment mode a work order has taken (normal or rush). The costs of these modes are later on added to the total interest costs.
7 Results and discussion
27
7.1 Descriptive statistics
The initial experimental design should have provided 135 different experiments. However, during the simulation runs it became already clear that both the biggest lot sizes as the order release strategy with a two weeks period generated significant higher results on total production costs than every other setting and were thus excluded from the research. The elimination of those 2 settings of planning decision variables has resulted in 60 different experiments that could be analyzed. An overview of all experiments is provided in appendix C.
The problem statement (§ 2.1) mentioned two important stakeholders; KMWE and the OEM. For KMWE, the main objective consists of finding an optimal planning strategy that minimalized the total production costs. These production costs were determined by the interest that had to be paid over invested financial resources and the costs of the surface treatment activity. The actual outcomes of all 60 experiments were between about €460.000,00 and € 1.450.000,00 with an average of € 750.000,00. A table of the top 10 results concerning total production costs are displayed in figure 8. The planning strategy with the initial setting of the lot sizes, low safety stock levels, LSF dispatching rule, and one week periodic order release strategy came out as the most optimal in terms of total production costs with an estimated total costs of € 460.136,45.
Figure 8: Overview of total productions costs of the top 10 experiments The OEM’s main concern is the assurance of delivery. KMWE and the OEM agreed upon a maximum sales order lead time of 4 weeks. This means that sales orders with a lead time longer than 28 days should be evaluated as undesirable. In order to test the simulation runs on this objective, the amount of sales orders that were delivered out of bounds should be considered as the most important one. It was impossible to avoid sales order lead time that were out of bounds completely. The simulation model uses straightforward dispatching rules that would not hurry a work order because a sales order could be delivered out of bounds. In the real world, dispatching rules could be overruled by the immediate need for a certain work order to be processed. The percentage of sales orders that were delivered on time were between the 99,75% and 96,49% for all experiments. An overview of the top
28
10 experiments are displayed in figure 9. The most optimal results was obtained by the experiment with the initial setting of the lot sizes, large safety stock levels, FCFS dispatching rule, and continuous order release strategy.
Figure 9: Overview of the % of sales orders that were delivered on time of the top 10 experiments
7.2 Statistical analysis
An independent sample t-test showed that the total production costs of all experiments that used settings of low lot sizes and a one week periodic release strategy together were significant higher than the other experiments (p. 0.00). This indicated that low lot sizes combined with a periodic release strategy have a strong negative effect on total production costs. Since this relationship is very strong, the experiments that have this specific settings on lot sizes and order release strategy were excluded from the research so they will not influence the other relationships among the planning decision variables.
The new set of experiments that need to be examined have a range lower limit of € 460.000,00 and an upper limit of € 650.000,00. This means that the choice of planning decision variables definitely has an influence on the final outcome. To test the effect of a single planning decision variable regardless of the setting of the other planning decision variables, two statistical tests were conducted; an independent sample t-test for the settings with only 2 possible settings, an independent samples Kruskal-Wallis test for settings with multiple possible settings. When the distribution of outcomes is the same across the different settings of a planning decision variable, it can be concluded that there is no optimal setting for that specific planning decision variable with respect to the other planning decision variables. Subsequently, this means that the choice of the setting for that planning decision variable must be chosen together with other planning decision variables. If the distribution of outcomes is not the same across the different possible settings of the planning decision variable means
29
that an optimal setting of that planning decision variable exists. The outcomes of all statistical tests are included in appendix D.
7.1.1 Lot size
The planning decision variable lot size only had two possible settings; initial setting that was defined by KMWE and the initial setting – (1/3 of the initial setting). The Levene’s test for equality of means shows a p-value of 0,257 which means that both possible settings do not have equal variances. This results in a p-value of 0,005 in the independent sample t-test. This p-value indicates that the two possible settings of the lot size have a marginal difference between the outcomes. In conclusion the choice of lot size is very likely to have an optimal setting regardless of the other planning decision variables, but the outcome is not very convincing. The initial setting of KMWE (€550.123) scored better that the low lot sizes (€591.152).
