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Home Work Chapter to Book: Business Logistics/Supply Chain Management Ronald H Ballou Excel sheet: Logistics management.xlsx Student Name: Shaheen Sardar Course Name: Logistics Management Department: Industrial and Management Engineering, Hanyang University, South Korea Home Work Chapter 1: Business Logistics/Supply Chain Question 12: Suppose that a manufacturer of men's shirts can produce a dress shirt in its Houston, Texas, plant for $8 per shirt (including the cost of raw materials) Chicago is a major market for 100,000 shirts per year The shirt is priced at $15 at Houston plant Transportation and storage charges from Houston to Chicago amount to $5 per hundredweight (cwt.) Each packaged shirt weighs pound As an alternative, the company can have the shirts produced in Taiwan for $4 per shirt (including the cost of raw materials) The raw materials, weighing about pound per shirt, would be shipped from Houston to Taiwan at a cost of $2 per cwt When the shirts are completed, they are to be shipped directly to Chicago at a transportation and storage cost of $6 per cwt An import duty of $0.50 per shirt is assessed (a) From a logistics-production cost standpoint, should the shirts be produced in Taiwan? (b) What additional considerations, other than economic ones, might be considered before making a final decision? Solution: cwt Material Unit Transport Cost Production (Houston to Cost Plant Location Taiwan) Houston plant NO $8 (USA) Outsourcing to $2 $4 Taiwan (Asia) cwt Product Transportation/ storage charges (Houston to Chicago) $5 Note: hundredweight (cwt) = 100 pounds weight Each packed shirt weight = pound Raw material weight per shirt = pound Unit Material Unit Transport Cost Production (Houston to Cost Plant Location Taiwan) Houston plant NO $8 (USA) Outsourcing to $0.02 $4 Taiwan (Asia) Unit Material Transport Cost = Raw Material Density/CWT Unit Product Transport Cost = Product Density/CWT Example: $2/100 = $0.02 Unit Product Unit Product Unit Import Transportation/ Transportation Duty storage charges /storage charges (Houston to Chicago) (Taiwan to Chicago) $0.05 NO NO NO NO cwt Product Unit Import Transportation Duty /storage charges (Taiwan to Chicago) NO NO $6 $0.06 $0.50 $0.50 Following formulas are used • Total Material Transport Cost = Product Volume * Unit Material Transport Cost • Total Product Transport Cost = Product Volume* Unit Product Transport Cost • Total Production Cost = Product Volume * Unit Production Cost • Total Import Duty = Product Volume * Unit Import Duty • Total Cost = Total Material Transport Cost + Total Product Transport Cost + Total Production Cost + Total Import Duty • Total Price = Product Volume * Shirt Price/unit • Total Profit = Total Price - Total Cost Total Unit Total Total Shirt Product Material Product Total Production Import price/ Total price Profit Volume Transport Transport Cost Cost Duty unit Plant Location Cost Cost Houston plant 100000 $800,000 $5,000 $805,000 $15 $1,500,000 $695,000 (USA) Outsourcing to 100000 $400,000 $2,000 $6,000 $50,000 $458,000 $15 $1,500,000 $1,042,000 Taiwan (Asia) From a logistics-production cost standpoint, the shirts should be produced in Taiwan There is a cost for raw materials from Houston to Taiwan, but still is cheaper than the Houston plant when other costs are combined Following additional considerations might be considered before making a final decision • How long the shirts would be stored (holding cost) from plant-to-truck-to-final destination • Order processing cost for suppliers needs to be done strategically (to have least cost of shipping to Chicago) • How order is transported at least cost, most efficiently, and within the time allotted • Supplier availability in Taiwan • Capacity availability in Taiwan • Risk of late delivery in Taiwan • Quality and reliability issues in Taiwan • Effective inventory lot-sizing in Taiwan • Other strategic considerations in USA as well as in Taiwan Home Work Chapter 2: Logistics/Supply Chain Strategy and Planning Question 13: The traffic manager of the Monarch Electric Company has just received a rate reduction offer from a trucking company for the shipment of fractional horsepower motors to the company's field warehouse The proposal is a rate of $3 per hundredweight (cwt.) if a minimum of 40,000 pounds is moved in each shipment Currently, shipments of 20,000 pounds or more are moved at a rate of $5 per cwt If the shipment size falls below 20000 pounds, a rate of $9 per cwt applies To help the