The mechanism behind the so-called bull-whip effect, which involves the transmission of amplified demand fluctuations throughout a distribution chain, is actually very simple. It stems from a marketing-oriented approach to customer needs and the desire of individual links in the logistics chain to conduct business rationally.
The readiness of individual chain links to meet customer expectations means that each entity strives to accumulate a quantity of product equal to the forecasted sales plus a certain reserve in case of unexpected demand fluctuations. Therefore:
• the retailer receives information directly from the customer and accumulates the forecasted sales volume plus a reserve resulting from deviations in customer demand
• the wholesaler receives information from retailers (in the form of orders placed by them) and accumulates the forecasted sales volume plus a reserve resulting from deviations in demand reported by retailers
• the manufacturer receives information from wholesalers (in the form of orders placed by them) and accumulates the forecasted sales volume plus a reserve resulting from deviations in demand reported by wholesalers. In this way, each subsequent link maintains an increasingly larger inventory, as it is exposed to ever-greater demand fluctuations. The linear flow of information in the chain means that the longer the chain, the greater the accumulation of demand changes, and consequently, the larger the orders and inventory levels. The inventory held by the link furthest from the final consumer and user of the product in a given chain is many times greater than the actual market needs. The author presented a picture of how the bullwhip effect is created using a numerical example conducted as a simulation of ordering and warehousing policies carried out by individual links of the logistics chain over a period of 36 weeks. The observation focused on the demand for disposable diapers for children of similar age, and consequently, using the product in the same size.
• the retailer receives information directly from the customer and accumulates the forecasted sales volume plus a reserve resulting from deviations in customer demand
• the wholesaler receives information from retailers (in the form of orders placed by them) and accumulates the forecasted sales volume plus a reserve resulting from deviations in demand reported by retailers
• the manufacturer receives information from wholesalers (in the form of orders placed by them) and accumulates the forecasted sales volume plus a reserve resulting from deviations in demand reported by wholesalers. In this way, each subsequent link maintains an increasingly larger inventory, as it is exposed to ever-greater demand fluctuations. The linear flow of information in the chain means that the longer the chain, the greater the accumulation of demand changes, and consequently, the larger the orders and inventory levels. The inventory held by the link furthest from the final consumer and user of the product in a given chain is many times greater than the actual market needs. The author presented a picture of how the bullwhip effect is created using a numerical example conducted as a simulation of ordering and warehousing policies carried out by individual links of the logistics chain over a period of 36 weeks. The observation focused on the demand for disposable diapers for children of similar age, and consequently, using the product in the same size.
Model assumptions
The simulation forming the basis of these considerations was subject to strict assumptions. All chain links (including the most unpredictable end customers) followed a rational purchasing policy based on mathematically justified foundations. A product with regular consumption was chosen for the simulation, omitting all marketing aspects (promotions, discounts) and socio-cultural aspects (holidays, vacations) that could disrupt this regularity. Factors that could disturb the pattern established at the beginning were excluded. A supply chain consisting of four links was considered. Starting from the end of the chain, we have:
• 36 customers (mothers buying diapers for their children)
• 6 retailers (pharmacies A through F)
• two wholesalers X and Y
• a manufacturer
• 36 customers (mothers buying diapers for their children)
• 6 retailers (pharmacies A through F)
• two wholesalers X and Y
• a manufacturer
Customers
The manufacturer sells diapers in packs of 30. We assume that:
1. All children use 120 diapers per month – four packs per four weeks (we assume a month is four weeks).
2. Mothers shopping at one pharmacy do not know the location of other pharmacies and do not make any purchases there.
3. A temporary lack of goods in the pharmacy does not affect the mothers’ shopping habits – mothers do not buy a different quantity of packs than planned in the following week. Although children use the same number of diapers weekly, mothers’ purchases vary greatly. Some mothers buy one pack per week, others two packs every two weeks, and still others four packs once a month. A few mothers buy their entire supply of eight packs once every two months.
Retailers
Each retailer (pharmacy) sums up the demand reported by six consecutive customers and creates demand forecasts. Inventories are replenished when:
• the final inventory level in a given week is less than the demand forecast for the next week
• if the final inventory level is greater than the forecast – the retailer refrains from purchasing. In this way, the retailer generates a sequence of orders, which serves as the primary demand information for wholesalers. This sequence takes on values of order size Q or zero values. Since retailers are supplied by wholesalers, we are dealing with immediate order fulfillment. Replenishments arriving at the warehouse at the beginning of the week increase the initial inventory level and can be sold in that week. Potential shortages in the warehouse (situations where the inventory accumulated in a given week is not sufficient to meet customer orders) do not affect changes in retailer orders in subsequent weeks.
Each retailer applies the same ordering policy, however, each generates a different sequence of orders, buying a different batch of goods in a different week, because their inventory levels in individual weeks are shaped differently and the distribution of their customers’ purchases over time is different.
• the final inventory level in a given week is less than the demand forecast for the next week
• if the final inventory level is greater than the forecast – the retailer refrains from purchasing. In this way, the retailer generates a sequence of orders, which serves as the primary demand information for wholesalers. This sequence takes on values of order size Q or zero values. Since retailers are supplied by wholesalers, we are dealing with immediate order fulfillment. Replenishments arriving at the warehouse at the beginning of the week increase the initial inventory level and can be sold in that week. Potential shortages in the warehouse (situations where the inventory accumulated in a given week is not sufficient to meet customer orders) do not affect changes in retailer orders in subsequent weeks.
Each retailer applies the same ordering policy, however, each generates a different sequence of orders, buying a different batch of goods in a different week, because their inventory levels in individual weeks are shaped differently and the distribution of their customers’ purchases over time is different.
Wholesalers
Each wholesaler serves three consecutive pharmacies. Wholesalers do not know the purchase distribution of individual retailers’ customers, so they derive demand information from orders placed by retailers. To protect themselves against shortages in the warehouse, and consequently – lost benefits from the sale of goods, they conduct constant inventory monitoring:
• if the initial inventory level drops to a certain level s – an order of size Q is triggered
• if the inventory in the warehouse remains above the threshold level s – no delivery is ordered from the manufacturer.
• if the inventory in the warehouse remains above the threshold level s – no delivery is ordered from the manufacturer.
The level s determines the point in time called the reorder point. The manufacturer needs a week to process a wholesaler’s order. As in the case of retailers, the sequence of orders generated by wholesalers can take on values of Q or zero values.
Manufacturer
The product in question is manufactured by only one producer, from whom both wholesalers are supplied. Based on wholesaler orders, the manufacturer obtains information about demand. The manufacturer must base its production order policy on demand forecasts, because the lead time for orders received from wholesalers is one week, and the production cycle is two weeks. Therefore:
• if the initial inventory level in a given week is greater than a certain level B – the forecast size for the next week is ordered for production
• if the inventory drops below level B, the production order is: forecast size for the next period + the difference between inventory level B and the current warehouse stock
• if the inventory drops below level B, the production order is: forecast size for the next period + the difference between inventory level B and the current warehouse stock
Production orders increase warehouse stock two weeks after they are initiated.
The article comes from the magazine “Logistyka” 2002/6.