The advantages of the approach are illustrated in a case study from the semiconductor manufacturing industry. Supply chains in this industry show divergent material flows. Silicon wafers are transformed into dozens of different variants of integrated circuits. It also shows flexible processes. The machines in this industry are highly capital intensive, leading to the necessity of providing the flexibility to process different products on the same resources. Hence, supply chains in this industry show the product and process flexibilities exploited by the approach. Furthermore, the production cycle times of four to six months are typically much longer than customer OLTs. Therefore, production is started based on aggregate demand forecasts, which, due to this long horizon, are subject to significant demand mix uncertainty. For a more detailed description of the characteristics of semiconductor manufacturing, the interested reader is referred to Mönch et al. (2013).
The method is compared to conventional order promising described in Section 5.2 and a CTP approach that uses the supply network planning process for real-time order promising.
Therefore, first an overview of the used framework for the numerical study is given in Section 5.5.1. Afterwards, the design of experiments is discussed in Section 5.5.2.
5.5.1 Framework
For the numerical study, the planning processes presented in Figure 7 are implemented. Every time unit, aggregated demand forecasts are netted with already realised orders from earlier periods by subtracting the order quantity from the forecast quantity in the period of the requested delivery date. Afterwards, the remaining forecast quantities are disaggregated. Here, the rule employed at the case company is implemented, where the historical proportions of demands on finished product level are used to generate the demand mix.
For supply network planning the approach presented in Section 2.2.2 is used. Promises of not yet delivered orders are updated, if the master production schedule allows earlier delivery or requires a postponement. After that, the production completion times of products are used to generate the ATP information.
After supply network planning, several orders from different customers realise. On order arrival, ATP is cumulated (Section 5.3) and order promising is executed. The model used for order promising is an adaptation of the approach shown in Section 2.3.3. The model, which is modified to allow order promising based on CATP quantities and promise orders based on
61 virtual per-unit profits 𝑝𝑟𝑜𝑓𝑡 of fulfilling an order in period 𝑡, decides on the CATP quantities consumed to promise an incoming customer order 𝑜. Equations (43) to (46) describe the model.
Maximise
𝑧 = ∑ 𝑝𝑟𝑜𝑓𝑡 𝑡𝑐𝑡, (43)
subject to
∑ 𝑐𝑡 𝑡≤ 𝑞𝑜, (44)
𝑐𝑡 ≤ 𝑐𝑎𝑡𝑝𝑡, ∀𝑡 ∈ 𝑇; (45)
𝑐𝑡 ≥ 0, ∀𝑡 ∈ 𝑇. (46)
The objective function (43) maximises the profit generated by fulfilling 𝑜. To set the per-unit profits 𝑝𝑟𝑜𝑓𝑡, Equations (47) and (48) are used, which make sure that on-time fulfilment of an order is most preferable and early fulfilment is preferred over late fulfilment. The parameters 𝑝𝑟𝑜𝑓0, 𝑞𝑜, and 𝑡𝑜 are defined as a base profit, the ordered quantity, and the requested delivery period of 𝑜, respectively.
𝑝𝑟𝑜𝑓𝑡= 𝑝𝑟𝑜𝑓𝑞 0
𝑜 (𝑇 − 𝑡𝑜+ 𝑡), ∀𝑡 ∈ 𝑇|𝑡 ≤ 𝑡𝑜. (47)
𝑝𝑟𝑜𝑓𝑡= 𝑝𝑟𝑜𝑓𝑞 0
𝑜 (𝑇 − 𝑡) ∀𝑡 ∈ 𝑇|𝑡 > 𝑡𝑜. (48)
Constraints (44) ensure that the consumed CATP quantities do not exceed the ordered quantity.
Constraints (45) state that the consumed CATP quantities must not exceed available CATP, which is provided by the ATP cumulation step described in Section 5.3. The conventional order promising approach described in Section 5.2 does not use the ATP cumulation step but promises orders based on finished product ATP of the requested product alone. In this case, the parameters 𝑐𝑎𝑡𝑝𝑡 in Constraints (45) equal the ATP quantities derived from the master production schedule. Constraints (46) are non-negativity constraints.
After order promising, the promised delivery quantities are determined using Equations (29) and (30) from Section 2.3.3. Finally, the ATP information is updated in an ATP consumption step.
In the CTP approach, the supply network planning model is used to generate the real-time order promises.
As performance indicators the robustness, late and early promised orders are used, which are the share of orders, whose initially promised delivery date equals, is later or earlier than their delivery date, respectively. A decrease in the share of late promised orders represents an increase of the accuracy of order promises. The indicators early promises and late promises are defined in Equations (49) and (50), in which 𝑂 is the set of all customer orders that realised over the horizon 𝑇𝑠 of the numerical study, 𝑡𝑜𝑝 is the promised delivery period for order 𝑜, 𝑡𝑜𝑑 is the realised delivery period for order 𝑜, and 𝑑𝑞𝑜𝑡 is the delivered quantity for order 𝑜 in period 𝑡.
