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The lost sales case for constant lead times A study of effect of information sharing and lead-times on bullwhip effect in a serial supply chain
Increasing competition in the market generally leads to a high fluctuation in the demand of products. Such fluctuations pose a very severe problem at each stage of the supply chain, i.e., customer, retailer, warehouse, supplier and manufacturing, in deciding about the suitable inventory levels to maintain a good service level with minimum amount of holding cost. The problems compound further when the lead-times of replenishment are long and uncertain. Because of the longer lead-time, the uncertainty in the forecasting of the future demand increases, and consequently the variability of the order quantity increases. Any stage of the chain, apart from using the forecast values from its lower echelon, also has to do its own forecasting analysis while ordering to its next higher echelon. This naturally increases the variability of the order quantity. The phenomenon where there is an increase in the variance of the order quantity, as we move away from the end customer to the supplier in a supply chain, is defined as the bullwhip effect. The demand process, lead-times, inventory policies and the forecasting models employed have significant bearing on the bullwhip effect. Among these, forecasting models, inventory policies and to some extent lead-times are controllable and hence can be suitably decided upon to reduce the bullwhip effect. Further more, the importance of sharing of relevant information across various stages of the supply chain is being increasingly realized and has been found to reduce the over all bullwhip effect.
Few of the relevant assumptions when considering models (Figure 9.1) like these are:
- Demand Process : Many models assume a probability distribution with known parameters to represent the demand process. The stationary Poisson distribution is widely used to model the demands in inventory models; however, seasonal type items, short product life cycles, and volatility in the market place suggest that the probability distribution of demand tends to change over time. One flexible correlative demand process that has been studied in the supply chain literature is AR(1) model which is an autoregressive process of the first order. For our simple discussion we consider the end customer demand to be AR(1).
- Forecasting Model : An mean squared error (MSE) optimal forecasting scheme is generally employed for the assumed AR(1) demand process.
- Replenishment Policy : One can safely assume that all stages operate with a periodic-review policy with a common review period. At the end of a period, the on-hand inventory (or backorders) is calculated using the inventory balance equation. In each period each stage observes the demand either from an external customer or from its downstream stages, and places orders to its suppliers so as to replenish the demand of the product based on the observed demand. For low demand situation, generally one-for-one or base-stock policies are used for inventory replenishment. We simpy assume that each stage operates with an adaptive base-stock replenishment policy.
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