traffic manager make a decision, the following information has been gathered: Annual demand on warehouse 5,000 motors a year Warehouse replenishment orders 43 orders a year Weight of each motor, crated 175 lb per motor Standard cost of motor in warehouse $200 per motor Stock replenishment order handling cost $15 per order Inventory carrying cost as percentage of average value of inventory on hand for a year Handling cost at warehouse $ 0.30 per cwt Warehouse space unlimited 25% per year Should the company implement the new rate? Solution: Circumstance 1: Rate for shipment weight ≥ 40000 = $3 per cwt (New proposal) Circumstance 2: Rate for shipment weight ≥ 20000 = $5 per cwt (Present) Circumstance 3: Rate for shipment weight < 20000 = $9 per cwt (Present) Shipment size is more than 20000 or minimum 40000, so we will not investigate Circumstance Weight of total motors (annual requirement) = 5000 motors/year * 175 lb /motor = 875000 lb / year = 8750 cwt/year (i.e cwt = 100 lb.) Cost for Circumstance 1: (For new proposal) Trucking cost = $3/cwt * 8750 cwt / year = $ 26250/year Ordering cost = 21 orders * $ 15 /order = $ 315 Handling cost at warehouse = $0.3/cwt *8750 cwt / year = $ 2625 Total Cost = $ 26250 + $ 315 + $ 5715 + $ 2625 = $ 34905 Cost for Circumstance 2: (For present situation) Trucking cost = $5/cwt * 8750 cwt / year = $ 43750 Ordering cost = 43 orders * $ 15 /order = $ 645 Handling cost at warehouse = $0.3/cwt *8750 cwt/ year = $ 2625 Total Cost = $ 43750 + $ 645 + $ 2857 + $ 2625 = 49877 Circumstance Total Cost: (For new proposal) = $ 34905 Circumstance Total Cost: (For present situation) = $ 49877 Yes, the company should implement the new rate Home Work Chapter 3: Logistics/Supply Chain Product Question 11: Davis Steel Distributors is planning to set up an additional warehouse in its distribution network Analysis of item-sales data in its other warehouses shows that 25% of the items represent 75% of the sales volume The company also has an inventory policy that varies with the items in the warehouse That is, the first 20% of the items are the A items and are to be stocked with turnover ratio of The next 30% of the items, or B items, are to have turnover ratio of The remaining C items are to have a turnover ratio of There are to be 20 products held at the warehouse with sales forecasted to be $2.6 million annually What dollar value of the average inventory would you estimate for the warehouse? Solution: Number of items = N = 20 Sales = $2.6 million = $2600000 Cumulative sales proportion is Projected items sales = difference between cumulative sales for successive items Alternative Method Cumulative sales proportion is Cumulative sales () =$2600000* = 1,800,000 Projected Item Sales () = $1,800,000 Cumulative sales () =$2,600,000* = $2,340,000 The product group B sales will be A+B sales less A sales Projected Item Sales () = = $2,340,000- $1,800,000 = $540,000 Cumulative sales () =$2,600,000* = 2,600,000 The product group C sales will be A+B+C sales less A+B sales Projected Item Sales () = = 2,600,000-$2,340,000= $260,000 Dollar value of the average inventory for the warehouse is Question 12: Beta Products is planning to add another warehouse Ten products from the entire line are to be stored in the new warehouse These products will be the A and B items All C items are to be served out of the plant Forecasts of annual sales that are expected in the region of the new facility are million cases (A, B, and C items) Historical data show that 30 percent of the items account for 70 percent of the sales The first 20 percent of the entire line are designated as A items, the next 30 percent as B items, and the remaining 50% as C items Inventory turnover ratios in the new warehouse are projected to be for A items and for B items Each inventory item, on the average, requires 1.5 cubic feet of space Product is stacked 16 feet high in the warehouse What effective storage space is needed in square feet excluding aisle, office, and other space requirements? Solution: All C items are to be served out of the plant So, we will consider only A and B Number of items = N = 10 Sales = $3 million = $3000000 Cumulative sales proportion is Projected items sales = difference between cumulative sales for successive items Space requirement = 1.5 cubic feet Stack height requirement = 16 feet Effective storage space required = 33110 Question 13: An analysis of the product line items in the retail stores of the Save-More Drug chain shows that 20% of the items stocked account for 65% of