3.3 Problem knot
3.3.3 Phasing out not started on time
When the phasing out process is not started on time, there is not enough time for the stock to sell out or at least decrease to an acceptable level, based on the demand process. There are three causes for this problem, namely: the collection end time is not known, the collection end time is not monitored, and it is not known when to switch to PS. To assure that the phasing out process, i.e., switch the MRP type to PS, is started on time, it must be known when to start the phasing out process. This is mainly determined by the collection end time. When the end time is known, but not monitored, the decision whether to switch to PS or not is prompted. Finally, when both the collection end time is known and monitored, but no criteria regarding the MRP type change are stated (e.g., switch to PS two years before collection end time), the phasing out process is still not started on time. Another complication of this problem is that when the planners cannot see the βswitch to PS dateβ, they continue to order according to the current MRP type policy, while it can be sensible to postpone an order that is prompted a month before the MRP switch date. An example of this problem can be seen in Figure 3-4, where an order, that was placed end 2010 under PR, was delivered when the article was already switched to PS. To reduce the obsolete risk, actions such as postponing the order or ordering a smaller but costlier run could be have undertaken, if, however, it was known when the article would be switched to PS.
3.4
C
ONCLUSIONIn this chapter, the scope is quantified. It has been shown that the decorative window covering products have the highest impact on the stock reservations, mainly caused by the product lines Roller Blinds, Venetian Blinds, and PlissΓ© Shades. Next to that, only make to stock items are responsible for stock reservations. With this scope, the research focusses on 65% of the total reservations made. Following, a problem knot was made to identify the main causes of the high obsolete costs. These are a high minimum order quantity, amongst others caused by an inaccurate forecast, faulty (production/purchase) orders, and the fact that the phasing out process is not started on time. In the next chapter, the literature review regarding these subjects is presented.
PR PI PS PR PU PO 0 200 400 600 800 1000 1200 1400 1600 Qu an tity in m ete rs
Swing 1.98 m Pink/Orange
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LITERATURE REVIEW
In this chapter the relevant literature is described. There are four main categories introduced, namely demand uncertainty (Section 4.1), lot sizing (Section 4.2), intermittent demand (Section 4.3), and obsolescence (Section 4.4).
4.1
DEMAND UNCERTAINTY
Inventory control takes an important part in production systems. An improper policy of inventory control leads either to shortages, which generate expenses, or to needless stocks, which decrease capital assets (Dolgui & Prodhon, 2007). This is especially true when uncertainties occur. Koh, Saad, & Jones (2002) classify them in two main categories: input (as external supply or demand reliability) and process (as machine breakdown, etc.). To minimize the influence of these uncertainties, enterprises implement safety stocks, but stock is expensive. So the problem is to control inventories and to avoid stockout while maintaining a high level of service (Dolgui & Prodhon, 2007).
The safety stock is calculated in the following way (Fotopoulos, Wang, & Rao, 1988): πΊπΊπΊπΊ=π§π§πΌπΌΓοΏ½π π (πΏπΏ)πππ·π·2+ (π π (π·π·))2πππΏπΏ2 Where: πΊπΊπΊπΊ=πΊπΊπππππ π π π πΌπΌπΊπΊπ π πΊπΊπππ π π§π§πΌπΌ=πππππΌπΌπ π πΊπΊπΊπΊπ π πΊπΊπππ π βπ π πππΊπΊπΊπΊπππππππππ π πππ π πππππ π πππΌπΌπ π πΉπΉπππΊπΊπ π πΊπΊπππππ π π π πππΊπΊπππΊπΊπππΊπΊπ π πΊπΊπΌπΌπππππ π πππ π πΌπΌπ π πππΌπΌ π π (πΏπΏ) =π π πΉπΉπππ π πππ π π π πΉπΉπππ π πππΉπΉπ π πππππ π πππ·π·2=πΌπΌπππΊπΊπππππππππ π πΊπΊπππΉπΉπ π πππππππΉπΉ π π (π·π·) =π π πΉπΉπππ π πππ π π π πΉπΉπΉπΉπ π πππππππΉπΉ πππΏπΏ2=πΌπΌπππΊπΊπππππππππ π πΊπΊπππππ π πππΉπΉπ π πππππ π
A reorder point is than calculated in the following way: π π π π ππ=π π (πΏπΏ) Γπ π (π·π·) +πΊπΊπΊπΊ
Demand uncertainty is linked to the predictability of the demand for the product (Lee, 2002). Lee (2002) also states that when a company faces the pressure of excessive inventory, degraded customer service, escalating costs, its supply chain is out of control. A simple but powerful way to characterize a product when seeking to devise the right supply chain strategy is the βuncertainty frameworkβ (see Figure 4-1).
