In the initial solution of a transportation problem, the only restriction is that there should be non zero quantities in a majority of the boxes when demand must equal supply. all constraints must not be satisfied. all constraints must be satisfied. we must have a number which is equal to the number of rows plus the number of columns minus one of boxes which contain non zero quantities.
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- The Delta company uses three raw materials to make cakes. Delta is trying to reduce warehousing costs and establishes three policies to that end: i) The annual number of orders for all products must be at least 20 per contractual terms with transportation providers. ii) The average inventory in units must be a maximum of 1800. iii) Because the raw material is perishable, there can never be more than 2000 units in inventory of raw material 1. Raw material 2 has a maximum allowed of 1200 units and the raw material 3 can store maximum 400 units. The following table shows the product information: Materia Demanda Costos por unidad Costo por prima (u/año) ordenar ($) 2200 2 300 2 500 4 650 3 3000 10 100 Consider an interest rate of 10% per year. A) Formulate the problem as a mathematical programming model that minimizes the total annual cost. b) Represent the problem in a single equation including the constraints in terms of lambda c) Find the optimized batch sizes for the company's raw…In the fashion retail industry transshipment is the flow of the products from a retail location to another one to satisfy the demand at the receiver location. Sender only sends a product if it has excess inventory to its demand and it occurs to rebalance the inventory among retail locations. Assume that there is a retailer with I stores. There are O products nominated for transshipment. The available inventory rio, i = 1,2, ..., I, o = 1,2, ..., 0, and demand levels dio, i = 1,2, ..., I, o = 1,2, ..., 0, for all O, stores are known. Moreover, the sales prices of these products are known and are the same in all stores, po, o = 1,2, ... 0. There is a transportation cost when a product is sent from a store to another, Cij, i, j = = 1, 2, ... D which is independent for the type of the product. Assume that if a product o is transshipped from store i, all its available inventory, i.e., rio, must be sent to a single store, thus, partial transshipment is not allowed. However, a store can…Happy Henry’s car dealer sells an imported car called the EX123. Once everythree months, a shipment of the cars is made to Happy Henry’s. Emergencyshipments can be made between these three-month intervals to resupply the carswhen inventory falls short of demand. The emergency shipments require twoweeks, and buyers are willing to wait this long for the cars, but will generally goelsewhere before the next three-month shipment is due.From experience, it appears that the demand for the EX123 over a three-monthinterval is normally distributed with a mean of 60 and a variance of 36. The cost ofholding an EX123 for one year is $500. Emergency shipments cost $250 per carover and above normal shipping costs.a. How many cars should Happy Henry’s be purchasing every three months?b. Repeat the calculations, assuming that excess demands are back-ordered fromone three-month period to the next. Assume a loss-of-goodwill cost of $100 forcustomers having to wait until the next three-month period and a…
- The Frist Corporation has the followinginternal controls related to inventory:1. Only authorized inventory warehousing personnel are allowed in inventory storageareas.2. All inventory products are stored in warehousing areas that are segregated fromother storage areas used to house equipment and supplies.3. All inventory held on consignment at Frist Corporation is stored in a separatearea of the warehouse.4. The inventory purchasing system only allows purchases from pre-approved vendors.5. The perpetual inventory system tracks the average number of days each inventoryproduct number has been in the warehouse.6. Microchips are embedded in each product and when inventory items are removedfrom the warehouse to shipping, radio-frequencies signal a deduction of inventoryto the perpetual inventory system.7. On a weekly basis, inventory accounting personnel take samples of inventoryproducts selected from the perpetual inventory system and verify that the inventoryis on-hand in the warehouse…7. Maribel is considering installing ice cream stalls on Turtle Beach. The length of the beach is 5 miles long. On average, in a week, there are 1,000 subathers that come to the beach and each value an icecream at $5. Transportation costs are $2.5. Each icecream costs $0.5 to make and there are $40 as a fixed maintenance cost per stall. 1. Find the optimal number of stalls for Maribel? 2.What is the profit at optimal number of stalls?3. The cost of carrying one unit in inventory for a specified period of time, usually one year, is referred to as: OA) the material cost and is denoted by C. OB) the fixed ordering cost and is denoted by S. OC) the holding cost and is denoted by H. OD) the purchase price and is denoted by P.
