Arindam Roy, Bijoy Moktan & Prabir K Sarkar* Microbiology laboratory, Department of Botany, U... more Arindam Roy, Bijoy Moktan & Prabir K Sarkar* Microbiology laboratory, Department of Botany, University of North Bengal, Siliguri 734 013, West Bengal E-mail: pksarkar@sancharnet.in Received 9 May 2006; revised 10 October 2006
An antibiogram of 48 strains of Bacillus cereus isolated from 6 diVerent kinds of legume-based In... more An antibiogram of 48 strains of Bacillus cereus isolated from 6 diVerent kinds of legume-based Indian fermented foods (amriti, dhokla, dosa, idli, papad and wadi) was generated against 18 diVerent antibiotics that are commonly used against foodborne diseases, mainly gastroenteritis. Each of the isolates was found to be resistant against at least nine diVerent antibiotics. Production of extracellular enzymes, namely protease, lipase and amylase by 33%, 27% and 46%, respectively, of the isolates indicates their potentiality for food spoilage. In brain-heart infusion broth supplemented with glucose, the D 100°C -values for the tested 12 strains ranged from 3.0 to 9.2 min. In nutrient broth, the minimum and maximum pHs permitting growth of B. cereus were 5.3 and 11.6, respectively. The minimum inhibitory concentrations of sodium chloride, benzoic acid and sorbic acid for the growth of the isolates were 65-85 mg ml ¡1 , 400-700 g ml ¡1 (pH 5.0-4.2) and 500-600 g ml ¡1 (pH 5.0-4.8), respectively. Of the tested 10 strains, eight were resistant to 300 g nisin ml ¡1 (pH 5.0). While studying the combined eVect of selected hurdles on the growth of an isolate, the judicious combination considered was 20 mg sodium chloride, 300 g benzoic acid and 25 g nisin ml ¡1 at pH 5.6. The whole-cell protein Wngerprinting (WCPF) analysis using SDS-PAGE revealed a high level of diversity among the isolates. At 760% similarity level, the WCPF proWles could be grouped into four major clusters which were divided into 34 subclusters. Most of the subclusters were source-wise homogeneous.
A total of 105 samples of six diVerent types of legume-based popular fermented foods, namely amri... more A total of 105 samples of six diVerent types of legume-based popular fermented foods, namely amriti, dhokla, dosa, idli, papad and wadi, purchased from retail outlets in West Bengal, was analysed to determine their microbiological safety status. While dhokla and idli were of high-moisture foods (62 g (100 g) ¡1 ), others had a lower moisture level (14-27 g (100 g) ¡1 ). Papad was alkaline (pH 8.7), whereas all the other foods were acidic (pH 4.4-5.8). Every sample was found contaminated with total aerobic mesophilic bacteria (detection limit, 10 cfu g ¡1 ); 38% (40/105) of the samples contained more than 10 6 cfu g ¡1 . Aerobic mesophilic bacterial spores were found in 88% (92/105) of the samples (detection limit, 100 cfu g ¡1 ), whereas their anaerobic counterparts were present in 39% (41/105) of the samples (detection limit, 10 cfu g ¡1 ). Although all the samples, excepting one, were free from Staphylococcus aureus (detection limit, 100 cfu g ¡1 ), 20% (21/ 105) of the samples were found contaminated with Bacillus cereus (detection limit, 100 cfu g ¡1 ). Enterobacteriaceae were found in 46% (48/105) of the samples (detection limit, 10 cfu g ¡1 ). Of the Enterobacteriaceae isolates, 92% were coliforms and 57% were faecal coliforms. Escherichia coli (detection limit, 10 cfu g ¡1 ) was found in only one sample each of wadi and idli, at a load of 10 3 -10 4 g ¡1 . Salmonella (detection limit, 1 cell (25 g) ¡1 ) occurred in 12 samples of wadi, idli and papad, however was absent in the other three products. Clostridium perfringens (detection limit, 10 cfu g ¡1 ) and Shigella (detection limit, 1 cell (25 g) ¡1 ) could not be detected. The results obtained in the present study indicated that these foods were manufactured using poor-quality starting materials, processed under unhygienic conditions, or/and temperature-abused during transportation and storage. Based on these results, a guideline is recommended for obtaining safe products.
