In this study, a nonlinear stochastic optimization model is developed to maximize the expected profit under demand uncertainty. For solution efficiency, a stochastic programming-based genetic algorithm (SPA) is proposed to determine a profitable capacity planning and task allocation plan. The algorithm improves a conventional two-stage stochastic programming by integrating a genetic algorithm into a stochastic sampling procedure to solve this large-scale nonlinear stochastic optimization on a real-time basis. Finally, the tradeoff between profits and risks is evaluated under different settings of algorithmic and hedging parameters. Experimental results have shown that the proposed algorithm can solve the problem efficiently.
ABA II Introduction Stochastic resource planning and capacity allocation deals with the problem of how to find an optimal resource portfolio under uncertain demands. Such a portfolio planning has been explored in high-tech manufacturing industries uh to intensive capital and technology involvement as well as risky market demands and short product/equipment lifestyle. The purpose of this paper is to develop both a precise mathematical representation and the corresponding solving algorithm to maximize the expected profit under demand uncertainty. The following decisions are examined in this study. 1 . The optimal resource portfolio plan (including the type and amount of resources that must be procured, rented, transferred and/or sold-out) accounting for the time value of capital. 2.
The choice of the most profitable orders from pending orders. . The optimal allocation of tasks that specifies the optimal quantity of products produced in each time bucket. ABA Ill Problem formation This research focuses on a resource portfolio planning against demand uncertainty in high-tech industries and aims at maximizing expected production profit by taking a risk factor into account in a long-term planning horizon. The types of production make-to-order (MOT) is considered in the model. In order to decide the level of resources through alternatives such as: renting and transferring resources, a decision-support model is also provided here.
The optimal simultaneous resource portfolio plan, thus, is defined as the best simultaneous resource portfolio planning and configuration trajectory, so the expected profit can be maximized and the corresponding risk can be hedged. There are several assumptions that need to be considered as follows. 1 . Demands are presented as a set in which each demand consists of several types of products. Furthermore, the each demand was presented in discrete- time base. Usually, orders are placed In each week or month. 2. Resource procurement only occurs in the first period of a planning horizon, whereas source capacity can be adjusted in the intermediate periods through renting or transferring from other plants. 3. Target utilization and throughput rate of resource for individual products are known. 4.
There are finite resource configurations to coffin the technological feasibility for producing a product. Index All the notations of the model are listed in the following: M TO Index of demand pattern (make-to-order) Adjustable factor applied to tradeoff between profit and risk (Cosmos). When X O, the decision maker prefers the highest profits without considering the risk of investment. Conversely, when = 1, the investor is very conscious Of the risk Of investment. A Index Of auxiliary resource type (a -? Index of production planning period (p = , P) m . ,A)p Index of main resource type (m = M) Index of product type (t = 1 T) Index of resource outsourcing alternatives (z = 1 .
Parameters BP,t unit profit of product t produced in period p CM,trounces configurations capabilities between product and main resource CM,a,trounces configurations capabilities between product, auxiliary resource, and main resource DMS unit salvage value of phasing out a machine f main resource type m daunt salvage value of purchasing out an auxiliary resource type a me unit cost of purchasing a main resource type m EAI unit cost of purchasing an auxiliary resource type a Ip capital interest rate in period p JP,t the unit excess production cost OK,a number of auxiliary resource in the initial period OK,m number of main resource in the initial period Ip,t the unit lack production cost pop,t market demand for product tin period p arm,t theoretical throughput conducted by main resource arm,a,theoretical throughput conducted by main and auxiliary resource p,m,z unit cost of main resource obtained by outsourcing up,a,zenith cost of auxiliary resource obtained by outsourcing whom,parking hours of main resource WA,p working hours of auxiliary resource yap,m target utilization of main resource yap,a target utilization of auxiliary resource Decision Variable profit gained Up capital at the end of period Km number of in-house main resource Aka number of in-house auxiliary resource Xp,m,z number of main resource associated with resource acquisition alternative number of auxiliary resource associated with resource acquisition alternative quantity of product t produced by main resource annuity of product t produced by auxiliary resource ABA IV Model In the original paper, we know that the objective of the optimal simultaneous planning decision for level of capacity is to maximize the net profit in long- term periods and can be expressed formally as follows: Where is the tradeoff parameter of risk. We can see the tradeoff between the expected profits in all realized demands and risk that is modeled as the mean absolute deviation (MAD) of profits in function. But now we have to rebuild a new model, and there are the steps as follow: 1 . Changing the model into one demand scenario, and we can get this: . After finishing the first step, we let the model which is stochastic become deterministic. And the final model will be: ABA V Reconstruct We use this reconstruct as following: Required numbers of main resources 2. Configuration constraints of main resources and auxiliary resources 3.
Required number of auxiliary resources production balance from net market demand 4. 5. Capital balance equation 6. Profit off demand scenario gab VI Method We use MALAY with GA. Initially, the randomly generated population size N is called zero chromosomes, and then to evaluate the fitness of each chromosome obtained fitness value. Then according to the established selection mechanism to replicate individual genetic evolution. After that we decide whether to mate and produce offspring by probability of crossover. Deciding whether to further mutations after offspring produced according to probability of mutation. Mating major genetic operation, and the mutation is secondary operation.