Demand planning and supply network planning

The first step towards meeting the ultimate goal of supply chain management, i.e. to increase customer service levels, is to anticipate future customer demands as accurately as possible.

Then, subsequent planning activities are able to prepare the provision of supply in a way that customer orders can be fulfilled as close to their requested delivery date as possible while the resources of the supply chain are utilized efficiently (see e.g. Chen et al. 2007). Therefore, demand planning aims at predicting future customer demand as accurately as possible.

Furthermore, safety stock levels are planned to buffer uncertainties in this forecast (see. e.g.

Kilger and Wagner 2015). Accurately planned demand enables smooth production and procurement planning, because sudden changes in production and procurement plans due to unforeseen lacks or peaks of demand are prevented. This, in turn, leads to reduced cost for inventory and idle capacity (Vogel 2014).

There are three types of techniques to generate the demand forecast: statistical, judgemental, and collaborative forecasting (Kilger and Wagner 2015). Statistical techniques are solely using historical data. The data is analysed by time-series based or causal approaches in order to predict the future development of demands. Judgemental forecasting includes additional information, e.g. on future one-time events, into the forecasting process in order to derive a more accurate forecast. Collaborative forecasting extends the judgemental forecasting

25 approach by involving several internal or external partners into the forecasting process and combining their forecasts and views into one aligned demand forecast. For a deeper discussion of these techniques, the reader is referred to Hanke and Wichern (2008), Makridakis et al.

(1998), and Tempelmeier (2008).

The accuracy of demand forecasts is measured by quantifying the forecast error after demand realisation. This is determined by evaluating the difference between the volumes of the forecasted and the realised demands. When analysed over a longer time period, the accuracy of a forecast also quantifies the uncertainty contained in it.

A multitude of measures exists to measure the forecast error. Some of them are the mean error, the mean absolute deviation, the mean squared error, the root mean squared error, and the mean absolute percentage error (Meyr 2012). For a broad overview of measures and a discussion of the advantages and disadvantages, the interested reader is referred to Kilger and Wagner (2015).

According to Fildes and Kingsman (2011) the forecast error is composed of a random and a systematic component. The latter is called bias and refers to a constant over- or underestimation of future demands, which can result from rationing gaming (see Lee et al.

2004).

Although there are many other purposes for which the results of demand planning are used (e.g. financial forecasting, accounting, marketing, or logistic network planning), this thesis focusses on the interactions of demand planning with the supply network planning process.

Taking already known future and historical customer orders as well as ADI from customers into account, demand forecasts are generated on aggregated levels, like product family per customer segment. Supply network planning, however, oftentimes matches available resources with demands on finished product (also called stock keeping unit) level (Mentzer and Bienstock 1998). Consequently, the demand forecasts have to be disaggregated for supply network planning purposes. In most industrial settings, this disaggregation is done according to the historical share of individual finished products sold in one product family as well as the current share of products in ADI and already received, but not yet delivered orders.

The disaggregation of demand forecasts causes a second type of uncertainty, which in this thesis is called demand mix uncertainty. It is defined as the uncertainty of the demand forecast with regards to the ratio of the individual product volumes, when the total demand of the product family is given.

In Chapters 4 and 5, the symmetric mean absolute percentage error (SMAPE) (see e.g.

Armstrong 1985 or Ott et al. 2013) is used to determine the error of a forecast. It is chosen since it is widely used in the industry. The main reason for its use is its ease of implementation. It does not result in infeasibilities if there is no realised demand but a forecast or no forecast but final demand in certain time periods.

2.2.2 Supply network planning

In order to synchronize and coordinate the flow of materials between suppliers, production sites, warehouses, and customers, supply network planning balances demand with supply chain resources (see e.g. Albrecht et al. 2015). The process usually considers procurement, manufacturing, and deployment lead times and resource capacity constraints. It trades off the cost for additional in-house or external capacity, capacity usage, stock holding, transportation

26 between sites, and late or no fulfilment of demand for the entire supply chain. Supply network planning hence comprises the planning activities, which are called master planning in Figure 2.

