A local supermarket chain in Lima has a daily shopping program for hydroponic tomatoes in bags, whose stock in gondolas is renewed every day to ensure the premium quality of the product. For this reason, at the beginning of the day shift, all the tomatoes that are not sold from the previous day are discarded and sold to an intermediary who resells them as a by-product to a network of pig farms. The supermarket manager has a purchase price negotiated with his suppliers of S/4.00/bag, being S/10.00/bag, the sale price in the gondola with an average daily demand of 250 bags and a standard deviation of 34 bags.

After several negotiations with the intermediary, he agreed to buy the bags of discarded tomatoes at a price of S/1.50 per bag. You as a store manager have to decide how many bags of tomatoes the supermarket should buy for tomorrow.

22) An artifact store on Av Shell needs to determine an optimal order size for a high-value, medium-turnover artifact that is demanded annually for 1,000 units with a very low degree of uncertainty. Carrying the inventory of this device costs the store US$100 per year per unit, which he considers high because he is interested in optimizing the order size. The store estimates the cost of managing an order to the central warehouse at US$22, and the additional cost of inspection, during receipt, it estimates at US$3 per unit.

23) A store in the mall on Av. Salaverry, dedicated to the sale of household items, requires establishing an order policy to manage one of its SKUs with the highest turnover, bathroom sets, which included decorated floors and curtains for home bathrooms. For this reason, they tried to ensure a service level of 95%, being the case that the sales area has forecast an annual demand of 5,000 sets and estimated a standard deviation of 5 sets per day.

It is the store's policy to be open for sales 365 days a year and count inventory every 14 days to make a new order at that moment, which arrives regularly in 10 days. We are just on inventory taking day and 150 sets are recorded and you have to decide how many sets to order in the Purchase Order in such a way that it does not affect the proposed service level.

24) A renowned network of trattorias in Lima buys its supplies such as flour, oil, cheese and canned tomato sauce from a supplier that imports directly from Naples to ensure the high quality of the ingredients. From the moment the supplier receives the order from the trattoria network and launches its purchase orders to Italy, its orders arrive in Peru in two weeks, so it is only delivered to the central warehouse of the trattorias after three weeks. In a joint effort, both the trattoria and the supplier have estimated a joint forecast of 150 25 kg cans of tomato sauce per week with a std deviation of 30 cans/week and the supplier knows that the network central warehouse expects a 98% level chance not to run out of ketchup.

Usually, the supplier's sales agent visits them every four weeks, as is the case today, which is when inventory control is carried out, verifying that they have a stock of 500 tomato cans in the refrigerator. If you were the purchasing manager at the trattoria, how many cans of tomato sauce would you put on your purchase order?

25) An important importer of office supplies and school supplies is programming its purchases for the coming year of an item with high rotation and continuous follow-up, A4 spiral notebooks in a presentation of boxes for 5 units and has estimated an annual demand of 25,750 boxes whose acquisition value is US$ 10/box. The store, which is open 50 weeks a year, finds its current cost of $250 to fill an order and the annual inventory carrying cost of 33% of the item cost, are too high. However, the supplier supplies them within a week, which allows them to manage their inventory with a service level of 95%, which allows them to meet their demand, which registers 25 boxes / week as a standard deviation.

- Set PO size and reorder point in boxes.

- Determine the annual value of the cost of maintaining inventories and ordering.

- If there is a price reduction of US$50 per order for purchasing quantities of 2,000 boxes or more, would you take the opportunity? How much would you save per year?

26) In a recent vendor assessment analysis, a retailer found that it cost them $100 to fulfill an order and the vendor's average delivery time was consistently 4 weeks. The retailer expects to continue serving its market with an NSC (customer service level) of 98% and has also calculated that it costs them to maintain a unit of product US$0.65 per year, with the annual cumulative demand being 13,000 units over the 52 weeks. of the year, with a std.deviation of 40 units / week:

- What should be the reorder point?

- Assuming that management reports a reduction in safety inventory of that product of 100 units. what will be the new NSC?

27) An entrepreneur makes T-shirts for major music events and must decide how many to produce for a single upcoming concert. During the event date, which is a single date, you can sell for US$20/shirt, but at the end of the musical event you have to auction off the remaining ones at 20% of their original price. If its production cost is equivalent to 40% of its price and considering that the entrepreneur has estimated the probabilities of its sales according to the attached table. Suggest to the entrepreneur how many t-shirts he should produce for the next event?

Demand      Probability

300               0.05

400               0.10

500               0.40

600               0.20

700               0.15

800               0.10