- Just need help finding the sausage constraint quantity valueIn a large microelectronics plant, the assembly cell for circuit boards has a demand for 300 units an hour. Two feeder cells supply partsA and B to the assembly cell (one A and one B for each board). Standard containers that look like divided trays are used. A container will hold 22 As or 13 Bs. It takes 13 minutes to fill up a container with As and 22 minutes to fill up a container with Bs. Transit time to the assembly cell is 5 minutes for both A and B. No safety factor is used. Kanbans to be circulated Between Process A and Assembly cell? Kanbans to be circulated Between Process B and Assembly cell?Minimize z= 5.15x1+ 4.5x2 + 4.36x3 (hundreds of dollars) s.t: ?x1 + ?x2 + ?x3 > 140 ?x1 + ?x2 + ?x3 s 200 (production capacity: hours) (warehouse capacity; hundreds of sq. ft.) ?x1+?x2 = 5 (demand for 6 oz. giasses; hundreds of cases) x1, x2, x3 20 4.5X2 -1.25 Basis Св 5X1 4.36X3 S1 S2 a3 RHS -0.75 10.7 X3 1. 4.36 -0.13 11.25 1.25 -2.5 11.5 S2 0.1 X1 5.15 C-Z How much is it worth an extra hour added to b1 on the optimal solution?
- The GIIC -Company must determine a policy for ordering coal to operate 15 smelters. Each smelter requires exactly 5 tons of coal per day to operate, and the firm operates 360 days per year. The purchasing manager has negotiated a contract to obtain the coal for 5 BD per ton for the coming year. The purchasing manager has determined that the ordering cost is 40 BD per order, and the cost of holding coal is 20% per ton of its value. i. Determine the optimal quantity of coal to receive in each order. ii. Determine the total inventory-related costs associated with the optimal ordering policy (do not include the cost ii. If five days' lead time is required to receive an order of coal, how much coal should be on hand when an iv. Optimal quantity 1837.11 Tons, Total cost 1837.11 BD, Inventory during LT 275 Tons of the coal). order is placed? i. Optimal quantity 1469.694 Tons, Total cost 1469.694 BD, Inventory during LT 375 Tons ii. Optimal quantity 734.85 Tons, Total cost 1649.694 BD,…Irvine Consolidated Closets (ICC) builds and sells shelving for homes and offices. For a certain shelving unit, SS1, ICC has gross requirements of 500, 800, and 650 units in weeks 4, 5, and 6, respectively. The lead-time on the SS1 shelving unit is two weeks. ICC currently has 600 of the SS1 on hand and this product is ordered in lot sizes of 300, that is, the order in multiples of 300. Determine the MRP schedule for the SS1 unit over a time frame of weeks 1 through 6. When and for how many units should ICC place their orders for the SS1? A key component of the SS1 is the TT2. Each SS1 contains four TT2s. Currently TT2’s are ordered in lots of size 1000 and there are 800 on hand. TT2s have a one-week lead time. Determine the MRP schedule for the TT2 unit over a time frame of weeks 1 through 6. When and for how many units should ICC place their orders for the TT2? Suppose annual demand for the SS1 shelving unit is 32,500. ICC’s holding cost is $0.50 per week for each SS1…1. Suppose the demand of a product in a retail store is 800 per year and it occurs at a constant rate. Placement of an order of this product to an outside supplier by the store is 40 Dollar. The super market authority has calculated the inventory holding cost per unit per year as 90 cents. Assuming no occurrence of shortages of the product, find a) i. the minimal order quantity of the product from the outside supplier if the product is not allowed to sell during production. ii. the minimal number of orders per year. Explain whether the nearest integer number of orders per year is justified. iii. the cycle time of a lot in months. iv. the annual minimal total cost of ordering and inventory holding for that minimal order quantity. v. the reorder point if the lead time of delivering a lot is 2 days,? b) If the production rate of processing the product is 1200 per year and the set up cost per set up is 65 Dollar. If the selling of the product is allowed during production, determine i) the…