the dollar sales A typical store carries 5,000 items The items accounting for the top 75% of the sales are replenished from warehouse stocks The remainder is shipped directly to stores from manufacturers or jobbers How many items are represented in the top 75% of sales? Solution: From equation (1), we have Now From equation (2), we have 29% of the items represent the top 75% of sales Total number of items = 5,000 Number of items that represent 75% of sales = 0.29*5000 = 1450 Question 14: The cost associated with producing, distributing, and selling a domestically produced automotive component to Honda in Japan can be summarized as follows: Cost type Purchased materials Manufacturing labor Overhead Transportation Sales Profit Cost per Unit, $ 25 10 Varies by shipment size Transportation costs vary as follows If the purchase (shipping) quantity is 1000 units or less, the transportation cost is $5 per unit For more than 1000 units but less than or equal to 2000 units, the transportation cost is $4 per unit For more than 2000 units, the transportation cost is $3 per unit Construct a price schedule, assuming the vendor would like to pass the transportation economies on to the customer Indicate the discount percentage the customer will receive through buying at various quantities Solution: Case 1: Quantity is 1000 units or less Total cost = $25 + $10 +$5 + $5 + $8 + $5 = $58 Case 2: Quantity is more than 1000 units but less than or equal to 2000 units Total cost = $25 + $10 +$5 + $4 + $8 + $5 = $57 Discount rate between Case and Case 2: Case 3: Quantity is more than 2000 units Total cost = $25 + $10 +$5 + $3+ $8 + $5 = $56 Discount rate between Case and Case 3: Discount rate between Case and Case 3: Home Work Chapter 4: Logistics/Supply Chain Customer Service Question 6: The Cleanco Chemical Company sells cleaning compounds (dishwashing powders, floor cleaners, nonpetroleum lubricants) in a keenly competitive environment to restaurants, hospitals and schools Delivery time on orders determines whether a sale can be made The distribution system can be designed to provide different average levels of delivery time through the number and location of warehousing points, stocking levels and order processing procedures The psychical distribution manager has made the following estimates of how service affects sales and the cost of providing service levels: Estimated annual sales (millions of $) Cost of distribution (millions of $) Percentage of orders delivered in one day 60 70 80 90 95 8.0 10.0 11.0 11.5 11.8 6.0 6.5 7.0 8.1 9.0 50 4.0 5.8 100 12.0 14.0 (a) What level of service should the company offer? (b) What effect would competition likely have on the service level decision? Solution (a): Profit = Estimated annual sales – cost of distribution Estimated annual sales (millions of $) Cost of distribution (millions of $) 50 4.0 5.8 Profit (millions of $) -1.8 Percentage of orders delivered in one day 60 70 80 90 95 8.0 10.0 11.0 11.5 11.8 6.5 8.1 3.5 3.4 2.8 100 12.0 14 -2 Profit is $4 million at 80% service level Company maximizes the profit when it serves at 80% service level Company should offer 80% of service level Solution (b): Suppose the product’s price and quality is the same in all competing companies If a company A increases its service level, other competitor companies will also increase their service levels Based on competition, the company A will change its service level, resulting in change in its profit (otherwise loss of customers) Question 7: Five years ago, Norton Valves, Inc., introduced and publicized a program under which 56 items in its hydraulic valve line would be made available on a 24-hour-delievery basis, instead of normal 1-to 12-week delivery period Quick order processing, stocking to anticipated demand, and using premium transportation services when necessary were elements of the 24-hour delivery program Sales history was recorded for the five years before the service change as well as for a five-year period after the change Because only a portion of the product family was subject to the service improvement, the remaining products (102 items) served as a control group Statistics for one of the test product groups showing the before and after annual units sales levels are given as follows: Sales before service change Sales after service change 5-Year Average Standard 5-Year Average Standard Deviation Deviation Test group 1342 335 2295 576 Control group 185 61 224 76  Standard Deviation: For the individual sales  Test group: Products in family with 24-hour