3.3 Input and output data
3.3.2 Key Performance Indicators
The evaluation of the stocking strategies and production release approaches in section 6.3 is done according to the α-service levels as well as the total costs (TC). The service level indicates how well we satisfy customer orders. That is, whether we deliver on time and can meet customer demand. The KPIs are evaluated over several weeks (t= 1...T) and various simulation runs (r = 1...R). The service levels are measured at the end of the supply chain, that is, each week tthe incoming orders and outgoing deliveries are compared. Notice, in the simulation model week tcorresponds to time period t.
α-service level.
The α-service level gives the probability that the incoming demand during period t is com- pletely met by on-hand inventory. It either becomes 0% when demand is not met completely or it becomes 100% when demand is met completely. Note, that backorders of previous weeks are not considered as part of the incoming demand for period t [60]. The α-service level is defined by [60]:
α-sevice level =P{demand during time period t≤on-hand inventory (3.1)
at beginning of time period t} (3.2)
It is implemented in the simulation model by aggregating over all sales products (p = 1...P), weeks (t= 1...T), and replications (r = 1...R):
α-sevice level = PR r=1 PP p=1 PT t=1αrpt R∗P ∗T (3.3)
CHAPTER 3. SIMULATION MODEL
Next to theα-service level, the simulation model also provides theβ- andγ-service level. For an detailed explanation we refer toAppendix Dsince we do not use them to evaluate the approaches. Nevertheless, they may be used in addition to the α-service level.
Costs.
Next to achieving a high service level, we aim to keep the total costs considerable low. TheTC are the fixed capital costs bind in products. It is calculated by the weighted average cost of capital (wacc) times the value of the WIPand the stock locations:
T C= wacc * (value of WIP + value of stock points) (3.4) In the simulation model the calculation of the costs is divided into two task: the distri- bution of the total bound capital along the facilities and the weekly calculation of the total value in the supply chain [13].
The distribution of the costs along the facilities is done top down. First, costs are split proportionally between front end(costF E) andback end(costBE) according to the ‘front end cost share’ and then further divided between the facilities. The costs are based on the cost per unit (costunit) which is defined by the difference between the average selling price (asp) and its profit margin:
costunit= (1−margin)asp (3.5)
costF E =costunit∗costshareF E (3.6)
costBE =costunit∗(1−costshareF E) (3.7) (3.8) The costs at the facilitiesFABand sort in front end as well as atassembly (ASSY)and test in back end are assigned according to the cycle time (CT) of each processing step denoted by CTprocessing step. Moreover, the costs of the fabrication are split between fabrication 1 (FAB1), incurred before the product enters the master storage, and fabrication 2 (FAB2), incurred after the master storage and before the sort step:
Costs in front end:
costF AB=costF E CTF AB/CTF E
(3.9)
costF AB1=costF AB CTF AB1/CTF AB
(3.10)
costF AB2=costF AB CTF AB2/CTF AB
(3.11)
costSORT =costF E CTSORT/CTF E
(3.12) Costs in back end:
costASSY =costBE CTASSY/CTBE
(3.13)
costT EST =costBE CTT EST/CTBE
(3.14) The second tasks considers the weekly calculation of the value in the supply chain. It is calculated by the average value of WIP and inventory at all facilities and stock points denoted by valueSC. The WIP value at each facility is calculated as the WIP units times the average cost of each unit at the respective facility. The same procedure is done for the inventory value:
CHAPTER 3. SIMULATION MODEL
the total stock units times the cost of the units at the respective stocking point. The costs at the stock points are the accumulated costs of the previous facilities. Thetotal costs(TC) are the value of goods in the supply chain times the the weighted average cost of capital(wacc), which describes the rate of return that could have been earned when investing elsewhere. We define the T C over all replications and weeks as follows:
T C= PR
r=1PTt=1wacc∗valueSCRT
R∗T (3.15)
Note, that we do not consider idle costs as input of the total costs since we concentrate on the trade off between keeping enough products in stock at the various locations and the costs of storing these products.
3.4
Conclusion
To improve the supply chain planning process we use discrete event simulation since it is able to capture complex relations between processes. The existing model represents the supply chain of Infineon with its plan and make process. The plan functions are responsible for starting production whereas the make functions concern the processing steps. This model can be used to study various stocking strategies and production release approaches. The evaluation of the various procedures is done by considering the respective service level and costs. However, before we use the model for our simulation study we need to parametrize it according to the situation of the two exemplary basic types. This includes to generate demand similar to the observed one. In chapter 4we study how we can assess the fit between the generated and observed demand.
Chapter 4
Literature review
The aim of this thesis is to improve stocking levels of two basic types as well as determining the release quantity in front end by using discrete event simulation. In order to receive precise results, the demand arrival process has to generate demand data that captures the stochastic behaviour of the observed demand data. The closer the generated demand data is to the observed data the more accurate are the simulation results. Thus, we are interested in a measure that assesses the fit between the generated and observed data. In the literature, there exist various measures to compare time series. One can compare two time series using forecast accuracy measures explained insection 4.2. Forecast accuracy measures evaluate the residual, also called error term, between forecasted and observed values. Another way of evaluating the similarity between two time series are time series similarity measures, which we elaborate insection 4.3. Similarities can be based on the distance, on features of the two series, or on the shape of the series. Last, insection 4.4we consider hypothesis tests or also called ‘goodness of fit’ tests to assess the fit between two data series. One can distinguish these tests between one- sample and two-sample tests. One-sample tests evaluate whether an empirical distribution is drawn from some known distribution whereas two-sample tests evaluate whether two empirical distributions are drawn from the same unknown underlying distribution. In this case, we speak of consistent data. We are interested in the two-sample tests to compare the generated and observed demand and evaluate whether they are consistent. Before we discuss the several methods, we give some theoretical background in section 4.1 on how demand data can be classified, we provide definitions for time series as well as stochastic processes, and introduce two basic concepts of forecasting demand.