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Figure 4-1: Uncertainty framework (Lee, 2002)
Demand for functional products is much easier to forecast, while demand for innovative products is highly unpredictable. Due to the differences in product lifecycle and the nature of the product, functional products tend to have lower product profit margins, but the cost of obsolescence is low; whereas innovative products tend to have higher product profit margins, but the cost of obsolescence is high. Figure 4-2 shows the two kinds of strategies that improve supply chain performance through uncertainty reductionβdemand uncertainty reduction and supply uncertainty reduction.
Figure 4-2: Uncertainty reduction strategies (Lee, 2002)
In many cases, the bullwhip effect is one of the causes of demand uncertainty. The bullwhip effect is an amplification of order variability as one goes upstream along a supply chain (Lee, Padmanbhan, & Whang, 1997). Only through information sharing and tight coordination can one regain control of supply chain efficiency. Sharing of demand information and synchronized planning across the supply chain are crucial for this purpose. Lee (2002) states that given the different nature of demand and supply uncertainties of different products, different supply chain strategies are needed for different products. With highly unpredictable demand, excessive inventory may result. The cost of inventory for innovative products can be significant, since the product lifecycles are short. Companies with such products should pursue strategies with a responsive supply chain. Rather than focusing on accurate
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forecasting and inventory planning, companies with a very stable process and product technology can make use of the concept of postponement to pursue aggressive build to order strategies.
4.2
L
OT SIZINGAccording to Dolgui & Prodhon (2007) it is often better to group orders together, instead of ordering by a lot-for-lot rule (LFL), i.e., to order only the net needs for a single period. The LFL permits reducing inventory but does not take into consideration economic aspects and organizational constraints. Sometimes, the ordering cost is very expensive in relation to the holding cost, so lot- sizing is needed. The principal lot-sizing rules are:
- The economic order quantity (EOQ);
- The periodic order quantity (POQ);
- The Wagner-Whitin algorithm (WW).
According to Winston (2003) the assumptions of the EOQ model are:
- Demand is deterministic and occurs at a constant rate;
- If an order of any size (say, q units) is placed, an ordering and setup cost K is incurred;
- The lead time for each order is zero;
- No shortages are allowed;
- The cost per unit/year of holding inventory is h;
- D is the annual demand.
The economic order quantity is: ππβ=οΏ½2πΎπΎπ·π·
β
This function minimizes the total annual costs which consists of the annual costs of placing orders, annual purchasing costs, and annual holding costs. From the EOQ, it can be deduced the POQ: an optimal constant time between orders is calculated, and from the optimal constant time, the necessary quantity to order for each period is obtained (Dolgui & Prodhon, 2007). The Wagner- Whitin algorithm is a procedure that determines the minimal order cost for a dynamic deterministic demand without capacity constraint. The classical lot sizing model of Wagner and Whitin and its extensions deal with the problem of finding the optimal replenishment plan for an item under the assumption that inventory can be carried for an indefinite number of periods. This assumption cannot be justified if one considers potentially obsolete or perishable product (Jain & Silver, 1994). Dolgui & Prodhon (2007) conclude that with demand and lead time uncertainties, the relative efficiency of lot-sizing rules performances is not stable.
The materials managers of manufacturing firms are facing the task of replenishing high quality components in the right quantities, at the right time, and at the right price (Benton & Park, 1996). Large orders usually lower a unit purchase price through quantity discounts and enhance customer service level as well, but they result in increased inventory cost. Therefore, the buyers should consider the tradeoffs between the costs and the benefits resulting from larger orders and come up with reasonable purchasing decisions (Benton & Park, 1996). Although the recent purchasing strategy has focused on how to acquire flexible resources and high quality components to gain competitive advantages in the current market, lowering cost is still one of the critical competitive priorities to win the market. Consequently, reduction of purchasing cost will be a key concern to the materials managers.
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Many companies face the challenge of managing inventory that has the potential to suddenly become obsolete (Emsermann & Simon, 2007). These circumstances render traditional inventory analysis unsuitable for balancing reordering costs with costs of overstocking. Emsermann & Simon (2007) consider the problem of determining the optimal ordering and reordering policy for an inventory in which the entire stock will simultaneously become obsolete at some random future time. They study a continuous-review and stochastic-demand obsolescence inventory model, and calculate its optimal control policy. Emsermann & Simon (2007) show that when the number of weeks since the last obsolescence of a the researched product increases, the optimal order quantity decreases.