delivery  Control group: Products in family with 1-to 12-week delivery Product Family The average value of products in this family was $95 per unit The incremental cost for the improved service was $2 per unit, but the company did not intend to pass along the costs as a price increase Instead it hoped that additional sales volume would more than offset the added costs The profit margin on sales at the time was 40 percent (a) Should the company continue the premium service policy? (b) Appraise the methodology as a way of accuracy determining the sales-service effect Solution: (a) • Before: (1342+185)*95*0.40 = $58026 • After: (2295+224)*95*0.40 – (2295*2) = $91132 • Company should continue the premium service policy Solution: (b) We appraise the methodology as a way of accurately determining the sales-service effect Question 8: A food company is attempting to set the customer service level (in-stock probability in its warehouse) for a particular product line item Annual sales for the item are 100,000 boxes, or 3846 boxes biweekly The product cost in inventory is $10, to which $1 is added as profit margin Stock replenishment is every two weeks, and the demand during this time is assumed to be normally distributed with a standard deviation of 400 boxes Inventory carrying costs are 30% per year of item value Management estimates that a 0.15% change in total revenue would occur for each 1% change in the in-stock probability (a) Based on this information, find the optimum in-stock probability for the item (b) What is the weakest link in this methodology? Why? Solution: (a) Optimum service level is the point where the change of cost equals to the change of profit (∆p = ∆c) ∆p = Trading margin*sales response rate *annual sales ∆p = $1*0.0015*100000 ∆p = $150 per year (per 1% change in the service level) ∆c = annual carrying cost * standard product cost * ∆z*demand standard deviation over replenishment lead time ∆c = 0.30*$10*∆z*400 ∆c = $ 1200 ∆z ∆p = ∆c $150 = $1200*$∆z For the change in z found in a normal distribution table, the optimum in-stock probability during the lead time is about 96-97% Solution: (b) The weakest link in methodology is that ∆p is assumed as constant for all service levels, in fact, in most cases ∆p is a decreasing function of service level We not have the correct data about interrelation of service level and sales (Weakest link in this analysis is estimating the effect that a change in service will have on revenue) Question 9: An item in the product line for the food company discussed in question has the following characteristics: Sales response rate = 0.15% change in revenue for a 1% change in the service level Trading margin = $0.75 per case Annual sales through the warehouse = 80,000 cases Annual carrying cost = 25 % Standard product cost = $10 Demand standard deviation = 500 cases per week lead time Lead time = week Find the optimum service level for this item • • No U-turns are permitted The bus has adequate capacity to transport all the children on the route Use a ruler or linear grid to determine the total distance for the bus tour Solution: This problem can be used effectively as an in-class exercise Although the problem might be solved using a combination of the shortest route method to find the optimum path between stops and then a traveling salesman method to sequence the stops, it is intended that students will use their cognitive skills to find a good solution The class should be divided into teams and given a limited amount of time to find a solution They should be provided with a transparency of the map and asked to draw their solution on it The instructor can then show the class each solution with the total distance achieved From the least-distance solutions, the instructor may ask the teams to explain the logic of their solution process Finally, the instructor may explore with the class how this and similar problems might be treated with the aid of a computer Although the question asks the student to use cognitive skills to find a good route, a route can be found with the aid of the ROUTER software in LOGWARE The general approach is to first find the route in ROUTER without regard to the rectilinear distances of the road network Because this may produce an infeasible solution, specific travel distance are added to the database to represent actual distances traveled or to block infeasible paths from occurring A reasonable routing plan is shown in the Figure below: The total distance for the route is 9.05 miles and at a speed of 20 miles