7.1.2 Safety stock
The planning decision variable safety stock possesses three different settings. Since this decision variable has multiple possible settings the independent samples Kruskal-Wallis test was conducted. This test checks whether or not the distribution of outcomes is the same across all possible settings. The outcome of this test can be interpreted straightforward. In case of the safety stock, the distribution of the outcomes is not the same across the possible settings of the safety stock (p-value of 0,000). This indicates that there is an optimal setting for the safety stock levels regardless of the choice of the other planning decision variables. After analysis of the descriptive statistics of these settings it can be concluded that the setting of low safety stock levels is the most optimal in practically all situations.
7.1.3 Dispatch rule
Since the dispatch rule also contains multiple possible settings, the same independent samples Kruskal-Wallis test was conducted. With a p-value of 927,000, the test provides convincing evidence that the setting of the most optimal dispatch rule is highly dependable on the choice of the other planning decision variables.
7.1.4 Order release strategy
30
€545.470, the periodic order release strategy scored better that the continuous release strategy (€572.963).
7.2 Conclusions and discussion
The main purpose of this study was to find an answer to the following research question:
What is the effect of different planning strategies on the total production costs of a production process?
In order to understand the effect of the different planning strategies, the different planning strategies were separated into the effect of a single planning decision variables with respect to the other planning decision variables. The different planning decision variables that were included within this research were; lot size, safety stock, dispatch rule, and order release strategy. After analysis of the outcomes, it can be concluded that the effects of the safety stock levels and the order release strategy had a direct effect on the total production costs of the production process. This means that an optimal setting of these planning decision variables will ultimately reduce the total production costs. The direct effect of both lot size and dispatch rule is not proven within this research. In other words, the settings of both lot size and dispatch rules are dependent on the settings of safety stock levels and order release strategy in order to minimalize the total production costs. Figure 8 provides a new conceptual model on how the different planning strategies influence the total production costs of a production process.
Figure 8: conceptual model influence of different planning decision variables on total production costs One of the main practical objectives was to find an optimal planning strategy for KMWE to lower the total production costs of their production process without neglecting the delivery promises that were made towards the OEM. The most optimal setting consists of the initial setting of lot sizes, low safety stock levels, a LSF dispatch rule, and a one week periodic order release strategy. With this planning strategy, KMWE should deliver on average 98,74% of the total sales orders within the 28 days limit. If KMWE wants to increase this percentage at least 99%, the new planning strategy would have a total production cost of €497.770 instead of the €460.163 in the most optimal situation.
31
optimal with respect to delivery assurance. Moreover, the low safety stock levels do not necessarily lead to lower total production costs. The outcomes of the simulation model do not give a clear explanation about the origin of this phenomenon. The preliminary results on the two weeks order release strategy, the experiments that were excluded from this research due to extremely high total production costs and unacceptable sales order lead times, show that an sudden release of a reasonable amount of work orders result in a not properly working production process.
One of the main contributions of this research is that the effect of planning decision variables should always be considered together with the setting of other planning decision variables. The optimization of a single decision variable, without investigating other planning decision variables does not necessarily lead to a more preferable final outcome.
8 Limitations and assumptions
The following chapter will elaborate on the limitations, assumptions, and directions for further research of this research. The first section will provide information about the limitations. Subsequently the assumptions of the simulation model will be provided.
The majority of this research consisted of the design and development of a simulation model because there was no existing simulation model available. Together with the tight time schedule caused a significant limitation to the possibilities on behalf of the research itself. The application of more sophisticated methods could make the simulation model more lifelike. Moreover, since KMWE is located in the south of the Netherlands and the software program “Technomatix Plant Simulation”, that was used for the development of the simulation model, was only available on campus of the RUG, the travelling distance also became a big limitation. Also, the lack of programming knowledge made it impossible to construct a method that could prioritize work orders according to the selected dispatch rule, but also hurry work orders for which the stock level of its product family were depleted. This has caused simulation outcomes with some sales order lead times that are longer than would be the case in real life. With more possible programming time or more programming knowledge at the start of the research, the simulation model could become even more comprehensive. Although I strongly believe that the current model is perfectly capable of simulating lifelike situations with valid outcomes.
