Supply Chain Assignment

According to the continuous review policy, the inventory is continuously reviewed and an order is placed when the inventory level reaches the Reorder level R which is equal to the daily average demand times the lead time plus the safety stock: AGV x L + ?× ??? ×√?, during the lead time only the quantity AVG x L is used, and if the order is received exactly at the end of the lead time L, the expected level inventory after receiving the order is the new order quantity Q plus the safety stock ?× ??? ×√? Consider the base-stock in periodic review. Explain why the expected level of inventory after receiving an order is equal to ? ×??? +? ×??? × √? +? while the expected level of inventory before an order arrives is ?× ??? ×√? + ? . 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 ? ×???, and from the order point until the next receiving the daily average demand is L ×???, thus, the safety stock which represent a buffer during the lead time is ? ×??? × √? +? ( 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 ? ×??? × √(? +?).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+?) ×??? +? ×??? × √(? +?)-L.AVG= ? ×??? +? ×??? × √? +? 3-Imagine 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 the 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)

Although 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 , inflations …etc. , for example the inventory related fixed cost for a stock that was in inventory for 2 years will vary from the first year to the second year by some percentage.

When is a model such as the economic lot sizing model, which ignores randomness, useful? 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 the 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, 1-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 the 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

Give a specific example of risk pooling

(a) Across locations: when we centralise warehouses that were located in several location into one warehouse. For instance, we combine 2 warehouses that were located 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 of 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 is less than the average demand. 9-Consider a supply chain consisting of a single manufacturing facility, a cross dock, and two retail outlets. Items are shipped from the manufacturing facility to the cross-dock facility and from there to the retail outlets. Let ?1 be the lead time from the factory to the cross-dock facility and ?2 be the lead time from the cross dock facility to each retail outlet. Let ? = ?1 +?2. In the analysis below, we fix ? and vary ?1 and ?2. a. Compare the amount of safety stock in two systems, one in which lead time from the cross-dock facility to a retail outlet is zero (i.e., ?1 = ? Land ?2 = 0 ) and a second system in which the lead time from the factory to the cross-dock facility is equal to zero (i.e., ?1 = 0 Land ?2 = ?). b. To reduce safety stock, should the cross-dock facility be closer to the factory or the retail outlets?

First we need to calculate the lead time at the cross docking facility, Le= the lead time between the retailers and the cross docking+ the lead time between the cross docking and its supplier L= L1+L2, STD: is the standard deviation of aggregate demand across all retailers. Thus the safety stock at the Cross docking: Z*STD * √ L1+L2, Case 1: (i.e., ?1 = ? Land ?2 = 0)

At the cross docking the safety stock is equal to: Z*STD * √ L1= Z*STD * √ L At retailer: the safety stock is equal to zero.
Case 2: (i.e., ?1 =0 Land ?2 = L)
At the cross docking the safety stock is equal to: Z*STD * √ L2= Z*STD * √ L At retailer: the safety stock is equal to: Z*STD * √ L
Thus to reduce the safety stock, the cross docking should be closer to the retailer L2 small or equal to zero, and when L1 increases the risk pooling is more effective because we will take advantage of the cross docking facility before distributing the stock to retailers. EX 10: KLF Electronics is

Answers:
a -If the demand in the five regions is very similar, and the average demand is above the average in all the regions, the daily demand is positively correlated in the five market and thus the risk pooling system will not be effective.
b- If we compare the centralized (at Los Angeles because the inbound transportation costs less) and the decentralized systems, we can conclude that the centralized system at Los Angeles with 97% of service level increased the average stock levels and the holding costs, but at the same time it decreased the transportation costs .My recommendation is to go for the centralized system with better service level, the saving in the transportation costs compensates the holding costs, The total costs for the centralized system are only 6313 dollars per week while the decentralized costs 9678 dollars ( see table below)
c- In the case of the new system with the lead time = 0.5, the cost of transportation increased, consequently, the total cost increased by 9 %( see table below), thus I don`t recommend this new strategy because when we decreased the lead time we lost the advantages of risk pooling strategy.