per hour, the route time is approximately 30 minutes The ROUTER database that generates it is given below Question 6: Dan Pupp is a jewelry salesperson who calls on store accounts in the Midwest One of his territories is shown in Figure 7-23 (see Book) His mode of operation is to arrive at the territory the night before making his calls to stay at one of the local motels He covers the region in two days and leaves the morning of the third day Since he pays his own expenses, he would like to minimize his total costs for serving the accounts Accounts to are covered the first day, and the remainder are visited the second day He would like to compare two strategies: Strategy 1: Stay at Motel M2 all three nights at $49.00 per night Strategy 2: Stay at Motel M1 to visit accounts to 9, staying there two nights at $40.00 per night Then, stay at Motel M3 one night at $45.00 per night to visit accounts 10 to 18 After visiting accounts to 9, he returns to M to stay overnight before moving to M He then stays overnight at M before moving on the next morning The distance between M1 and M3 is 36 miles Disregard any distance that he travels to and from the territory Dan figures mileage costs at $0.30 per mile Which strategy seems best for Dan? Solution: Strategy is to stay at motel M and serve the two routes on separate days Using the ROUTESEQ module in LOGWARE gives us the sequence of stops and the coordinate distance The routes originating at M would be as follows: Question 7: A bakery delivers daily to five large retail stores in a defined territory The driver person for the bakery loads goods at the bakery, makes deliveries to the retail stores, and returns to the bakery A diagram for the territory is shown in Figure 7-24 (see Book) The associated network travel times in minutes are: To  Bakery From Bakery 22 47 39 57 21 24 35 27 42 16 50 32 17 18 57 38 23 15 16 21 55 45 21 14 41 20 18 60 25 42 (a) What is the best routing sequence for the delivery truck? (b) If loading or unloading times are significant, how might they be included in the analysis? (c) Retail store is located in such a densely populated urban area that the travel times to and from this point may increase by as much as 50 percent, depending on the time of the day Travel times for other points remain relatively unchanged Would the solution in part (a) be sensitive to such variations? Solution: (a) Since distances are asymmetrical, we cannot use the geographically based traveling salesman method in LOGWARE Rather, we use a similar module in STORM that allows such asymmetrical matrices, or the problem is small enough to be solved by inspection For this problem, the minimal cost stop sequence would be as follows: Bakery →Stop → Stop 3→ Stop 4→ Stop 2→Stop 1→Bakery (with a tour time of 130 minutes) (b) Loading/unloading times may be added to the travel times to a stop Problem may then be solved as in part a (c) Travel times between stop and all other nodes are increased by 50 percent Remaining times are left unchanged Optimizing on this matrix shows no change in the stop sequence However, tour time increases to 147.50 minutes Question 8: Sima Donuts supplies its retail outlets with the ingredients for making fresh donuts A central warehouse from which trucks are dispatched is located in Atlanta Trucks can leave the Atlanta warehouse as early as A.M to make pallet-load deliveries to the Florida market and make returns at any time The trucks may also pick up empty containers and supplies from vendors in the general area Pickups are allowed only after all deliveries on a route are made A simple linear grid is placed over the Georgia-Florida area and grid coordinates found for warehouse, retail, and vendor sites The 0, coordinates are in the northeast corner For example, the Atlanta warehouse is located at X = 2084, Y = 7260 The scaling factor on the map, including a road circuitry factor, is 0.363 The total time on a route may be 40 hours and total route distance may be up to 1400 miles Team drivers are used so that no overnight breaks are required, but one-hour rest breaks are allowed at 12-noon and P.M each day Average driving speed is taken to be 45 miles per hour Additional data about the stops are as follows: No 10 11 Stop location Tampa, FL Clearwater, FL Daytona Beach, FL Fort Lauderdale, FL North Miami, FL Oakland Park, FL Orlando, FL St Petersburg, FL Tallahassee, FL West Palm Beach, FL Miami-Puerto Rico Stop Volume, XYLoading/ Unloading type Pallets Coordinate Coordinate Time (Min.) Delivery 20 1147 8197 15 Pickup 