Uncertainty demand

Uncertainty in market demand introduces randomness in constraints for production requirements of intermediates and saleable products, as given by Equation (6.4). The sampling methodology employed for scenario construction is similar to the case of price uncertainty in Approach 1, involving the generation of representative scenarios of demand uncertainty for N number of products with the associated probabilities that indicate their comparative frequency of occurrence. 

Compensating slack variables accounting for shortfall and/or surplus in production are introduced in the stochastic constraints with the following results (i) inequality constraints are replaced with equality constraints (ii) numerical feasibility of the stochastic constraints can be ensured for all events and (iii) penalties for feasibility violations can be added to the objective function. Since a probability can be assigned to each realization of the stochastic parameter vector (i.e., to each scenario), the probability of feasible operation can be measured. In this 

To ensure that the original information structure associated with the decision process sequence is honored, for each of the products whose demand is uncertain, the number of new constraints to be added to the stochastic model counterpart, replacing the original deterministic constraint, corresponds to the number of scenarios. Herein lies a demonstration of the fact that the size of a recourse model increases exponentially since the total number of scenarios grows exponentially with the number of random parameters. In general, the new constraints take the form  

---

In order to investigate the performance of a deterministic online scheduler, we apply it to the example problem under demand uncertainty for three periods. The model of the scheduling problem used in the scheduler considers a prediction horizon of H = 2 periods. Only the current production decision Xi(ti) is applied... 

Robust short-term scheduling of multiproduct batch plants under demand uncertainty. Industrial and Engineering Chemistry Research, 40, 4543 1554. 

Several simulation-based optimization models in the context of supply chain management can be found e.g. in the area of supply chain network optimization (Preusser et al. 2005) or to simulate rescheduling of production facing demand uncertainty or unplanned shut-downs (Tang/Grubbstrom 2002 Neuhaus/Giinther 2006). A basic approach of simulation-based optimization is presented by Preusser et al. 2005, p. 98 illustrated in fig. 24. 

Commodity-related models focus on demand volatility and uncertainty in volumes and prices as with sales quantity flexibility. Several authors proposed models to handle demand uncertainty in general focusing on quantities (Cheng et al. 2003 Gupta/Maranas 2003 Cheng et al. 2004 Chen/Lee 2004). Uncertainty is reflected by demand quantity scenarios and/or probabilities. Proposed models maximize expected or robust profit. Process industry-specific models use simulation to address demand uncertainty and to determine optimal inventory levels (Jung et al. 2004). 

Gupta/Maranas (2003) as one example for a demand uncertainty model present a demand and supply network planning model to minimize costs. Production decisions are made here and now and demand uncertainty is balanced with inventories independently incorporating penalties for safety stock and demand violations. Uncertain demand quantity is modeled as normally distributed random variables with mean and standard deviation. The philosophy to have one production plan separated from demand uncertainty can be transferred to the considered problem. Penalty costs for unsatisfied demand and normally distributed demand based on historical data... 

Gupta A, Maranas CD (2003) Managing demand uncertainty in supply chain planning. Computers Chemical Engineering 27 (8-9) 1219-1227... 

Jung JY, Blau G, Pekny JF, Reklaitis GV, Eversdyk D (2004) A simulation based optimization approach to supply chain management under demand uncertainty. Computers Chemical Engineering 28 2087-2106... 

Tang O, Grubbstrom RW (2002) Planning and replanning the master production schedule under demand uncertainty. International Journal of Production Economics 78 (3) 323-334... 

Tsiakis, P., Shah, N., and Pantelides, C.C. (2001) Design of multiechelon supply chain networks under demand uncertainty. 

It is desirable to demonstrate that the proposed stochastic formulations provide robust results. According to Mulvey, Vanderbei, and Zenios (1995), a robust solution remains close to optimality for all scenarios of the input data while a robust model remains almost feasible for all the data of the scenarios. In refinery planning, model robustness or model feasibility is as essential as solution optimality. For example, in mitigating demand uncertainty, model feasibility is represented by an optimal solution that has almost no shortfalls or surpluses in production. A trade-off exists... 

The major capacity limitations as well as the availability constraints are shown in Table 7.1. Raw materials, product prices, and demand uncertainty were assumed to... 

Mo Y, Harrison TP (2005) A conceptual framework for robust supply chain design under demand uncertainty. In Geunes J, Pardalos PM (eds) Supply Chain Optimization. Springer, Berlin et al., pp 243-263... 

Tsiakis P, Shah N, Pantelides CC (2001) Design of Multi-echelon Supply Chain Networks under Demand Uncertainty. Industrial Engineering Chemistry Research 40 3585-3604... 

For consequence analysis, we have developed a dynamic simulation model of the refinery SC, called Integrated Refinery In-Silico (IRIS) (Pitty et al., 2007). It is implemented in Matlab/Simulink (MathWorks, 1996). Four types of entities are incorporated in the model external SC entities (e.g. suppliers), refinery functional departments (e.g. procurement), refinery units (e.g. crude distillation), and refinery economics. Some of these entities, such as the refinery units, operate continuously while others embody discrete events such as arrival of a VLCC, delivery of products, etc. Both are considered here using a unified discrete-time model. The model explicitly considers the various SC activities such as crude oil supply and transportation, along with intra-refinery SC activities such as procurement planning, scheduling, and operations management. Stochastic variations in transportation, yields, prices, and operational problems are considered. The economics of the refinery SC includes consideration of different crude slates, product prices, operation costs, transportation, etc. The impact of any disruptions or risks such as demand uncertainties on the profit and customer satisfaction level of the refinery can be simulated through IRIS. 

J. Balasubramanian, l.E. Grossmatm, 2004, Approximation to multistage stochastic optimization in multiperiod batch plant scheduling rmder demand uncertainty. Ind. Eng. Chem. Res., 43, 3695-3713. 

F. Bernstein and A. Federgruen, Decentralized Supply Chains with Competing Retailers under Demand Uncertainty, Management Science (2001). 

Supply chain networks Simultaneous maximization of (1) participants expected profits, (2) average safe inventory level (for plants, distribution centers and retailers), (3) average customer service levels (for retailers), (4) robustness of selected objectives to demand uncertainties and fair profit distribution. A two-phase fuzzy decisionmaking method Chen and Lee (2004) extended the smdy of Chen et al. (2003) by including uncertainty in product demands and prices. Cheu et al. (2003b) Cheu and Lee (2004)... 

---