For fixed $u$ and $v$ such that $0\leq u<v<1/2$, the monotonicity of the quotients of Jacobi thet... more For fixed $u$ and $v$ such that $0\leq u<v<1/2$, the monotonicity of the quotients of Jacobi theta functions, namely, $\theta_{j}(u|i\pi t)/\theta_{j}(v|i\pi t)$, $j=1, 2, 3, 4$, on $0<t<\infty$ has been established in the previous works of A.Yu. Solynin, K. Schiefermayr, and Solynin and the first author. In the present paper, we show that the quotients $\theta_{2}(u|i\pi t)/\theta_{2}(v|i\pi t)$ and $\theta_{3}(u|i\pi t)/\theta_{3}(v|i\pi t)$ are convex on $0<t<\infty$.
This paper develops a production-inventory model for a deteriorating item with stock-dependent de... more This paper develops a production-inventory model for a deteriorating item with stock-dependent demand under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. The effects of learning in set-up, production, selling and reduced selling is incorporated. Different inflation rates for various inventory costs and time value of money are also considered. A hybrid genetic algorithm is designed to solve the optimization problem which is hard to solve with existing algorithms due to the complexity of the decision variable. To illustrate the model and to show the effectiveness of the proposed approach a numerical example is provided. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.
An inventory model for a deteriorating item with stock dependent demand is developed under two st... more An inventory model for a deteriorating item with stock dependent demand is developed under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. For crisp deterioration rate, the expected profit is derived and maximized via genetic algorithm (GA). On the other hand, when deterioration rate is imprecise then optimistic/pessimistic equivalent of fuzzy objective function is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to maximize the optimistic/pessimistic return and finally fuzzy simulation-based GA is developed to solve the model. The models are illustrated with some numerical data. Sensitivity analyses on expected profit function with respect to distribution parameter λ and confidence levels α 1 and α 2 are also presented.
This paper investigates a production-remanufacturing system for a single product over a known-fin... more This paper investigates a production-remanufacturing system for a single product over a known-finite time horizon. Here the production system produces some defective units which are continuously transferred to the remanufacturing unit and the constant demand is satisfied by the perfect items from production and remanufactured units. Remanufacturing unit uses the defective items from production unit and the collected used-products from the customers and later items are remanufactured for reuse as fresh items. Some of the used items in the remanufacturing unit are disposed off which are not repairable. The remanufactured units are treated as perfect items. Normally, rate of defectiveness varies in a production system and may be approximated by a constant or fuzzy parameter. Hence, two models are formulated separately with constant and fuzzy defective productions. When defective rate is imprecise, optimistic and pessimistic equivalent of fuzzy objective function is obtained by using credibility measure of fuzzy event by taking fuzzy expectation. Here, it is assumed that remanufacturing system starts from the second production cycle and after that both production and remanufacturing units continue simultaneously. The models are formulated for maximum total profit out of the whole system. Here the decision variables are the total number of cycles in the time horizon, the duration for which the defective items are collected and the cycle length after the first cycle. Genetic Algorithm is developed with Roulette wheel selection, Arithmetic crossover, Random mutation and applied to evaluate the maximum total profit and the corresponding optimum decision variables. The models are illustrated with some numerical data. Results of some particular cases are also presented.
An inventory model of deteriorating seasonal products with Maximum Retail Price (MRP) for a whole... more An inventory model of deteriorating seasonal products with Maximum Retail Price (MRP) for a wholesaler having showrooms at different places under a single management system is considered under random business periods with fuzzy resource constraints. The wholesaler replenishes the products instantaneously and earns commissions on MRP which vary with the ordered quantities following All Unit Discount (AUD), Incremental Quantity Discount (IQD) or IQD in AUD policy. Demand at showrooms are imprecise and related to selling prices by 'verbal words' following fuzzy logic. The wholesaler shares a part of commission with customers. The business periods follows normal distribution and converted to deterministic ones through chance constraint technique. The fuzzy space and budget constraints and fuzzy relations are defuzzified using possibility measures, surprise function and Mumdani fuzzy inference technique. The model is formulated as profit maximization for the wholesaler and solved using a real coded Genetic Algorithm (GA) and illustrated through some numerical examples and some sensitivity analysis. A real-life problem of a developing country is presented, solved using the above mentioned procedures and an appropriate inventory policy is suggested.
An inventory model for a deteriorating item (seasonal product) with linearly displayed stock depe... more An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.