14 1206 8203 45 Delivery 18 1052 7791 45 Delivery 557 8282 45 Delivery 527 8341 45 Pickup 565 8273 45 Delivery 1031 7954 45 Pickup 1159 8224 45 Delivery 1716 7877 45 Delivery 607 8166 45 Delivery 527 8351 45 Total 80 Time Windows Open Close 6:00 A.M 12:00 A.M.a 6:00 A.M 12:00 A.M 6:00 A.M 12:00 A.M 3:00 A.M 12:00 A.M 6:00 A.M 12:00 A.M 3:00 A.M 12:00 A.M 3:00 A.M 12:00 A.M 3:00 A.M 12:00 A.M 10:00 A.M 12:00 A.M 6:00 A.M 12:00 A.M 6:00 A.M 12:00 A.M a Midnight There are three trucks with a 20-pallet capacity, one with a 25-pallet capacity, and one with a 30-pallet capacity The cost for drivers and truck is $1.30 per mile Design the routes for this set of deliveries and pickups Which trucks are to be assigned to which routes? What is the dispatch plan? What is the cost for dispatch? Solution: This may be solved by using the ROUTER module in LOGWARE The screen set up for this is as follows: Making a run with ROUTER, we have route deign as given in the following Figure: Question 9: Queens Lines operates a fleet of tanker ships to transport crude oil worldwide One scheduling problem concerns the movement of oil from Middle East ports to four European ports in England, France, and Belgium The sailing time in days between ports is Middle east ports A 20 17 European Discharge ports B C D 18 12 14 10 Within the next three months, deliveries are to be made according to the following schedule: From loading port At discharge port Day D 19 C 15 A 36 B 39 C 52 A 86 Assume that ships are available to start anywhere and can end up at any port How many ships are needed to meet the schedule, and how should they be deployed? ( Hint: Requires solving the linear programming transportation problem) Solution: Given sailing times and dates when deliveries are to be made, loadings need to be accomplished no later than the following dates: To: Fro m: A B 16 C 40 D 69 25 The problem can be expressed as a transportation problem of linear programming There will be initial states [(1,1), (2,5), (1,16), (2,25), (1,40), and (2,69)] and terminal states [(D,10), (C,15), (A,36), (B,39), (C,52), and (A,86)] The linear program is structured as shown in Figure below: Using a transportation solution method, we determine one of the optimum solutions There are several The solution is read by starting with the slack on initial loading state This tells us to next select the cell of terminal state In turn, this defines initial state and hence, terminal state And so it goes until we reach the terminal state slack column This procedure is repeated until all initial state slacks are exhausted Our solution shows two routings The first is (1,1) → (D,10) → (1,16) → (A,36) → (2,69) → (A,86) The second is (2,5) → (C,15) → (2,25) → (B,39) → (1,40) → (C,52) Two ships are needed Question 10: The Maxim Packing Company is considering a freight consolidation program for serving the Kansas market The program would involve the small-volume customers located at Hays, Manhattan, Salina, and Great Bend The proposal is to hold all orders from these areas for several weeks in order to realize lower transportation charges Assume all orders now shipped LTL directly from Fort Worth, Texas, to their destination in Kansas Average biweekly orders from the Kansas territory are as follows: Hays Manhattan Salina Great Bend 200 cases 350 325 125 The average case weighs 40 pounds Orders could be shipped in the biweekly period that they are received, held and shipped after two biweekly order periods, or held and shipped after three biweekly order periods The potential loss of sales has been estimated at $1.05 per case for each additional biweekly period that orders are held Transportation rates to Kansas are given in Table 7-7 Should the program be implemented? If so, how long should orders be held before shipment? Table 7-7: Trucks rate between Fort Worth Texas, and selected destination points in Kansas From Fort Worth to Truck AQa Hays 12.78 Manhattan 12.78 Salina 10.26 Great Bend 12.27 a Any quantity less than 10000 lb Rates ($/cwt.) ≥ 10000 lb ≥ 20000 lb 5.19 4.26 5.19 4.26 4.08 3.42 4.98 4.08 ≥ 40000 lb 3.06 2.22 2.46 2.94 Solution: This is a problem of freight consolidation brought about by holding orders so they can be shipped with orders from subsequent periods The penalty associated with holding the orders is a lost sales cost Question 11: The Sunshine Bottling Company bottles soft drinks that it distributes to retail outlets from nine warehouses in the Michigan area A single bottling plant is located in Flint, Michigan The product is