In industrial settings, the mathematical models used for supply network planning are usually deterministic and aim at cost minimisation or profit maximisation (Stadtler 2012). Because of the heterogeneity of customer OLTs in industrial practice, companies usually plan their production to the finished product storage location. Otherwise, if production was planned only to an intermediate product storage location, orders coming in with short lead times could not be fulfilled on time.

For a basic linear programming model, the reader is referred to Fleischmann and Meyr (2003). In the following, a supply network planning model is presented, which is based on Leachman (1993). The model, which is used in Chapter 5, decides on the production quantities 𝑦_𝑗𝑔^′_𝑔𝑡 for production of product 𝑔 ∈ 𝑀 ∪ 𝑃 started in period 𝑡 ∈ 𝑇 with predecessor product 𝑔^′∈ 𝑅 ∪ 𝑀 on resource 𝑗 ∈ 𝐽. The sets 𝑅, 𝑀, and 𝑃 are defined as the sets of raw materials, intermediate products, and finished products, respectively. For better readability 𝜃 ∈ Θ is defined as an existing combination of 𝑗, 𝑔^′, and 𝑔. The combinations 𝜃 are characterized by a resource consumption factor 𝑎_𝜃, a bill of material (BOM) coefficient 𝑛_𝜃, and cycle time 𝑐𝑡_𝜃. The BOM coefficient indicates the number of units of products 𝑔 that are produced from on unit of product 𝑔^′ on resource 𝑗. The subsets Θ_𝑗, Θ_𝑔, and Θ_𝑔^′ are defined as the sets of combinations 𝜃 containing process 𝑗, 𝑔 as produced product, and 𝑔 as transformed product, respectively. The model further decides on the delivery quantities 𝑥_𝑑𝑡 used to fulfil demand 𝑑 ∈ 𝐷 in period 𝑡.

Because of the heterogeneous customer OLTs in industrial environments, the set 𝐷 consists of both customer orders and demand forecasts. Equations (1) to (8) describe the production planning model.

Maximise

𝑧 = ∑ ∑ 𝜌_{𝑑 𝑡 𝑑𝑡}𝑥_𝑑𝑡− 𝜉^𝑝∑ ∑ 𝑦_{𝜃 𝑡 𝜃𝑡}− 𝜉^𝑖∑ ∑ 𝑖𝑛𝑣_{𝑔 𝑡 𝑔𝑡}, (1) subject to

∑ 𝑥_{𝑡 𝑑𝑡} ≤ 𝑞_𝑑, ∀𝑑 ∈ 𝐷; (2)

𝑖𝑛𝑣_𝑔⁻¹+ ∑_𝜏≤𝑡∑_{𝜃∈Θ𝑔}𝑛_𝜃∙ 𝑦_{𝜃𝜏−𝑐𝑡𝜃} = 𝑖𝑛𝑣_𝑔𝑡+ ∑_𝜏≤𝑡∑_{𝑑∈𝐷𝑔}𝑥_𝑑𝜏, ∀𝑔 ∈ 𝑃, 𝑡 ∈ 𝑇; (3) 𝑖𝑛𝑣_𝑔⁻¹+ ∑_𝜏≤𝑡∑_{𝜃∈Θ𝑔}𝑛_𝜃∙ 𝑦_{𝜃𝜏−𝑐𝑡𝜃} = 𝑖𝑛𝑣_𝑔𝑡+ ∑_𝜏≤𝑡∑_{𝜃∈Θ𝑔}^′ 𝑦_𝜃𝜏, ∀𝑔 ∈ 𝑀, 𝑡 ∈ 𝑇; (4)

∑_{𝜃∈Θ𝑗}𝑎_𝜃 ∙ 𝑦_𝜃𝑡≤ 𝑐_𝑗𝑡, ∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇; (5)

𝑦_𝜃𝑡 = 𝑌_𝜃𝑡, ∀𝜃 ∈ Θ, 𝑡 ∈ 𝑇^{ℎ𝑖𝑠𝑡}; (6)