32
33
Bibliography
Abdi, R. 2012. Product Family formation and selection of reconfigurability using analytical network process. International Journal of Production Research. 50(17): 4908-4921
Agliari, A., Diligenti, M., & Zavanella, L. 1995. Variable priority dispatching rules: An analytical approach. International Journal of Production Economics. 41(1/3): 51-58
Al-Sayed, M., & Dugdale, D. 2016. Activity-based innovations in the UK manufacturing sector: Extent, adoption process patterns and contingency factors. British Accounting Review. 48(1): 38-58
Albey, E., & Bilge, U. 2011. A hierarchical approach to FMS planning and control with simulation-based capacity anticipation. International Journal of Production Research. 49(11): 3319-3342
Baraldi, E., Proença, J., Proença, T., & de Castro, L. M. 2014. The supplier’s side of outsourcing: Taking over activities and blurring organizational boundaries. Industrial Marketing Management. 43(4): 553-563
Boulaksil, Y., & Fransoo, J. 2009. Order release strategies to control outsourced operations in a supply chain. International Journal of Production Economics. 119(1): 149-160
Caramia, M., & Guerriero, F. 2008. A heuristic approach to long-haul freight transportation with multiple objective functions. Omega. 37(3): 600-614
Chang, T-M., & Yih, Y. 1994. Determining the numver of kanbans and lotsizes in a generic Kanban system: a simulated annealing approach. International Journal of Production Research. 32(8): 14
Chiou, C-W., Chen, W-M., & Wu, M-C. 2013. A combined dispatching criteria approach to scheduling dual flow-shops. International Journal of Production Research. 51(3): 927-939 Choi, S., & Noble, J. 2000. Determination of economic order quantities (EOQ) in an integrated
material flow system. International Journal of Production Research. 38(14): 3203-3226 Couillard, J. 1995. The role of project risk in determining project management approach. Project
Management Journal. 26: 3-15
Cuatrecasas-Arbós, L., Fortuny-Santos, J., Ruiz-de-Arbulo-López, P., & Vintró-Sanchez, C. 2015. Monitoring processes through inventory and manufacturing lead time. Industrial Management & Data Systems. 115(5): 951-970
De Treville, S., Bicer, I., Chavez-Demoulin, V., Hagspiel, V., Schürhoff, N., Tasserit, C., & Wager, S. 2014. Valuing lead time. Journal of Operations Management. 32(6): 337-346
Duncan, E., & Ritter, R. 2014. Next frontiers for Lean. McKinsey Quarterly. 2(2): 82-89
Gansterer M., Almeder, C., & Hartl, R., F. 2014. Simulation-based optimization methods for setting production planning parameters. International Journal of Production Economics. 151: 206-213
34
Kumar, S., & Krob, W. 2005. Supply chain management challenges for aerospace control technologies leader. Technovation. 25(1): 53-58
Land, M., Stevenson, M., & Thürer, M. 2014. Integrating load-based order release and priority dispatching. International Journal of Production Research. 52(4): 1059-1073
Meixell, M., & Norbis, M. 2008. A Review of the transportation mode choice and carrier selection literature. International Journal of Logistic Management. 19(2): 183-211
Mintzberg, H., & Quinn, J. B. 1996. The strategy process: concepts, contexts, cases. Harlow: Pearson Education Limited.
Molinder, A. 1997. Joint optimization of lot-sizes, safety stocks and safety lead times in an MRP system. International Journal of Production Research. 35(4): 983-994
Nicholas, J. 2011. Lean Production for Competitive Advantage: a comprehensive guide to lean methodologies and management practices. New York: Taylor & Francis Group.