Time value of money Random planning horizon Genetic algorithm with varying population size Fuzzy ... more Time value of money Random planning horizon Genetic algorithm with varying population size Fuzzy rule base a b s t r a c t A production inventory model for a newly launched product is developed incorporating inflation and time value of money. It is assumed that demand of the item is displayed stock dependent and lifetime of the product is random in nature and follows exponential distribution with a known mean. Here learning effect on production and setup cost is incorporated. Model is formulated to maximize the expected profit from the whole planning horizon. Following . A fuzzy-based lifetime extension of genetic algorithms. Fuzzy Sets andSystems, 149, 131-147], a genetic algorithm (GA) with varying population size is used to solve the model where crossover probability is a function of parent's agetype (young, middle-aged, old, etc.) and is obtained using a fuzzy rule base and possibility theory. In this GA a subset of better children is included with the parent population for next generation and size of this subset is a percentage of the size of its parent set. This GA is named fuzzy genetic algorithm (FGA) and is used to make decision for above production inventory model in different cases. The model is illustrated with some numerical data. Sensitivity analysis on expected profit function is also presented. Performance of this GA with respect to some other GAs are compared.
International Journal of Production Economics, 2010
This paper develops an inventory model of a volume flexible manufacturing system for a deteriorat... more This paper develops an inventory model of a volume flexible manufacturing system for a deteriorating item with randomly distributed shelf life, continuous time-varying demand, and shortages over a finite time horizon. It is assumed that the produced units deteriorate over time with uncertainty that follows different distributions (Uniform distribution, two parameters Weibull distribution). Total cost is derived for the system and minimized. Genetic algorithm (GA) is developed with Roulette wheel selection, arithmetic crossover, random mutation and applied to evaluate the minimum total cost and the corresponding optimum decision variables. The model is illustrated with some numerical data. Here we present the fractional factorial design approach for this model along with its practical implication. Also some sensitivity analyses for the total cost with respect to some system parameters are presented.
This paper develops multi-item Economic Order Quantity (EOQ) inventory models for breakable units... more This paper develops multi-item Economic Order Quantity (EOQ) inventory models for breakable units with stock dependent demand under imprecise constraints. The units are damaged due to the accumulated stress of the stocked items kept in stacked form and the damaged function, i.e. rate of breakability per unit time may be linear or non-linear function of current stock level. Here shortages are not allowed. Both the crisp and fuzzy models have been formulated as profit maximization problems with crisp/imprecise space and budget constraints and solved by using a gradient based non-linear programming technique, Generalised Reduced Gradient (GRG) Method. The models are illustrated with a numerical example and some sensitivity analyses have been presented.
Arindam Roy, Bijoy Moktan & Prabir K Sarkar* Microbiology laboratory, Department of Botany, U... more Arindam Roy, Bijoy Moktan & Prabir K Sarkar* Microbiology laboratory, Department of Botany, University of North Bengal, Siliguri 734 013, West Bengal E-mail: pksarkar@sancharnet.in Received 9 May 2006; revised 10 October 2006
An antibiogram of 48 strains of Bacillus cereus isolated from 6 diVerent kinds of legume-based In... more An antibiogram of 48 strains of Bacillus cereus isolated from 6 diVerent kinds of legume-based Indian fermented foods (amriti, dhokla, dosa, idli, papad and wadi) was generated against 18 diVerent antibiotics that are commonly used against foodborne diseases, mainly gastroenteritis. Each of the isolates was found to be resistant against at least nine diVerent antibiotics. Production of extracellular enzymes, namely protease, lipase and amylase by 33%, 27% and 46%, respectively, of the isolates indicates their potentiality for food spoilage. In brain-heart infusion broth supplemented with glucose, the D 100°C -values for the tested 12 strains ranged from 3.0 to 9.2 min. In nutrient broth, the minimum and maximum pHs permitting growth of B. cereus were 5.3 and 11.6, respectively. The minimum inhibitory concentrations of sodium chloride, benzoic acid and sorbic acid for the growth of the isolates were 65-85 mg ml ¡1 , 400-700 g ml ¡1 (pH 5.0-4.2) and 500-600 g ml ¡1 (pH 5.0-4.8), respectively. Of the tested 10 strains, eight were resistant to 300 g nisin ml ¡1 (pH 5.0). While studying the combined eVect of selected hurdles on the growth of an isolate, the judicious combination considered was 20 mg sodium chloride, 300 g benzoic acid and 25 g nisin ml ¡1 at pH 5.6. The whole-cell protein Wngerprinting (WCPF) analysis using SDS-PAGE revealed a high level of diversity among the isolates. At 760% similarity level, the WCPF proWles could be grouped into four major clusters which were divided into 34 subclusters. Most of the subclusters were source-wise homogeneous.