The values of the indicators robustness and accuracy are derived as defined by Equations (33) and (34) in Section 2.3.4.
𝑒𝑎𝑟𝑙𝑦 𝑝𝑟𝑜𝑚𝑖𝑠𝑒𝑠 =∑𝑜∈𝑂,𝑡∈𝑇𝑠|𝑡𝑜𝑝 𝑑𝑞𝑜𝑡
<𝑡𝑜𝑑
∑𝑜∈𝑂𝑞𝑜 (49)
62 𝑙𝑎𝑡𝑒 𝑝𝑟𝑜𝑚𝑖𝑠𝑒𝑠 =∑𝑜∈𝑂,𝑡∈𝑇𝑠|𝑡𝑜𝑝 𝑑𝑞𝑜𝑡
>𝑡𝑜𝑑
∑𝑜∈𝑂𝑞𝑜 (50)
To be able to investigate the pure effects of demand mix uncertainty on the performance of the order promising approaches and eliminate all other sources of uncertainty typically appearing in a real world environment, the following assumptions are made:
Capacities and cycle times of processes are fixed, constant and deterministic.
No buffer stocks are considered.
There is no restriction on the availability of raw materials.
Customers do no cancel or reschedule orders.
Aggregated demand forecasts do not contain a forecast error.
5.5.2 Experimental design
The semiconductor industry shows divergent material flows and heterogeneous customer OLTs.
The raw materials are silicon wafers, while intermediate products are processed wafers or separated unfinished chips and finished products are the finished chips. The processes modelled in supply network planning are called bottlenecks. These are representations of machine groups which are typically constraining the capacity of a semiconductor supply chain. Two diode production lines of a large European company are investigated. The products have process cycle times between five and eight weeks.
Each cumulation logic is tested for every combination of levels of the factors supply chain flexibility, demand mix uncertainty, and customer OLT heterogeneity. For the factor cumulation logic, the four CATP types presented in Section 5.3 are implemented, the conventional ATP approach described in Section 5.2 and the CTP approach mentioned in Section 5.5.1.
For the factor supply chain flexibility, two product lines of the case company are investigated, which show low and high supply chain flexibility. To measure the supply chain flexibility of a product line an indicator defined in Chatterjee et al. (1984) as the average number of alternative parts that can be manufactured on a production sequence is used. The investigated product lines show flexibility values of 1.5 (low) and 4.5 (high). The capacity of each process is chosen such that the expected capacity utilization of each process equals 80%, which is the value used at the case company to plan production.
To represent demand mix uncertainty, first, two orders with a random customer OLT for each product and period are generated. In order to generate low, medium, or high demand mix uncertainty, one product within each product family is chosen randomly, to which the total demand of one, two, or three randomly chosen products of the same product family is assigned.
To choose products, a uniform distribution is used. The resulting demand mix uncertainty is measured in terms of the SMAPE. The described approach results in SMAPE values of 30% (low), 35% (medium), and 43% (high) for Product Line I and 35%, 52%, and 69%, for Product Line II.
Note that, even though the order stream is generated before each run, customer orders are not known to the demand fulfilment processes until they realise.
For the factor customer OLT heterogeneity, the levels MTO-skewed, ATO-skewed, MTS-skewed, and uniform are investigated. Note that customer OLTs remain heterogeneous for all levels. In the MTO-skewed case, the majority of orders arrives with an OLT greater than the production cycle time. This case represents businesses, in which the majority of the products produced are highly customer specific and costumers provide long term demand forecasts. For
63
Table 3: Design of experiments for CATP methodology
Factor Levels Count
Cumulation logic conventional, SUM, PROD, PROC, CUM, CTP 5 Supply chain flexibility low flexibility, high flexibility 2
Demand mix uncertainty low, medium, high 3
customer OLT heterogeneity MTO-skewed, ATO-skewed, MTS-skewed, uniform 4
Replications 10
1200 the level ATO-skewed, the majority of orders arrives before the final assembly step. Here, the majority of the products are not customer specific during production but in product assembly, so that customers place their orders with a customer OLT longer than the assembly cycle time.
The level MTS-skewed stands for environments, in which the majority of products are not customer specific and orders arrive with short customer OLTs. In the perfectly heterogeneous case, orders arrive with a uniformly distributed customer OLT. A planning horizon length of 13 weeks is used and the maximum and minimum customer OLTs are set to 13 and 0 weeks, respectively.
Ten replications for each combination of factors are generated and the replication length is set to 52 weeks. Table 3 summarizes the described design of experiments. The material flow diagrams of the investigated supply chains as well as graphical representations of the used customer OLT profiles can be found in Appendix B.