Demand Forecasts, Stocks and Supply

The following equations representation and formalise an intuitive ordering policy based on the principles discussed by (Moseklide et al., 1991). First of all the orders must be non-negative, i.e.:

(1) where is the new order and IOt denotes the indicated order rate and the subscript t indicates that the value of the variable is considered at time t.

With the exception of the Manufacturing agent, forecasts for each SKU are generated by the replenishment system based on each agent needing to adjust their demand projections in each period. The forecasting technique considers the trend as well as the series average ignoring the trend will cause the forecast to always be below (with an increasing trend) or above (with a decreasing trend) actual demand.

At each time weekly period breakdown (t), the agents weight the current demand and the expected demand for this period to estimate the demand for the next period:

(2) where and are the expected demand at time t and t-1, respectively. is the customer’s demand at time t. θ is the parameter controlling the rate at which expectations are updated (smoothing parameter between 0 and 1).

The demand for chocolate is highly dependent on the weather and has a highly erratic demand profile, so sales and stock levels are monitored frequently. Forecasts are adjusted to account for the latest weather reports, seasonality, national holidays (for example, Christmas, New Year, Easter), special occasions (such as Mothers’ Day, Valentines’ Day, Chinese New Year, etc.) and events (particularly sporting events such as the Football World Cup or Olympics), as they change people’s shopping habits in terms of the size of their purchase and/or the mix of products. These forecasts can also change depending on promotions and marketing activities such as the product being in the power bay, multi-offer promotions

and media activity. Finally the local store manager has the opportunity to indicate that a local event is likely to increase the demand for specific product categories.

The order rate to the distribution centre for all the ordering agents are defined by the equation:

(3) where is the indicated order, are the backorders, is the stock, are the orders in pipeline at time t. α is the moving average constant (parameter between 0 and 1), β is the relative weight attached to the pipeline vs. stock discrepancies from desired levels (between 0 and 1), q is the measure of the desired inventory relative to the desires supply line (always ≥0).

(4) where are the orders in the pipeline at time t-1, are the shipment received from the distribution agent, is the new order to the distribution at period t-1.

To determine what is supplied to fulfil the existing customer demand at any agent the following equation was used:

(5) where is the stock at t-1, is the shipment received from the distribution agent for the period t.

For both the Retail Customer and Mail Order Customer agents, it is considered that their demand is fulfilled if there is stock in the retailer and in the distribution centre respectively, with no time delays (meaning that all the orders are fulfilled within the week). For the retailer, if stock is not available to fulfil customer demand this means sales losses - as product substitution is not considered, or delays in fulfilling those orders (e.g., the customer going back to the store to full demand). Furthermore, in real circumstances, the lack of repeated availability means that the customers will not return back to the store to look for their favourite product(s), which will reflect in future sales loss but that loss is hard to quantify.

In this scenario for the retailer only agent, no stock means sales loss so there are no backorders, so (retailer) equals to zero, so the quantity to supply is given by the following equation:

(6)

The backorders for all agents is determined by the following equation. This equation also corresponds to the lost sales for the mail order customer and retail customer agents:

(7) where are the backorders quantities at t-1.

The stock at any point for each tick t is determined by the following equation:

(8)

Where is the stock at period t -1, is the quantity supplied at period t, is stock losses when the product reaches its best-before-end date, corresponds to received shipment at period t.

The distribution agent has the same equations as the previous equations but the tasks of Receive Orders, Supply and Backorders are split into five corresponding to subsequent elements (Retailer Agent, Mail Order Customer Agent, US Hotel Chocolat Agent, Wholesaler Agent, and Middle East Franchising Agent).

From the analysis of the results of Moseklide et al. (1991), when a model starts with zero stock, the model takes much longer to achieve to a normal equilibrium, as the system has to work much harder to get the necessary stock levels (Figure 6).

Figure 6 Beer Game Inventory Plot (Source: Moseklide et al., 1991).

Considering this fact, the following stocks were considered for each one of the SC agents, which corresponds to roughly four weeks of demand, at t equal to three. The reason why it is considered t = 3 as the starting point is that the manufacturing agent starts to produce at t = 1 (2 weeks before the stock needs to be available in the warehouse to fulfil the downstream orders) and to avoid the time lag that the system naturally needs to reach a position where the warehouse can start to fulfil orders.

inventoryRetailer.set(3, 2500);

inventoryMailOrder.set(3, 1350);

inventoryUS.set(3, 60);

inventoryWholesale.set(3, 600);

inventoryMiddleEast.set(3, 90);