A total of 105 samples of six diVerent types of legume-based popular fermented foods, namely amri... more A total of 105 samples of six diVerent types of legume-based popular fermented foods, namely amriti, dhokla, dosa, idli, papad and wadi, purchased from retail outlets in West Bengal, was analysed to determine their microbiological safety status. While dhokla and idli were of high-moisture foods (62 g (100 g) ¡1 ), others had a lower moisture level (14-27 g (100 g) ¡1 ). Papad was alkaline (pH 8.7), whereas all the other foods were acidic (pH 4.4-5.8). Every sample was found contaminated with total aerobic mesophilic bacteria (detection limit, 10 cfu g ¡1 ); 38% (40/105) of the samples contained more than 10 6 cfu g ¡1 . Aerobic mesophilic bacterial spores were found in 88% (92/105) of the samples (detection limit, 100 cfu g ¡1 ), whereas their anaerobic counterparts were present in 39% (41/105) of the samples (detection limit, 10 cfu g ¡1 ). Although all the samples, excepting one, were free from Staphylococcus aureus (detection limit, 100 cfu g ¡1 ), 20% (21/ 105) of the samples were found contaminated with Bacillus cereus (detection limit, 100 cfu g ¡1 ). Enterobacteriaceae were found in 46% (48/105) of the samples (detection limit, 10 cfu g ¡1 ). Of the Enterobacteriaceae isolates, 92% were coliforms and 57% were faecal coliforms. Escherichia coli (detection limit, 10 cfu g ¡1 ) was found in only one sample each of wadi and idli, at a load of 10 3 -10 4 g ¡1 . Salmonella (detection limit, 1 cell (25 g) ¡1 ) occurred in 12 samples of wadi, idli and papad, however was absent in the other three products. Clostridium perfringens (detection limit, 10 cfu g ¡1 ) and Shigella (detection limit, 1 cell (25 g) ¡1 ) could not be detected. The results obtained in the present study indicated that these foods were manufactured using poor-quality starting materials, processed under unhygienic conditions, or/and temperature-abused during transportation and storage. Based on these results, a guideline is recommended for obtaining safe products.
For fixed $u$ and $v$ such that $0\leq u<v<1/2$, the monotonicity of the quotients of Jacobi thet... more For fixed $u$ and $v$ such that $0\leq u<v<1/2$, the monotonicity of the quotients of Jacobi theta functions, namely, $\theta_{j}(u|i\pi t)/\theta_{j}(v|i\pi t)$, $j=1, 2, 3, 4$, on $0<t<\infty$ has been established in the previous works of A.Yu. Solynin, K. Schiefermayr, and Solynin and the first author. In the present paper, we show that the quotients $\theta_{2}(u|i\pi t)/\theta_{2}(v|i\pi t)$ and $\theta_{3}(u|i\pi t)/\theta_{3}(v|i\pi t)$ are convex on $0<t<\infty$.
This paper develops a production-inventory model for a deteriorating item with stock-dependent de... more This paper develops a production-inventory model for a deteriorating item with stock-dependent demand under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. The effects of learning in set-up, production, selling and reduced selling is incorporated. Different inflation rates for various inventory costs and time value of money are also considered. A hybrid genetic algorithm is designed to solve the optimization problem which is hard to solve with existing algorithms due to the complexity of the decision variable. To illustrate the model and to show the effectiveness of the proposed approach a numerical example is provided. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.
An inventory model for a deteriorating item with stock dependent demand is developed under two st... more An inventory model for a deteriorating item with stock dependent demand is developed under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. For crisp deterioration rate, the expected profit is derived and maximized via genetic algorithm (GA). On the other hand, when deterioration rate is imprecise then optimistic/pessimistic equivalent of fuzzy objective function is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to maximize the optimistic/pessimistic return and finally fuzzy simulation-based GA is developed to solve the model. The models are illustrated with some numerical data. Sensitivity analyses on expected profit function with respect to distribution parameter λ and confidence levels α 1 and α 2 are also presented.
This paper investigates a production-remanufacturing system for a single product over a known-fin... more This paper investigates a production-remanufacturing system for a single product over a known-finite time horizon. Here the production system produces some defective units which are continuously transferred to the remanufacturing unit and the constant demand is satisfied by the perfect items from production and remanufactured units. Remanufacturing unit uses the defective items from production unit and the collected used-products from the customers and later items are remanufactured for reuse as fresh items. Some of the used items in the remanufacturing unit are disposed off which are not repairable. The remanufactured units are treated as perfect items. Normally, rate of defectiveness varies in a production system and may be approximated by a constant or fuzzy parameter. Hence, two models are formulated separately with constant and fuzzy defective productions. When defective rate is imprecise, optimistic and pessimistic equivalent of fuzzy objective function is obtained by using credibility measure of fuzzy event by taking fuzzy expectation. Here, it is assumed that remanufacturing system starts from the second production cycle and after that both production and remanufacturing units continue simultaneously. The models are formulated for maximum total profit out of the whole system. Here the decision variables are the total number of cycles in the time horizon, the duration for which the defective items are collected and the cycle length after the first cycle. Genetic Algorithm is developed with Roulette wheel selection, Arithmetic crossover, Random mutation and applied to evaluate the maximum total profit and the corresponding optimum decision variables. The models are illustrated with some numerical data. Results of some particular cases are also presented.
