Stochastic demand determination

Forecast models can be used to prepare a statistical demand forecast. It is based on previous consumption or future demand trends of an reference number. A simple, powerful, forecast model is the first-order exponential smoothing . 

To determine the new demand forecast, the difference between the forecast and actual consumption of the last period is assessed with a smoothing factor ALPHA and added to the old demand forecast using the formula 

Actual consumption in the previous period (at least 10 working days) 

This forecast method only needs a small amount of information. It is easy for users to understand and extremely efficient. When different ALPHA values are used, the forecast displays different sensitivities. When consumption fluctuates greatly, a relatively little sensitivity (small alpha) is required, as is shown in Fig. 58 with ALPHA = 0.1. 

If there is little fluctuation in consumption, the sensitivity should be greater (large Alpha) to better follow trends. 

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Stackelberg game) demand uncertainty random defaults. The paper analyzes the effect of correlation under deterministic and stochastic demand, determines optimal timing for supplier payments and optimal wholesale price under supply disruption risk... 

Chien TW (1993) Determining profit-maximizing product/shipping policies in a one-to-one direct shipping, stochastic demand environment. Eur J Oper Res 64(1) 83-102... 

But experiments with stochastic input signal demand a long measuring period to determine the cross correlation fimctions with sufficient accuracy. 

Describing the stochastic process for a given decision problem is an exercise in modeling. The modeler has to determine an appropriate choice of state description for the problem. The basic idea is that the state should be a sufficient, and efficient, summary of the available information that affects the future of the stochastic process. For example, for the revenue management problem, choosing the state to be the amount of the product in inventory may be an appropriate choice. If there is a cost involved in changing the price, then the previous price should also form part of the state. Also, if competitors prices affect the demand for the product, then additional information about competitors prices and behavior should be included in the state. 

Fixed reorder quantity inventory model—A form of independent demand item management model in which an order for a fixed quantity, Q, is placed whenever stock on hand plus on order reaches a predetermined reorder level, R. The fixed order quantity Q may be determined by the economic order quantity, by a fixed order quantity (such as a carton or a truckload), or by another model yielding a fixed result. The reorder point R, may be deterministic or stochastic, and in either instance is large enough to cover the maximum expected demand during the replenishment lead time. Fixed reorder quantity models assume the existence of some form of a perpetual inventory record or some form of physical tracking, e.g., a two-bin system, that is able to determine when the reorder point is reached. These reorder systems are sometimes called fixed order quantity systems, lot-size systems, or order point-order quantity systems. 

Eppen G., and R. Martin. 1988. Determining Safety Stock in the Presence of Stochastic Lead Time and Demand, Management Science 34, 1380-1390. 

Similarly, Thowsen [151] considers the determination of price and production in a nonstationary model where demand is a general function of price and has an additive stochastic component. Thowsen assumes proportional ordering costs (without set-up) and convex holding and stockout costs, and he considers the conditions of backlogging, partial backlogging, and lost sales as well as partial spoilage of inventory under a number of common-sense assumptions. A critical number inventory policy is considered, denoted by later researchers as (p,p), which is similar to critical number inventory policies, and conditions for optimality are shown. 

In [63], the same authors extend their work to focus on a multi-market problem, with multiple products charing common resources. They model demand as a stochastic point process function of time and the prices of all products the vector of demand for n products, A = (A A, ..., A ), is determined by time and the vector of prices, p = As before, revenue is assumed... 

As the number of node enterprises which constitute the supply chain can be infinitely expanded, to solve the stochastic chance-constrained programming model, a computational layer is to be divided from the stmcture of supply chain in planning period T. Then the layered computation is adopted on demand. Firstly the overall strncmre of the supply chain should be determined in planning period T before computation. Secondly, the upstream and the downstream enterprises of the supply... 

Abstract This chapter presents a stochastic optimization model for disaster management planning. In particular, the focus is on the integrated decisions about the distribution of relief supplies and evacuation operations. The proposed decisionmaking approach recommends the best relief distribution centers to use as storage locations and determines their optimal inventory levels. The model also incorporates the priorities for the evacuation of particular communities, as well as specific disaster scenarios with estimates of the transportation needs and demand for aid. A case study is presented to determine the distribution of aid for a flood emergency in Thailand that uses a flood hazard map. 

For a given distribution of the demand with 1 client and given distributions for the stochastic processes D(r),L(0 and /(/), we have to determine the action as a function of the population size N t). The object should be the maximisation of the profit. The profit is given by the revenues of the orders minus the costs for set-ups and the holding costs. We do not have penalty costs in this situation, since the costs of lateness are now expressed in the demand and the number of clients. 

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