# Is a "multistep" or "multiphase" Newsvendor model possible?

I'm trying to address the question of how many times should I order a product from my supplier, assuming highly stochastic demand.

In my mind there would be something like the Newsvendor model, but would not only provide me with an optimal buy quantity, but also the optimal number of times I should reorder (i.e. should I buy again tomorrow and the next day? Should I buy once a day for the next week? etc...)

• Check the $(S,s)$ policy and the related inventory policies. Oct 25 '19 at 21:53
• @KonstantinosI.Stouras Your answer can be improved. You can help the OP by providing more detail or references. You can also use comments to ask for more clarification.
– EhsanK
Oct 26 '19 at 2:24

There are several models available to make the sort of decisions you are asking about. Most tend to make ordering decisions based on inventory level rather than on time: That is, they say things like "when the IL = 12, order 25" rather than "order 25 every 3 days".

The newsvendor problem is usually interpreted as a periodic-review model, so if you're looking for a multi-periodic model that is analogous, consider either the base-stock model or the $$(s,S)$$ model. Both assume that the period length is already fixed (e.g., 1 day). The base-stock model assumes we order every period, while the $$(s,S)$$ model assumes there is a fixed ordering costs, which means the orders are spaced out more.

The main model that uses order interval as a decision variable (i.e., focusing on time, not IL) is the $$(r,T)$$ model.

In continuous review, the relevant model is the $$(r,Q)$$ model, but I wouldn't exactly think of that as multi-period newsvendor, since it's continuous review.

If the newsvendor model is needed, the asset is assumed to have a short selling season and forward procurement is required. Usually, one-time procurement with fixed lead time is considered in newsvendor problems, so the primary concern is to decide the quantity. When there are multiple procurement opportunities, the dynamic procurement strategy can be beneficial in many ways.

The newsvendor can place multiple orders with increasing ordering cost over time to satisfy demand that realizes at the end of the planning horizon. [wang2012multiordering]

In general, you must balance the precision of your demand forecasts and procurement costs. Usually, as lead time decreasing, you have more accurate forecasts and face higher costs.

There are many types of dynamic procurement problems with different forecasts, costs, supply modes. For example, in [wang2012multiordering], future costs are known in advance for sure. While in power systems [nair2014energy] [secomandi2014optimal], your future costs are unknown and correlated. In [zheng2015newsvendor], optimal one-time procurement with flexible lead times is discussed in two supply modes.

• [wang2012multiordering]: Wang, T., Atasu, A., & Kurtuluş, M. (2012). A multiordering newsvendor model with dynamic forecast evolution. Manufacturing & Service Operations Management, 14(3), 472-484.
• [nair2014energy]: Nair, J., Adlakha, S., & Wierman, A. (2014, June). Energy procurement strategies in the presence of intermittent sources. In The 2014 ACM international conference on Measurement and modeling of computer systems (pp. 85-97).
• [secomandi2014optimal]: Secomandi, N., & Kekre, S. (2014). Optimal energy procurement in spot and forward markets. Manufacturing & Service Operations Management, 16(2), 270-282.
• [zheng2015newsvendor]: Zheng, M., Wu, K., & Shu, Y. (2016). Newsvendor problems with demand forecast updating and supply constraints. Computers & Operations Research, 67, 193-206.