An inventory model of deteriorating seasonal products with Maximum Retail Price (MRP) for a whole... more An inventory model of deteriorating seasonal products with Maximum Retail Price (MRP) for a wholesaler having showrooms at different places under a single management system is considered under random business periods with fuzzy resource constraints. The wholesaler replenishes the products instantaneously and earns commissions on MRP which vary with the ordered quantities following All Unit Discount (AUD), Incremental Quantity Discount (IQD) or IQD in AUD policy. Demand at showrooms are imprecise and related to selling prices by 'verbal words' following fuzzy logic. The wholesaler shares a part of commission with customers. The business periods follows normal distribution and converted to deterministic ones through chance constraint technique. The fuzzy space and budget constraints and fuzzy relations are defuzzified using possibility measures, surprise function and Mumdani fuzzy inference technique. The model is formulated as profit maximization for the wholesaler and solved using a real coded Genetic Algorithm (GA) and illustrated through some numerical examples and some sensitivity analysis. A real-life problem of a developing country is presented, solved using the above mentioned procedures and an appropriate inventory policy is suggested.
An inventory model for a deteriorating item (seasonal product) with linearly displayed stock depe... more An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.
Time value of money Random planning horizon Genetic algorithm with varying population size Fuzzy ... more Time value of money Random planning horizon Genetic algorithm with varying population size Fuzzy rule base a b s t r a c t A production inventory model for a newly launched product is developed incorporating inflation and time value of money. It is assumed that demand of the item is displayed stock dependent and lifetime of the product is random in nature and follows exponential distribution with a known mean. Here learning effect on production and setup cost is incorporated. Model is formulated to maximize the expected profit from the whole planning horizon. Following . A fuzzy-based lifetime extension of genetic algorithms. Fuzzy Sets andSystems, 149, 131-147], a genetic algorithm (GA) with varying population size is used to solve the model where crossover probability is a function of parent's agetype (young, middle-aged, old, etc.) and is obtained using a fuzzy rule base and possibility theory. In this GA a subset of better children is included with the parent population for next generation and size of this subset is a percentage of the size of its parent set. This GA is named fuzzy genetic algorithm (FGA) and is used to make decision for above production inventory model in different cases. The model is illustrated with some numerical data. Sensitivity analysis on expected profit function is also presented. Performance of this GA with respect to some other GAs are compared.
International Journal of Production Economics, 2010
This paper develops an inventory model of a volume flexible manufacturing system for a deteriorat... more This paper develops an inventory model of a volume flexible manufacturing system for a deteriorating item with randomly distributed shelf life, continuous time-varying demand, and shortages over a finite time horizon. It is assumed that the produced units deteriorate over time with uncertainty that follows different distributions (Uniform distribution, two parameters Weibull distribution). Total cost is derived for the system and minimized. Genetic algorithm (GA) is developed with Roulette wheel selection, arithmetic crossover, random mutation and applied to evaluate the minimum total cost and the corresponding optimum decision variables. The model is illustrated with some numerical data. Here we present the fractional factorial design approach for this model along with its practical implication. Also some sensitivity analyses for the total cost with respect to some system parameters are presented.
This paper develops multi-item Economic Order Quantity (EOQ) inventory models for breakable units... more This paper develops multi-item Economic Order Quantity (EOQ) inventory models for breakable units with stock dependent demand under imprecise constraints. The units are damaged due to the accumulated stress of the stocked items kept in stacked form and the damaged function, i.e. rate of breakability per unit time may be linear or non-linear function of current stock level. Here shortages are not allowed. Both the crisp and fuzzy models have been formulated as profit maximization problems with crisp/imprecise space and budget constraints and solved by using a gradient based non-linear programming technique, Generalised Reduced Gradient (GRG) Method. The models are illustrated with a numerical example and some sensitivity analyses have been presented.
Uploads
Papers by Arindam Roy