Probabilistic Models

When a certain production process begins with a set of inventories in tow, it’s taken that demand that will be generated and amount that will be produced would be known. However, in certain cases it so happens that the exact demand is not known and one has to seek help from certain forecasts or analysis that has been made.

With help of a probabilistic model, an approximate distribution of possible outcomes are to be found and based on that certain demand decisions are to be taken. It not only describes the outcomes but also provides an idea as to how these outcomes are likely to occur.

• The First model that is used in this case is known as Discrete case model.

In thiscase, it’s assumed that demand is created on an instant basis, and there is no associated set up cost while lead time is taken to be nil.

• The Second model is taken as Continuous

In thiscase, it’s taken that demand is taken at the very beginning with no set up cost associated and no lead time is available.

• The Third model is known as Discretecase, but Demand is Uniform.

In this case, it is taken that demand is constantly maintained over a certain time period.

• The Fourth model is known as Uniform Demand but with a Continuous case

Here it is taken that demand is uniform and stated at the beginning.

Here are some of the problems that are associated with various models that are given in this case. Solving these questions will help you get a better idea.

 Sums based on Models 1 and 3:

1. It is taken that in an inventory company; usage of $36,000 is to be made for getting goods that cost $18 per unit. This detail is found after an analysis of its production and total accounting records. If the carrying charges of inventory are 163% of the average charges for inventory, and purchasing cost is taken at $40 per order, what would be the total number of years on an annual basis if economic view is to be taken into account, what are the average day’s supply that is taken into consideration for placing the order and the most EOQ during a specific time period.

2. An order of 500 units of a particular product is made on a regular basis. If it is taken that the per unit cost is $50, while annual demand is $1000, then what would be the total loss that would be incurred by that particular company? It is also taken that total ordering cost amounts to $600, and 40% is the total inventory carrying cost.

3. A supplier has to provide 10000 bearing to a particular producer on a regular basis. While production process is being carried out, it can be seen that close to 25,000 units of bearing can be produced on a regular basis. If it is taken that an annual count consists of 300 days and cost associated with production set up is $1800, and cost of holding back a singular amount is taken as $2, then what is the rate at which this production rate should be maintained?

4. It can be seen that a particular company makes usage of 50,000 widgets which on an annual rate costs $10 per unit. If details are that carrying costs are taken at 15% on an annual note and ordering costs are taken at $150, then what is the EOQ amount? Also, if it is taken that the company decides on producing widgets within the factory itself, and a machine having a capacity of 2,50,000 widgets per annum is installed. In such a scenario, what is the EOQ amount?

5. An airplane company makes use of rivets on an annual amount of 5000 per annum per kg. It is also given that cost of those rivets are taken at $20, while $200 is to be spend on getting the total amount of order, and carrying cost of inventory is taken at 10%. In such a scenario, what is the total amount order that is to be placed and at which frequency is this order to be placed?

6. In a factory that manufactures paints, it can be seen that changing over the paints will amount to $100 for every batch. Along with that, it is given that annual sale amount of a specific type of paint amounts to 20,000 liters while rate of production is thrice the rate of sales, and carrying cost of inventory is taken at $1 per liter. With such details, what is the number of batches that can be bought on a yearly basis, optimal yearly cost that is to be incurred, and what is the economic size that should be ordered on an annual basis?

Sums based on Model 4:

1. If the demand for a particular good is taken at $24,000 on an annual amount.The company can produce an amount of 2500 units of that particular product and total cost for setting up manufacturing unit comes at $300, while shortage cost is taken at $20 units and holding cost at $0.3 per unit basis. Given these the details, what is the manufacturing time that is found, what is the shortage number and quantity of optimum manufacturing of that product?

Sums based on Models 1 and 2:

1. If demand for a certain good is taken at 30 units and production cost is fixed at $10, then what is the size of the production unit and how long would it run? Also given, production cost is $2 and holding cost is taken at $0.30, and shortage cost is taken at $1.5 on a monthly basis.

2. As per the given sum, there is a uniform withdrawal of 150 units of a particular good on a monthly basis. If set-up cost is taken at $0.12 and holding cost is taken at $0.25 on a monthly basis, then what is the range of production run if shortage cost is taken at $1?

Sums based on Probabilistic Models:

1. If demand is taken as uniform and a particular good is manufactured at a rate of 200 pieces and sold at 30 pieces on a daily basis. If cost of setting the unit up comes at $300 and holding cost comes at $0.05, then what will be the production run of optimum number, batch size and production period?

2. If a rectangular distribution has been found between two products with a range of 500 and 4000, shortage cost comes at $7, and storage cost comes at $1, and purchasing cost comes at $10, then how to find optimal amount of expected total costs?

Links of Previous Main Topic:-

• Introduction to statistics
• Knowledge of central tendency or location
• Definition of dispersion
• Moments
• Bivariate distribution
• Theorem of total probability addition theorem
• Random variable
• Binomial distribution
• What is sampling
• Estimation
• Statistical hypothesis and related terms
• Analysis of variance introduction
• Definition of stochastic process
• Introduction operations research
• Introduction and mathematical formulation in transportation problems
• Introduction and mathematical formulation
• Queuing theory introduction
• Inventory control introduction

Links of Next Statistics Topics:-

• Simulation introduction
• Time calculations in network
• Introduction of game theory