Pattloch, M., Schmidt, G., & Kovalyov, M. 2001. Heuristic algorithms for lotsize scheduling with application in the tobacco industry. Computers and Industrial Engineering. 39(3-4): 235-253 Pettersen, J. 2009. Defining lean production: some conceptual and practical issues. TQM Journal.
21(2): 127-142
Pinedo, M. 2009. Planning and scheduling in manufacturing and services. Springer: New York.
Renna, P. 2015. Workload control policies under continuous order release. Production Engineering. 9(5): 655-664
Robinson, S. 2004. Simulation: the practice of model development and use. Chichester: John Wiley & Sons Ltd.
Roderick, L., Phillips, D., & Hogg, G. 1992. A comparison of order release strategies in production control systems. International Journal of Production Research. 30(3): 611-627
Rossetti, C. & Choi, T. 2005. On the dark side of strategic sourcing: Experiences from the aerospace industry. Academy of Management Executive. 19(1): 46-60
Ray, S., Gerchak, Y., & Jewkes, E. 2004. The effectiveness of investment in lead time reduction for a make-to-stock product. IIE Transactions 36(4): 333-344
Ruiz-Torres, A., & Mahmoodi, F. 2010. Safety stock determination based on parametric lead time and demand information. International Journal of Production Research. 48(10): 2841-2857 Sana, S. 2010. An economic production lot size model in an imperfect production system. European
Journal of Operational Research. 201(1): 158-170
Shah, R., & Ward, P. 2007. Defining and developing measures of lean production. Journal of Operations Management. 25(4): 785-805
Sinha, P., Whitman, L., & Malzahn, D. 2004. Methodology to mitigate supplier risk in an aerospace supply chain. Supply Chain Management: An International Journal. 9(2): 154-168
Slack, N., & Lewis, M. 2011. Operations Strategy. Harlow: Pearson Education Limited.
Stadtler, H. 1988. Medium term production planning with minimum lotsizes. International Journal of Production Research. 26(4): 553-567
35
dyadic multiple-case study. Industrial Marketing Management. 50: 128-141
Tersine, R., & Hummingbirg, E. 1995. Lead-time reduction: the search for competitive advantage. International Journal of Operations & Production Management. 15(2): 8-18
Thürer, M., Mark Silva, C., Land, M., & Fredendall, L. 2012. Workload control and order
release: A lean solution for make-to-order companies. Production and Operations Management. 21(5): 939-953Van der Zee, D-J. 2013. Family based dispatching with batch availability. International Journal of Production Research. 51(12) 3643-3653
Van Kampen, T., van Donk, D-P, & van der Zee, D-J. 2010. Safety stock or safety lead time: coping with unreliability in demand and supply. International Journal of Production Research. 48(24): 7463-7481
Yang, J. & Deane, R. 2002. A lotsize reduction model for just-in-time manufacturing systems. Integrated Manufacturing Systems. 13(7): 471-488
36
Appendix A – Overview of all product families
Id no Machine group Annual demand Processingtime Setup time Initial lot size Initial safety stock Value in €
37
Appendix B – Calculation unavailability operators
Machine group Total capacity Total occupation % occupation Remaining sec Qty orders Operator unavailability
after work order
38
Appendix C – Overview of all experiments
Experiment = Number of the experiment LS = Lot size setting: 1) initial lot size 2) low lot size SS = Safety stock setting 1) initial safety stock 2) low safety stock
3) high safety stock
DR = Dispatch rule 1) FCFS 2) LSF 3) MEF 4) SST 5) WSPT
OR = Order release strategy 1) continuous 2) one week periodic
Experiment LS SS DR OR Total interest costs
Total
surface treatment costs Total costs
40
Appendix D – SPSS outcomes
SPSS output independent samples t-test: lot sizeSPSS output independent samples Kruskal-Wallis test: safety stock
41