4.3
I
NTERMITTENT DEMANDSyntetos, Boylan & Croston (2005) has proposed the following categorization of demand patterns.
Figure 4-3: Demand pattern categorization matrix (Syntetos et al., 2005)
In the figure above, demand variability is expressed with CV2, which is the squared coefficient of
variation of demand sizes. The demand interval is expressed with p, which is the average inter- demand interval expressed in number of forecast review periods.
Intermittent demand is random demand with significant periods of no demand activity (Silver, 1981). Demand that is intermittent is often also βlumpyβ, meaning that there is great variability among the nonzero values (Willemain, Smart, & Schwarz, 2004). According to Willemain et al. (2004) accurate forecasting of demand is important in inventory control, but the intermittent nature of demand makes forecasting especially difficult. Intermittent demand is a highly recognized challenge and many models have been created to face this challenge. Three promising models are explained below.
4.3.1 Model of Croston
Exponential smoothing is frequently used for forecasting demand in a routine stock control system when large numbers of products may be involved (Croston, 1972). It has be shown that for some low and intermittent demand items the stock levels of the system appeared to be excessive. Croston (1972) proposes the following model:
33 | M a s t e r T h e s i s β M . K . v a n d e r H o e v e n πππ‘π‘:π·π·π π πππππππΉπΉπππΊπΊπΊπΊπππππππ π π π πππππππππ π πΊπΊπππΊπΊπΉπΉπ π . ππβ² π‘π‘:π π πΊπΊπ π πππππππ π π π πΊπΊπππππ π πππππΉπΉπ π πππππππΉπΉπππ π πΊπΊπππ π πΊπΊπππΊπΊπΉπΉπππππΉπΉπ π πππππππ π πΊπΊπππΊπΊπΉπΉπ π πππΊπΊπΊπΊπππ π πΊπΊπππΊπΊπΉπΉπ π + 1 π§π§β² π‘π‘:π π πΊπΊπ π πππππππ π π π πΊπΊπππππ π πππππΉπΉπ π πππππππΉπΉπΊπΊπππ§π§π π πππππππ π πΊπΊπππΊπΊπΉπΉπ π . πππ‘π‘:π΄π΄πππ π π π πππππΉπΉπ π πππππππΉπΉπππππ π π π πΊπΊπΌπΌπππππππππππ π πΊπΊπππΊπΊπΉπΉπ π . ππβ²π‘π‘:π π πΊπΊπ π πππππππ π π π πΊπΊπππππ π πππππΉπΉπ π πππππππΉπΉπππππ π π π πΊπΊπΌπΌπππππππππππ π πΊπΊπππΊπΊπΉπΉπ π . πΌπΌ,π½π½:πππππΊπΊπΊπΊπ π βπππππππππΊπΊπππΊπΊπ π πππππ π πΊπΊ (0β€ πΌπΌ,π½π½ β€1).
The model: Explanation:
πΌπΌπππππ‘π‘ = 0 π π βπ π ππ If there is no demand in period t then
ππβ²π‘π‘ =ππβ²π‘π‘β1 Estimate of mean demand interval stays the same
π§π§β²π‘π‘ =π§π§β²π‘π‘β1 Estimate of mean demand size stays the same
ππβ²π‘π‘ =ππβ²π‘π‘β1 Estimate of mean demand per period stays the same
πΌπΌπππππ‘π‘ > 0 If there is demand in period t then
ππβ²π‘π‘ =ππβ²π‘π‘β1+π½π½(πππ‘π‘β ππβ²π‘π‘β1) Update estimate of mean demand interval by smoothing constant Ξ²
π§π§β²π‘π‘ =π§π§β²π‘π‘β1+πΌπΌ(πππ‘π‘ β π§π§β²π‘π‘β1) Update estimate of mean demand size by smoothing constant Ξ±
ππβ²π‘π‘ =π§π§β²π‘π‘/ππβ²π‘π‘ Update mean demand / period with mean demand size and interval
Crostonβs estimator relies upon separate exponentially smoothed estimates of the interval between consecutive demands and the size of demands. The estimates are updated only in periods with positive demand.
4.3.2 Model of Willemain et al.
The model of Willemain et al. (2004) adopts bootstrapping to forecast intermittent data. A summary of the steps in the bootstrap approach is:
Step 0: Obtain historical demand data in chosen time buckets (e.g. days, weeks, months). Step 1: Estimate transition probabilities for two-state (zero vs. nonzero) Markov model.
Step 2: Conditional on last observed demand, use Markov model to generate a sequence of zero/nonzero values over forecast horizon.
