Study Selection and Use of Inventory Models

Study, Selection, Built up and Use of Inventory Models

Study:

The great difficulty = in learning inventory models stems from the need to translate reality (as often expressed in cases or other word problems) into formal treatment.   Basically there are three challenges. The challenge to identify the correct model and the challenge to distinguish among inputs ba= sed on the reading. A final chall= enge is to identify the desired out put. &= nbsp;

These challenges requ= ire conceptual comprehension of each model, its essence, inputs and output.

Drawing the distincti= ve graph for the model is a necessary part of the study and would be helpful for conceptual understanding.

One way to testing comprehension, is to build the various formulae independently, based on con= ceptual understanding. In particular,= after learning the material, I would recommend trying to work in two directions.<= span style=3D'mso-spacerun:yes'> First try to work in reverse, buil= ding independently first the Total Costs formula for the model, and then work backward to establish its components, if necessary. Building the formula conceptually should be done before inserting the proper formula.

If the values of the outputs are not clear, it would then be worth while to begin with conceptual understanding = of the inputs followed by the assignment of values or computation of the value= s of the inputs. Finally the outpu= ts should be identified and computed. <= /span>Building the formula conceptually should be done before inserting the proper formula.

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The greatest challeng= e in using inventory models is the selection of the right model. Let us present a conceptual approa= ch for selection.   <= /span>

All together we have 5 different models and 7 model variation to select from.

There are 3 models wi= th Deterministic Demand, i.e., models where t= he annual demand is given or can be computed exactly. These are: Model 1) Regular EOQ mo= del, Model 2) Inventory with Backorder, and Model 3) Inventory with Production.<= span style=3D'mso-spacerun:yes'>

There are 2 models wi= th Stochastic (Probabilistic) Demand: They differ ba= sed on the nature of their distribution system. In Model 4), the probability of the demand is Discrete.    In Model 5), the proba= bility of the demand is Con= tinuous. In the case of continuous distribu= tion we are limiting the study to Normal Distribution of the demand.<= /span>

Hence, if the annual = demand is deterministic (i.e. not probabilistic) The ri= ght model is either Model 1) or Model 2) or Model 3). It cannot be Model 4) or Model 5). If the demand (for = the cycle) is probabilistic it must be either Model 4) or Model 5). If the demand is probabilistic and = is discrete it must be model 4) and if the distribution of the demand is a nor= mal distribution, it must be model 5). <= /span>

How to distinguish am= ong the deterministic models?

Model 1: If the quant= ity is ordered and we do not deal with Back Order and Production it must be model 1.

In this case there are no inputs of penalty (per unit p) or serv= ice standard (L) or rate of production (B).

Model 2: In case we d= eal with backorder and waiting list, it is model 2.= In this case only either penalty for being on the waiting lis= t (p per item ) or alternatively service level (L) must be supplied.

Model 3: In case of i= nventory with production, it is model 3. In this case only , the annual production rate (B) must either be gi= ven or can be calculated.

Within Model 2, we distinguish between two variations.

Model 2a: The penalty= per item on the waiting list, p, is given directly. In this variation, you may proceed directly to compute the various formulae. You can also find the service lev= el.

Model 2b: The service= level, designating the probability of finding the item on the shelf, L is given directly. In this case one ne= eds to find the imputed waiting list penalty p, before proceeding to deal with var= ious formulae. The formulae for p is , where h i= s the cost

o= f holding a unit of inventory of an item in inven= tory for a year and c the cost per unit of the ordered item.

How to distinguish am= ong Probabilistic models?

M= odel 4. T= he probability of the demand is discrete.

M= odel 5. T= he probability of the demand is continuous.&n= bsp; In our study, it is a normal distribution whose mean μ and stan= dard deviation σ must be given. In dealing with Model 5, we distinguish between two variations:

Model 5a: In this case we do find that the O= ptimal Ordered Quantity Q is higher than the mean demand μ.

Mode 5b: In this case, we do find that the optimal Ordered Quantity Q is lower than the mean demand μ.

The treatment that fo= llows in computing variety of formulae in each variation is distinctive. =

II. Once you had iden= tified the correct model or model variation, proceed to use of formulae.

Step 1: For the selected model, list the i= nputs. Sometimes you may need to com= pute some of the inputs. So you mu= st understand conceptually the meaning of each input. Conceptual understanding is needed= in order to distinguish every input from all other inputs.

Step 2: Identify the required outputs

Step 3: For every required output find the= right formula.

Step 4: Perform computation.

That’s it no mo= re steps.

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Answerin= g Problems in Inventory: A check List

1. Ident= ify and declare the correct Model in the Problem or Part of the Problem. (This is the most crucial element.= In case of misidentification, all = the answers will be false).

2.   List the inputs (parameters) of the model. Provide notation and definition for each input. Be aware full of the unit of measu= rement of each input.

3.   Write the formulas for the Objective of the Model.

4.   Draw the graph(s) of the model.

4.   For each required sub problem write the formula for the desired unknown (Output= ).

5.   Compute the numerical answer for the desired unknown (output) in 4.

General Comments

1. In yo= ur computations, be aware of the unit of measurement of each input and output.=

2. Be aware whether you may or need providing a rounding = of the output or whether rounding is not allowed as it may represents a conceptual mistake.