shipped from plant to the nine warehouses in full truckload quantities The typical plat-to-warehouse movement is to transport a trailer of palletized soft drink to the warehouse, drop off the loading trailer, and bring a trailer of empty pallets back to the plant The unloading and hitching of the trailer at the warehouse takes 15 minutes Since the routes are traveled frequently, travel times, unloading times, and break times are known with a greater deal of certainty The number of trips needed to meet demand and the route times for a typical week are as follows (see Table below) Flint Alpena Saginaw Lansing Mt Pleasant W Branch Pontiac Traverse City Petoskey a Round trip time Distance, Miles 20 350 80 118 185 210 90 376 428 Number of Weekly Trips 43 21 12 43 Driving Time, HR.a 1.00 9.00 2.00 3.25 4.50 5.00 2.50 9.00 10.00 Unloading Time, hr 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 Break/Lunch time, hr 1.25 0.25 0.75 0.75 1.25 1.50 Total Route Time, hr 1.25 10.50 2.25 3.75 5.50 6.00 2.75 10.50 11.75 It is desirable to schedule trucks to leave the plant at or after 4:00 A.M and to return no later than 11:00 P.M the same day Unloading can take place only when the warehouse is open, which is from 6:30 A.M to 11:00 P.M By sequencing the routes to maximize truck utilization, determine the minimum number of trucks that is needed to serve all the routes The company was using 10 trucks Solution: Routes are built by placing the trips end-to-end throughout the day from a.m until 11 p.m., respecting the times that a warehouse can receive a shipment This is a 19-hour block of time per day, or there are 95 hours per week per truck in which a truck may operate If there were no delivery time restrictions on warehouses and trips could be 29 placed end-to-end for a truck without any slack at the end of the day, the absolute minimum number of trucks can be found multiplying the number of trips by the route time, and then dividing the total by the 95 hours allowed per week That is as follows: For 539 trip hours, 539/95 = 5.67 rounded to six trucks needed per week Now, it is necessary to adjust for the problem constraints A good schedule can be found by following a few simple rules that can be developed by examining the data First, begin the day with a trip where the driving time to a warehouse is just long enough for the truck to arrive at the warehouse just after it opens One-half the driving time should exceed 6:30 - 4:00 = 2:30, or hr Trips to Alpena, Traverse City, and Petoskey qualify Second, use the short trips at the end of the day to avoid slack time Third, allocate the trips to the days using the longest ones first Make sure that the total trip time for a day does not exceed 19 hours For a minimum of six trucks, the following feasible schedule can be developed by inspection Although this schedule meets the requirements of the problem, it might be improved by better balancing the workload across the trucks and the days Question 12: The Nockem Dead Casket Company supplies funeral homes with caskets throughout the state of California The funeral homes for a particular warehouse territory are located as shown on the map in Figure 7-25 (see Book) (a) Suppose that the funeral home locations (•) and associated number of caskets for each funeral home represents a single, daily dispatch If the company has six trucks with capacities of 20 caskets each, develop a routing plan using the “sweep” method (Use a counterclockwise sweep with a due north start.) Place your design on the map How many trucks are actually used and what is the total travel distance for the route design? You may scale distances from the diagram (b) Appraise the sweep method as a good method for truck routing and scheduling Solution: (a) A sweep method solution is shown on the following figure Five trucks are needed with a total route distance of (30+29+39+44+19.5)10 = 1,615 miles (b) The sweep method is a fast and relatively simple method for finding a solution to rather complex vehicle routing problems Solutions can be found graphically without the aid of a computer However, there are some limitations Namely, • The method is heuristic and has an average error of about 10 to 15 percent • This error is likely to be low if the problem contains many points and the weight of each point is small relative to the capacity of the vehicle • The method does not handle timing issues well, such as time windows Too many trucks may be used in the route design Question 13: As an adjunct to its retail business, Medic Drugs