Step 3: Replace every nonzero state marker with a numerical value sampled at random with replacement from the set of observed nonzero demands.
Step 4: Jitter the nonzero demand values.
Step 5: Sum the forecast values over the horizon to get one predicted value of lead time demand. Step 6: Repeat step 2β5 many times.
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4.3.3 Model of Teunter et al.
The model of Teunter et al. (2011) (TSB, after Teunter, Syntetos, and Babai) links the forecasting of intermittent demand to obsolescence. The method uses separate simple exponentially smoothed estimates of the demand probability and the demand size. The estimate of the probability of occurrence is updated every time period. The estimate of the demand size is only updated at the end of periods with positive demand (Teunter, Syntetos, & Zied Babai, 2011).
Teunter et al. (2011) introduces the following notation: πππ‘π‘:π·π·π π πππππππΉπΉπππΊπΊπΊπΊπππππππ π π π πππππππππ π πΊπΊπππΊπΊπΉπΉπ π . ππβ² π‘π‘:π π πΊπΊπ π πππππππ π π π πΊπΊπππππ π πππππΉπΉπ π πππππππΉπΉπππ π πΊπΊπππ π πΊπΊπππΊπΊπΉπΉπππ π π π βπ π π π πππΉπΉπΊπΊπππππ π πΊπΊπππΊπΊπΉπΉπ π πππΊπΊπΊπΊπππ π πΊπΊπππΊπΊπΉπΉπ π + 1. π§π§π‘π‘:π΄π΄πππ π π π πππππΉπΉπ π πππππππΉπΉπΊπΊπππ§π§π π πππππππ π πΊπΊπππΊπΊπΉπΉπ π . π§π§β² π‘π‘:π π πΊπΊπ π πππππππ π π π πΊπΊπππππ π πππππΉπΉπ π πππππππΉπΉπΊπΊπππ§π§π π πππ π π π βπ π π π πππΉπΉπΊπΊπππππ π πΊπΊπππΊπΊπΉπΉπ π . πππ‘π‘:π·π·π π πππππππΉπΉπΊπΊπππππ π πΊπΊπ π πππππ π πππππΉπΉπππππππ π πΊπΊπΊπΊπππΊπΊπΊπΊπππ π πΊπΊπππΊπΊπΉπΉπ π ,πΊπΊπΊπΊπ π βπππ π : πππ‘π‘ =οΏ½0 1 πΊπΊπ π βπ π πΊπΊπππππΊπΊπ π πππππΉπΉπ π πππππππΉπΉ πΊπΊπππππ π πΊπΊπΊπΊπππ π π π πππππ π π π (ππ.π π .πππ‘π‘ > 0) ππβ²π‘π‘:π π πΊπΊπ π πππππππ π π π πΊπΊπππ π βπ π πππΊπΊπΊπΊπππππππππππππ π πΌπΌπΊπΊπππππΉπΉπ π πππππππΉπΉπΊπΊπππππ π πΊπΊπΊπΊπ π πππππ π πππ π π π βπ π π π πππΉπΉπΊπΊπππππ π πΊπΊπππΊπΊπΉπΉπ π . πΌπΌ,π½π½:πππππΊπΊπΊπΊπ π βπππππππππΊπΊπππΊπΊπ π πππππ π πΊπΊ (0β€ πΌπΌ,π½π½ β€1).
The method: Explanation:
πΌπΌπππππ‘π‘ = 0 π π βπ π ππ If there is no demand in period t then
ππβ²
π‘π‘ =ππβ²π‘π‘β1+π½π½οΏ½0β ππβ²π‘π‘β1οΏ½ Negatively update the chance of demand with smoothing constant Ξ²
π§π§β²
π‘π‘ =π§π§β²π‘π‘β1 Estimate of mean demand size stays the same
ππβ²
π‘π‘ =ππβ²π‘π‘π§π§β²π‘π‘ Estimate of mean demand is estimate of demand size times chance
πΌπΌπππππ‘π‘ = 1 π π βπ π ππ If there is demand in period t then
ππβ²
π‘π‘ =ππβ²π‘π‘β1+π½π½οΏ½1β ππβ²π‘π‘β1οΏ½ Positively update the chance of demand with smoothing constant Ξ²
π§π§β²
π‘π‘ =π§π§β²π‘π‘β1+πΌπΌ(π§π§π‘π‘β π§π§β²π‘π‘β1) Update estimate of mean demand size with smoothing constant Ξ±
ππβ²
π‘π‘ =ππβ²π‘π‘π§π§β²π‘π‘ Estimate of mean demand is estimate of demand size times chance