𝑦_𝜃𝑡 ≥ 0, ∀𝜃 ∈ Θ, 𝑡 ∈ 𝑇; (7)

𝑥_𝑑𝑡 ≥ 0, ∀𝑑 ∈ 𝐷; 𝑡 ∈ 𝑇. (8)

The objective function (1) maximises profits calculated from the per-unit inventory holding cost 𝜉^𝑖, the per-unit production cost 𝜉^𝑝, and the per-unit revenues 𝜌_𝑑𝑡 generated from fulfilling one unit of demand 𝑑 in period 𝑡. Here, 𝑖𝑛𝑣_𝑔𝑡 is the inventory of product 𝑔 held at the end of period 𝑡. Constraints (2) ensure that the delivered quantity does not exceed the demand quantity 𝑞_𝑑. Constraints (3) and (4) are inventory balance constraints with the starting inventory 𝑖𝑛𝑣_𝑔⁻¹ of product 𝑔 and the set 𝐷_𝑔 of all demands requesting product 𝑔. Constraints (5) are capacity constraints. Constraints (6), in which 𝑇^{ℎ𝑖𝑠𝑡} contains all time periods in the past, fix 𝑦_𝜃𝑡 to 𝑌_𝜃𝑡,

27 which is the production quantity started on combination 𝜃 in period 𝑡 ∈ 𝑇^{ℎ𝑖𝑠𝑡} not yet being finished. Constraints (7) and (8) are non-negativity constraints.

The per-unit revenues 𝜌_𝑑𝑡 are determined by Equations (9) and (10), which make sure that on-time fulfilment of demands is most preferable and early fulfilment is preferred over late fulfilment. The parameters 𝜌_𝑑, 𝑞_𝑑, and 𝑡_𝑑 are defined as a base revenue, the demand quantity, and the due date of 𝑑, respectively.

𝜌_𝑑𝑡= ^𝜌_𝑞^𝑑

𝑑(|𝑇| − 𝑡_𝑑+ 𝑡), ∀𝑑 ∈ 𝐷, 𝑡 ∈ 𝑇|𝑡 ≤ 𝑡_𝑑. (9) 𝜌_𝑑𝑡 = ^𝜌_𝑞^𝑑

𝑑(|𝑇| − 𝑡) ∀𝑑 ∈ 𝐷, 𝑡 ∈ 𝑇|𝑡 > 𝑡_𝑑. (10)

The result of the supply network planning process is the master production schedule which contains the product quantities to be produced or procured, which must be made available at a certain storage location at a certain point in time. The master production schedule serves as the main input for the subsequent production planning and demand fulfilment processes (Vogel 2014). For demand fulfilment, the information contained in the master production schedule is translated into the so-called ATP information, which defines the quantities of current and future product supply that can be used to fulfil incoming customer orders. For example, the ATP quantities 𝑎𝑡𝑝_𝑔𝑡 for product 𝑔 becoming available in time period 𝑡 can be calculated using Equations (11), in which 𝐹_𝑔 is defined as the subset of 𝐷 containing only demand forecasts for product 𝑔.

𝑎𝑡𝑝_𝑔𝑡 = ∑_{𝑑∈𝐹𝑔}𝑥_𝑑𝑡, ∀𝑔 ∈ P, 𝑡 ∈ 𝑇. (11)

For a discussion of other types of ATP and their generation from the master production schedule, the reader is referred to Geier (2014).

As mentioned above, supply network planning in industrial environments oftentimes matches capacities with demand on finished product level. Therefore, aggregated demand information on product family level, which is provided by demand planning, needs to be disaggregated, leading to uncertainty of demand regarding the product mix. Obviously, this uncertainty is carried on in the ATP information generated from the master production schedule. If customer orders realise that deviate from the demand forecast, the following supply network planning run exploits flexibilities in the supply chain to change the master production schedule and meet requested delivery dates of the customers. Order promises to the customers are typically updated according to the result of supply network planning. Hence, demand mix uncertainty endangers the robustness of real-time order promises, which are generated based on ATP information.