A shoe store orders shoes from the manufacturer and sells them at a mall. Storing shoes at the store costs $8 per shoe pair for a year. When reordering shoes from the manufacturer, there is a fixed cost of $16 per order as well as $4 per shoe pair. The retail store sells 750 shoe pairs each year. Find a function that models the total inventory costs as a function of the number of shoe pairs in each order from the manufacturer.
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- A firm uses the order-up-to model to manage its inventory. It wants to increase its in-stockprobability while decreasing its holding costs (i.e., reducing its average inventory). Which ofthe following actions will help to achieve this goal? (Consider each action independently.)I. Decrease the lead time.II. Increase the order-up-to level.III. Increase the average quantity on order.a. Only Ib. Only IIc. Only IIId. I and IIe. I and IIIf. II and IIIg. Any of them will help (that is I, II, or III).h. None of them will help.The lead time demand for bathing suits is governed bythe discrete random variable shown in Table 11. Thecompany sells an average of 10,400 suits per year. The costof placing an order for bathing suits is $30, and the cost ofholding one bathing suit in inventory for a year is $3. Thestockout cost is $3 per bathing suit. Use marginal analysisto determine the optimal order quantity and the reorderpoint.Lead TimeDemand Probability180 .30190 .30200 .15210 .10220 .15Rocky Mountain Tire Centre sells 20,000 tires of a particular type per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20. per tire if fewer than 500 tires are ordered, $18. Per tire if more than 500 but fewer than 1,000 tires are ordered and $17. per tire if 1,000 or more tires are ordered. Quantity Unit Price 1-499 $20. 500-999 $18. 1000 & over $17 Based on available information, lead time demand for CD-ROM drives averages 50 units (normally distributed), with a standard deviation of 5 drives. Management wants a 97% service level. What value of Z should be applied? How many drives should be carried as safety stock?
- A company would like to classify its inventory systems using ABC Inventory classification system. The rules for ABC dassification are STRICTLY applied such that 80% cumulative budget is assigned to A class inventory items. The next 15% cumulative budget is assigned to B class inventory items, and Only 5% of the cumulative budget is assigned to class inventory itemsThe inventory items are XYZ1, XYZ2, XYZ3and respectively. The Annual demands (units per year) for these items are 290,457159, and 577 respectively. Also, the corresponding per unit prices are 19 33, 126and respectively measured in OMR. Which items (among XYZ1, XYZ2, XYZ3, and XYZ4) are classified as Adass inventoryAfter taking a production seminar, Al Weiss, the owner of Weiss’s paint storementioned in Problem 14, decides that his stock-out cost of $10 may not be veryaccurate and switches to a service level model. He decides to set his lot size by theEOQ formula and determines his reorder point so that there is no stock-out in90 percent of the order cycles.a. Find the resulting (Q, R) values.b. Suppose that, unfortunately, he really wanted to satisfy 90 percent of hisdemands (that is, achieve a 90 percent fill rate). What fill rate did he actuallyachieve from the policy determined in part (a)?ABC firm uses roughly 3,400 pounds of chemical dye a year. Currently, the firm purchases 300 pounds per order and pays P120.00 per pound. The supplier has just announced that orders of 1,000 pounds or more will be filled at a price of P80.00 per pound. The manufacturing firm incurs a cost of P4,000.00 each time it submits an order and assigns an annual holding cost of 17% of the purchase price per pound. a. Determine the order size that will minimize the total cost.b. If the supplier offered the discount at 1,500 pounds instead of 1,000 pounds, what order size would minimize total cost?
- Rocky Mountain Tire Center sells 20,000 go-cart tires per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year.The purchase price is $20 per tire if fewer than 500 tires are ordered, $18 per tire if 500 or more-but fewer than 1,000- tires a re ordered, and $17 per tire if I ,000 or more tires areordered.a) How many tires should Rocky Mountain order each time it places an order?b) What is the total cost of this policy?The best quantity to order One of the formulas for inventorymanagement says that the average weekly cost of ordering, payingfor, and holding merchandise iswhere q is the quantity you order when things run low (shoes,TVs, brooms, or whatever the item might be); k is the cost ofplacing an order (the same, no matter how often you order); c isthe cost of one item (a constant); m is the number of items soldeach week (a constant); and h is the weekly holding cost per item(a constant that takes into account things such as space, utilities,insurance, and security). Find dA>dq and d2A>dq2.A wholesaler has a steady demand for 50 items of a given product each month.The purchase cost of each item is 6 MU and the holding cost for this item is estimated tobe 20% of the stock value per annum. Every order placed by the wholesaler cost 10 MUin administration charges regardless of the number ordered? Please mention formulas and do it in detail so I can understand.
- A coffee shop uses approximately 250 pounds of a particular type of coffee every week. The shop is open 52 weeks a year. The annual carrying charge for the coffee is 20%. If 1 pound of coffee costs the shop $12.00 and the cost associated with each order is $39, how many pounds of this coffee should be ordered each time an order is placed in the shop wants to minimize its total annualized inventory-related costs?A company manufactures 5,000 units of a product per month. The cost of placing an order is Rs. 100. The purchase price of the raw material is Rs. 10 per kg. The re-order period is 4 to 8 weeks. The consumption of raw materials varies from 100 kg to 450 kg per week, the average consumption being 275 kg The carrying cost of inventory is 20% per annum. You are required to calculate- (a) Re-order Quantity (b) Re order Level (c) Maximum Level (d) Minimum Level le) Average Stock LevelSolve this please theoretically not on excel A detergent manufacturer manages a plant for a major retail. The average monthly demand is 12,000 jugs of detergent. Each jug costs $(1.3) and is sold to the retailer at a wholesale price of $8. The manufacturer and the retailer use an annual holding cost of (29)%. For each order placed, the retailer incurs an ordering cost of $80. Manufacturer incurs the cost of transportation and loading which totals $2,000 per order shipped. a. To minimize its inventory-related costs, what lot size will be the best for the retailer? What is the annual inventory-related cost of the manufacturer and the retailer as a result of this policy? b. What lot size minimizes the inventory-related costs across both the manufacturer and the retailer? How much reduction in cost relative to (a) results from this policy? c. Design an all-unit quantity discount that results in the retailer ordering the quantity in (b