Contributed Session Mon.2.MA 144

Monday, 13:15 - 14:45 h, Room: MA 144

Cluster 22: Stochastic optimization [...]

Production, inventory and project management


Chair: Takashi Hasuike



Monday, 13:15 - 13:40 h, Room: MA 144, Talk 1

Wen-Lung Huang
Optimal aggregate production planning with fuzzy data

Coauthor: Shih-Pin Chen


This paper investigates the optimization problem of aggregate production planning (APP) with fuzzy data. From a comprehensive viewpoint of conserving the fuzziness of input information, this paper proposes a method that can completely describe the membership function of the performance measure. The idea is based on the well-known Zadeh’s extension principle which plays an important role in fuzzy theory. In the proposed solution procedure, a pair of mathematical programs parameterized by possibility level is formulated to calculate the bounds of the optimal performance measure. Then the membership function of the optimal performance measure is constructed by enumerating different values. An example is solved successfully for illustrating the validity of the proposed approach. Solutions obtained from the proposed method contain more information, and can offer more chance to achieve the feasible disaggregate plan. This is helpful to the decision-maker in practical applications.



Monday, 13:45 - 14:10 h, Room: MA 144, Talk 2

Ali Cem Randa
Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem

Coauthors: Mustafa Kemal Doğru, Cem İyigün, Ulas Ozen


We consider a single-stage inventory system facing non-stationary stochastic demand of the customers in a finite planning horizon. Motivated by practice, the replenishment times need to be determined and frozen once and for all at the beginning of the horizon while decision on the exact replenishment quantities can be deferred until the replenishment time. This operating scheme is referred as a static-dynamic uncertainty strategy in the literature. We consider dynamic fixed/variable cost of ordering, linear holding costs as well as dynamic penalty costs, and upper/lower limits on order quantities. We prove that the optimal ordering policy is a base stock policy. We develop heuristics for computing the optimal policy parameters for longer planning horizons because the optimal ordering periods and the associated base stock levels need exponentially exhaustive search based on dynamic programming. We then evaluate the efficiency of our heuristics by numerical examples. We also investigate the NP hardness of the problem considering the computational time required with the size of the problem.



Monday, 14:15 - 14:40 h, Room: MA 144, Talk 3

Takashi Hasuike
Risk control approach to critical path method in mathematical programming under uncertainty


This paper considers a risk control approach to find a critical path in the project scheduling network under several uncertainties for each activity duration time and the improvement imputing some materials and human resources. As a mathematical model of proposed approach, the mathematical programming problem based on Critical Path Method is introduced. Furthermore, in order to formulate risk of control factors and each random relation between two successive processes mathematically, quantile-based robust parameters and a time expanded network for the given static project scheduling network are introduced. The proposed model is initially a multi-objective and stochastic programming problem, and hence, it is hard to solve this problem directly without setting some optimal criterion. In this paper, an integrated function for the multi-objective and randomness is introduced. By performing deterministic equivalent transformations, the strict solution algorithm is developed.


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