According the periodic review policy, the inventory level is reviewed at a regular basis and an order is placed right after the review to reach the Base-stock level, the daily average demand during the period r, which is the period between 2 consecutive reviews, is O and from the order point until the next receiving the daily average demand is L shoo, thus, the safety stock which represent a buffer during the lead time is 0 xxњњ x 1/0 +0 ( the time cycle is L+r). Consequently At the end of the lead time and before the reception of the order the inventory level equals to the safety stock CLC] x s/(D +0). After the order arrives, the expected inventory level which is supposed to cover the demand during the review period r reaches again the based stock level minus the daily average used during the lead time, which is ( L+O) axed +0 xњњњ x v/(D +њ)-L. BAG= t] xњњњ +0 x ’10 +1] 3-lamming that you operate a department store. List five products you sell, and order them from lowest target service level to highest target service level. Justify your ordering.

Sofa ( low service level , purchased every year or 2, so the facility will not order more than the average demand because ,because the sofa will be old fashioned so the order need to match the average demand ) Light bulb ( medium service level , the order quantity is higher than the average demand because it a product which is used by all customers) Tooth paste ( medium service level , because it’ s used daily by he customer and purchased monthly, the order quantity will be more than the average demand ) , Toilet paper (high service level because it’ s used daily by the customers, and it finishes within the week so the order quantity should cover the expected demand) bread, ( high service level ,because it’s a basic product , used daily by the customers and expires early which means high demand, the order quantity should match with the expected demand ) 4-Though we typically model inventory-related costs as either fixed or variable, in the real world the situation is more complex.

Discuss some inventory-related costs that are fixed in the short term but may be considered variable if a longer time horizon is considered The fixed inventory related costs that will be variable over the years are, Utility costs: the rent, the electricity, the inventory maintenance, the salaries Labor/handling duties costs that in charge of watching and monitoring the inventory, the increase of this initially fixed costs with time will cost more and more over the years because of the government regulations , inflation … Etc. , for example the inventory related fixed cost for a stock that was n inventory for 2 years will vary from the first year to the second year by some percentage. 5. When is a model such as the economic lot sizing model, which ignores randomness, useful?

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The economic models such as the lot sizing model which ignores variability in demand and assumes that the demand is stable over the time is, in fact, very useful for the reason that it allows decision makers to use this model to predict and calculate approximations of the average daily demand, the daily demand standard deviation and the safety stock ,the order quantity which are related the realistic complex cases ,besides this model is he base of the more developed policy reviews such as periodic and continuous reviews. 6. What are the penalties of facing highly variable demand? Are there any advantages? There are penalties related to the highly variable demand, for example, I-Holding costs, the higher the variability in demand the higher the total costs is, 2- the safety stock is associated directly to the standard deviation of the daily demand , which means the stocks levels increases with higher variation and thus all the costs related to the inventory Fixed and variables.

Forecasting and managing the variability in demand needs resources and time to look into he supply chain and come up with good strategies to manage the variability which is costly. The only advantage of the demand variability is the ability to handle this issue that make the company gain more skills in supply chain management and also help the company to asses it demand variability risks and share these methods with other companies in order to overcome difficulties related to demand variability 7. Give a specific example of risk pooling (a) Across locations: when we centralist warehouses that were located in several location into one warehouse.

For instance, we combine 2 warehouses that were coated in 2 cities , which have negatively correlated average demand, into one warehouse, to aggregate demand and reduce variability, and thus reduce safety stock and inventory level. (b) Across time, it is used to control the production levels, and capacity planning trough quarterly forecasting, instead of monthly forecasting, because longer term trends could appear during the quarter which maybe not appear in the monthly forecast . For example the trends in the sales of Chicago condos are not visible in monthly periods , (c) Across products: Delayed product differentiation which is the production f generic product that will be differentiated later to deal with the market uncertainty .

For example: production of white shirts that will be colored later according the season colors. 8. When would you expect demand for a product in two stores to be positively correlated? The demand in 2 stores will be positively correlated when the demand from the 2 stores is greater than the average demand. When would you expect it to be negatively correlated? The demand in 2 stores will be negatively correlated when the demand in one store is greater than the average demand, while the demand in the other store s less than the average demand. 9-Consider a supply chain consisting of a single manufacturing facility, a cross dock, and two retail outlets.


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