fills prescriptions for outlying nursing homes, extended cares facilities, rehabilitation centers, and retirement homes Part of this service is to deliver the prescription order to the customer site Station wagons having a capacity of 63 cartons are used for delivery Customer locations are geocoded by a linear grid overlay with a map-scaling factor of 4.6 per coordinate unit Customer data for a typical delivery day is given in the Table below (see full Table 7-8 in Book) The 0, coordinates on the grid are in the southwest corner Deliveries may begin as early as A.M (drivers leave depot) and drivers are to return to the base pharmacy by P.M Average driving speed is 30 miles per hour Drivers are allowed a one-hour lunch break after 12 noon Most customers may receive their deliveries between A.M and P.M., although there are a few exceptions The base pharmacy is located at X (horizontal coordinate) = 13.7, Y (vertical coordinate) = 21.2 If a driver returns early to the base pharmacy, the station wagon may be reloaded and sent on a second route (a) Design a dispatch route plan that will minimize the total distance traveled (b) Can any routes be assigned to the same station wagon to reduce the total number of drivers and vehicles needed to service the customers? If not, is there anything that might be done to accomplish this? Solution: This problem may be solved with the aid of ROUTER in LOGWARE The model input data may be formatted as shown in the Figure below (a) The solution from ROUTER shows that four routes are needed with a minimum total distance of 492 miles The route design is shown graphically in Figure below A summary for these routes is given in following partial output report (b) Note that route #1 is short and that a driver and a station wagon would be used for a route that takes 1.2 hours to complete By attaching route #1 to route #3, the same driver and station wagon may be used, and the constraints of the problems are still met The refilled station wagon can leave the depot by 3:30-3:45 p.m and still meet the customer’s time windows and return to the depot by p.m Thus, only three drivers and station wagons are actually needed for this problem Question 14: The Nockem Dead Casket Company sells and distributes caskets to funeral homes in the Columbus, Ohio, region Funeral homes place orders at a warehouse (X = 7.2, Y = 8.4) for delivery throughout the week The funeral home locations and the weekdays for delivery are given in Figure 7-26 (see Book) Number of caskets and the funeral home coordinates are given in Table 7-9 Deliveries are made using one 18-casket truck and one 27-casket truck Trucks leave the warehouse to make deliveries and return the same day Using the Principle for Good Routing and Scheduling, develop a good routing plan for the company Be creative Solution: There is no exact answer to this problem nor is one intended Several approaches might be taken to this problem We could apply the savings method or the sweep method to solve the routing problem for each day of the week, given the current demand patterns However, we can see that there is much overlap in the locations of the customers by delivery day of the week We might encourage orders to be placed so that deliveries form tight clusters by working with the sales department and the customers Perhaps some incentives could be provided to help discipline the order patterns The orders should form a general pattern as shown below Currently, the volume for Thursday exceeds the available truck capacity of 45 caskets Maybe the farthest stops could be handled by a for-hire service rather than acquiring another truck for such little usage It appears that the truck capacity is about right, given that some slack capacity is likely to be needed Once the pattern orders are established, either as currently given or as may be revised, apply principles numbers 1, 3, 4, 5, and ... Delivery 20 11 47 819 7 15 Pickup 14 12 06 820 3 45 Delivery 18 10 52 77 91 45 Delivery 55 7 828 2 45 Delivery 52 7 83 41 45 Pickup 56 5 8 27 3 45 Delivery 10 31 79 54 45 Pickup 11 59 822 4 45 Delivery 17 16 78 77 45 ... The associated network travel times in minutes are: To  Bakery From Bakery 22 47 39 57 21 24 35 27 42 16 50 32 17 18 57 38 23 15 16 21 55 45 21 14 41 20 18 60 25 42 (a) What is the best routing... 35 7. 8 A 12 3 21 . 3 50 .5 B 11 .8 3 21 . 8 60 .6 11 52 0 0 10 52 26 84 3 9 27 12 28 63 11 32 8 0 13 15 26 84 41 0 7 12 138 5 Service B appears to be less expensive Question 3: The Transcontinental Trucking Company wishes to