6578Assume the lead time is 1.5 weeks, the inventory period is 4.6 weeks, and thestockout level is 10%.Week Demand13247042446741242642648050748744910Note: Use Excel function to find Mean and Sample Demand Variance of the dataset.Q13.1. The Reorder point is approximately -Q13.2. The Lot size (Q) isFormulas: ROP = Mean*Lead time +Z*sqrt (Variance* Lead time)Lot size = Mean Demand * Inventory Period. (Q=M*T)401LL44LT

Economic order quantity (EOQ) is the optimal order quantity that helps in minimizing the total…

Answered: 7 69 6 8 5 3 4 Assume the lead time is…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section3.8: A Multiperiod Production Model

Problem 22P

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The table below provides demand data for 11 days (days 10-20 for the current year) for one product for the next 4 questions. The previous order was for 300 units at the end of day 9. The lead time is a constant two days. At the beginning of day 10 the inventory level is 450 units. Orders are made at the end of a day. Suppose inventory is managed with a reorder point system where Q=300 and the reorder point is 250. Day Demand Inventory 10 120 11 150 12 120 13 100 14 80 15 80 16 60 17 60 18 60 19 40 20 80 1) When is the next order? end of day ________ 2) How large is the next order? ________ 3) When is the subsequent order (after that above)? end of day _______ 4) How large is that order? _________
The demand for a clothing brand is shown in the table below. The cost per order is about $4000. Cost of each unit of clothing = $5. Carrying cost percentage = 25% per item per 5 months. The analysis period = 5 month duration. Month Demand 1 400 2 300 3 200 4 400 5 500 a. Using this data, compute the solutions using the Lot for Lot and Periodic Order Quantity heuristics? Which of these heuristics would perform better and why? b. Assuming that the demand follows a normal distribution with the mean and variance from the data given above, determine the optimal order should be greater or lesser than the single period EOQ model.
Penalty costs can be assessed only against the number of units of demand that cannot be satisfied, or against the number of units weighted by the amount of time thatan order stays on the books. Consider the following history of supply and demandtransactions for a particular part:Number of Items Demand duringMonth Received MonthJanuary 200 520February 175 1,640March 750 670April 950 425May 500 280June 2,050 550Assume that starting inventory at the beginning of January is 480 units.a. Determine the ending inventory each month. Assume that excess demands areback-ordered.b. Assume that each time a unit is demanded that cannot be supplied immediately,a one-time charge of $10 is made. Determine the stock-out cost incurred duringthe six months (1) if excess demand at the end of each month is lost, and (2) ifexcess demand at the end of each month is back-ordered.c. Suppose that each stock-out costs $10 per unit per month that the demandremains unfilled. If demands are filled on a first-come,…
Quantity discounts. This type of problem can be recognized when a list showing prices for eachquantity range is given along with the basic EOQ information.a. If unit holding cost is constant, use these steps to solve the problem:1. Use Formula 13–2 to find Q.2. Locate Q in the price schedule.3. Compute TC using Formula 13–1 for Q and for all lower-cost price breaks.b. If unit holding cost is a percentage of unit price, use these steps to solve the problem:1. Beginning with the lowest cost, and using the corresponding H for that cost, compute Qusing Formula 13–2. Continue moving up in unit cost until a feasible Q is found.2. Locate the feasible Q in the price schedule.3. Compute TC using Formula 13–9 for Q and for all lower-cost price breaks. Remember to usethe corresponding H for each price.A small manufacturing firm uses roughly 3,400 pounds of chemical dye a year. Currently the firmpurchases 300 pounds per order and pays $3 per pound. The supplier has just announced that ordersof…
Suppose demand is know and constant at 500 units per year (one year has 250 working days). The holding cost is $2 per unit per year and the ordering cost is $20 per order. Also assume that the lead time is 10 days. Compute the optimal order quantity (EOQ) and the optimal annual inventory cost. Draw a picture of the evolution of the inventory level with time. Indicate the ROP on the picture as well as the length of the cycle. Now assume that the lead time is 90 days. Indicate the ROP on the picture.
The demand for a certain article is 400 art/month. The ordering cost is $35 and the storage cost is $10/month. The purchase cost is $15 but if 70 items or more are purchased there is a discount andThey drop at $10. a) Obtain the optimal amount of inventory Yb) Obtain the total cost of inventoryc) Is it convenient to accept the discount?d) What is the cost of inventory with quantity m?
c. Once you find the optimal order quantity i.e., EOQ, create a Data Table that generates inventory cost within ±100 units (with 10units increment) from the optimal order quantity. For example, if the EOQ=150, then you need to generate Data Table for inventory cost starting from 50 to 250 with 10 increments. Explain the exact steps completed in excel to create the data table d. Create a Scatter plot with “smooth lines” for the Data Table created in c) to show the inventory cost. Label your plot clearly (axis and title). The optimum order quantity should indicate the minimum cost in your plot.
A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)d. Which method resulted in the lowest-cost policy for this problem?
A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)a. What ordering policy is recommended by the Silver–Meal heuristic?
A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)c. What ordering policy is recommended by the least unit cost heuristic?
A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)b. What ordering policy is recommended by the part period balancing heuristic?
A distribution center (DC) in Wisconsin stocks Sony plasma TV sets. The center receives its inventory from a mega warehouse in Kansas with a lead time (L) of 5 days. The DC uses a reorder point (R) of 300 sets and afixed order quantity (Q) of 250 sets. The current on-hand inventory (OH) at the end of Day 1 is 400 sets, there are no scheduled receipts (SR), and there are no backorders (BO). Assume that all demands and receipts occur at the end of the day. The inventory position is compared to the reorder point after demands and receipts are accounted for. If necessary, an order is placed and the inventory position is updated. Given the demand schedule in the table below, determine when to order using a (Q) system

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7 69 6 8 5 3 4 Assume the lead time is 1.5 weeks, the inventory period is 4.6 weeks, and the stockout level is 10%. Week Demand 1 470 424 467 412 426 426 2 480 507 487 401 H 10 Note: Use Excel function to find Mean and Sample Demand Variance of the dataset. int is approximately