A Possibility Approach for the Single Item Lot Sizing Problem with Fuzzy Parameters

2016 ◽  
pp. 100-132
Author(s):  
Manoj Kumar ◽  
Jyoti Raman ◽  
Priya Singh
Keyword(s):  
Lot Sizing ◽  
Fuzzy Model ◽  
Optimal Solution ◽  
Unit Price ◽  
Mixed Integer ◽  
Inventory Planning ◽  
Single Item ◽  
Lot Sizing Problem ◽  
Fuzzy Parameters

The main objective of this chapter is to deal with a single item lot sizing problem with fuzzy parameters, which is called the fuzzy single item lot sizing problem (F-SILSP). Since F-SILSP does not meet the crisp deterministic assumption, it cannot be solved by traditional mathematical programming. In this chapter, the possibility approach is chosen to convert the fuzzy model to be an equivalent crisp single item lot sizing problem (EC-SILSP). The equivalent crisp model from this transformation procedure is in the form of mixed integer linear programming (MILP). It can be solved by traditional solver to find an optimal solution for each pre-specified possibility level. A numerical example with both trapezoidal and triangular fuzzy parameters is illustrated to demonstrate that an equivalent crisp model can be used. In addition, the equivalent crisp model is employed in inventory planning in a case study of inventory planning for bituminous coal with trapezoidal fuzzy demand and triangular fuzzy unit price in a power plant of an example petrochemical company (Supreme Petro, India).

scholarly journals A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 878 ◽  
Author(s):  
Yajaira Cardona-Valdés ◽  
Samuel Nucamendi-Guillén ◽  
Rodrigo E. Peimbert-García ◽  
Gustavo Macedo-Barragán ◽  
Eduardo Díaz-Medina
Keyword(s):  
Lot Sizing ◽  
Mixed Integer ◽  
Lot Size ◽  
Penalty Cost ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing ◽  
Batch Ordering ◽  
New Formulation ◽  
Production Resources

This paper addresses the multi-product, multi-period capacitated lot sizing problem. In particular, this work determines the optimal lot size allowing for shortages (imposed by budget restrictions), but with a penalty cost. The developed models are well suited to the usually rather inflexible production resources found in retail industries. Two models are proposed based on mixed-integer formulations: (i) one that allows shortage and (ii) one that forces fulfilling the demand. Both models are implemented over test instances and a case study of a real industry. By investigating the properties of the obtained solutions, we can determine whether the shortage allowance will benefit the company. The experimental results indicate that, for the test instances, the fact of allowing shortages produces savings up to 17% in comparison with the model without shortages, whereas concerning the current situation of the company, these savings represent 33% of the total costs while preserving the revenue.

scholarly journals Dynamic lot sizing problem under uncertainty of returned products in remanufacturing industry

2018 ◽  
Vol 204 ◽  
pp. 07005
Author(s):  
Iman Setyoaji
Keyword(s):  
Bayesian Inference ◽  
Lot Sizing ◽  
Replacement Ratio ◽  
Total Cost ◽  
Lot Sizing Problem ◽  
Holding Cost ◽  
Dynamic Lot Sizing ◽  
Lot Sizes

Remanufacturing processes face uncertainty in the quality of the items being returned by customers, this significant variability complicates the control of inventories. Demands can be satisfied by procured new items, but also by remanufactured returned items. This paper develops dynamic lot sizing model for remanufacturing industry under uncertainty of returned items and proposes Bayesian Inference to estimate the replacement ratio of returned items that used to determine those lot sizes for new items. The objective of this paper is to minimize the total cost composed of holding cost and set-ups cost. A numerical example is provided based on case study. The result shows that total cost is reduced to be 45%.

scholarly journals Location Routing Problem with Consideration of CO2 Emissions Cost: A Case Study

2020 ◽  
Vol 21 (2) ◽  
pp. 225-234
Author(s):  
Ananda Noor Sholichah ◽  
Y Yuniaristanto ◽  
I Wayan Suletra
Keyword(s):  
Co2 Emissions ◽  
Time Windows ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Distribution Centers ◽  
Location Routing Problem ◽  
Routing Problem ◽  
Location Routing ◽  
Study Results

Location and routing are the main critical problems investigated in a logistic. Location-Routing Problem (LRP) involves determining the location of facilities and vehicle routes to supply customer's demands. Determination of depots as distribution centers is one of the problems in LRP.  In LRP, carbon emissions need to be considered because these problems cause global warming and climate change. In this paper, a new mathematical model for LRP considering CO2 emissions minimization is proposed. This study developed a new  Mixed Integer Linear Programming (MILP)  model for LRP with time windows and considered the environmental impacts.  Finally, a case study was conducted in the province of Central Java, Indonesia. In this case study, there are three depot candidates. The study results indicated that using this method in existing conditions and constraints provides a more optimal solution than the company's actual route. A sensitivity analysis was also carried out in this case study.

scholarly journals A cash constrained single item stochastic lot-sizing problem

2019 ◽  
Vol 52 (13) ◽  
pp. 1479-1483
Author(s):  
Zhen Chen ◽  
Roberto Rossi
Keyword(s):  
Lot Sizing ◽  
Single Item ◽  
Lot Sizing Problem
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