Transportation Problems


 Teresa Booker
 10 months ago
 Views:
Transcription
1 C H A P T E R 11 Transportation Problems Learning Objectives: Understanding the feature of Assignment Problems. Formulate an Assignment problem. Hungarian Method Unbalanced Assignment Problems Profit Maximization Problems Past Examinations Coverage: Year M13 N12 M12 N11 M11 N10 N10* M10 M10* N09 Q No b+3b 1d+4d 6 (a) 5 (a) 6 (b) 4 (b) 2 (b) Marks # 5+4 # # 4 # 4 # Year N09* J09 J09* N08 N08* M08 N07 M07 N06 M06 Q No. 4 (c) 4 (a) 4 (a) 6 (a) 1 (b) Marks 4 # 4 # 3 # 10 6 Year N05 M05 N04 M04 N03 M03 N02 M02 N01 M01 Q No. 5(c) 2 (b) 3 (b) 3 (c) 3 (c) Marks 8 3 # Year N00 M00 N99 M99 N98 M98 N97 M97 N96 M96 Q No. 3 (b) 4 (b) 2 (c) 3 (b) 4 (b) 5 (c) 2 (b) 4 (b) 2 (b) 2 (b) Marks * means questions from old syllabus # means theory questions CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.1
2 Advance Management Accounting Transportation: The transportation problem is concerned with the allocation of items between suppliers (called origins) and consumers (called destinations) so that the total cost of the allocation is minimized. The objective of the transportation problems is to determine the quantity to be shipped from each source to each destinations so as the transportation cost is lowest to maintain the supply and demand requirements. Applications: (i) (ii) (iii) Minimize shipping costs from factories to warehouses (or from warehouses to retail outlets) Determine lowest cost location for new factory; warehouse; office or other facility. Find minimum cost production schedule that satisfies firm s demand and production limitations (called Production Smoothing ) Conditions: To use the transportation algorithm; the following conditions must be satisfied. (i) (ii) (iii) (iv) The cost per item of each combination of origin and destination must be satisfied. The supply of items at each origin must be known. The requirement of items at each destination must be known. The total supply must equal the total demand. Stages in Transportation Problems: The transportation algorithm has four stages. Stages 1: Arrange the data in table format and set up the transportation table to find any feasible allocation. A feasible allocation is one in which all demand at the destinations is satisfied and all supply at the origin is allocated. Stages 2: Do preliminary check consist the following: (i) (ii) Verify Objective = Minimization. In case of Maximization or profit matrix, convert the same in to opportunity loss matrix by subtracting each element from the highest element of the matrix. Verify that the matrix is balanced i.e. Total Availability = Total Requirement. In case of unbalanced matrix, a dummy column or dummy row should be introduced with nil transportation cost. Stages 3: Develop an initial basic feasible solution (IBFS) by using any of the following methods. (i) (ii) (iii) Least Cost method. NorthWest corner Method. Vogel s Approximation Method. Stages 4: Test the IBFS solution for optimality. Modified Distribution (MODI) is the most common method and widely used for test the optimality. Stages 5: In case the IBFS solution is not optimal, develop the improved solutions. 1. Page 11.2
3 The Transportation Problems Method 1: NorthWest corner method: The practical steps in the NorthWest Corner cell are given below: Step 1: Make maximum possible allocation to the upperleft corner cell (known as NorthWest corner cell) in the first row depending upon the availability to supply for that row and demand requirement for the column containing that cell. Step 2: Move to the next cell of the first row depending upon remaining supply for that Row and the demand requirement for the next column. Go on till the Row totally is exhausted. Step 3: Move to the next row and make allocation to the cell below the cell of the preceding row in which the last allocation was made and follow Step1 and Step2. Step 4: Repeat the Step1 to Step3 till all requirements are exhausted i.e. entire demand and supply is exhausted. Method 2: Least Cost Method : The practical steps involved in the Least Cost are given below: Step 1: Make maximum possible allocation to the least cost cell depending upon the demand/supply for the column/row containing that cell. In case of tie in the least cost cell, make allocation to the cell by which maximum demand or capacity is exhausted. Step 2: Make allocation to the second least cost cell depending upon the remaining demand/supply for the column/row containing that cell. Step 3: Repeat the Step1 and Step2 till all requirements are exhausted i.e. entire demand and supply is exhausted. Method 3: Vogel s Approximation Method: This methods uses penalty costs. For each row and column the penalty cost is the difference between the cheapest available route and the next cheapest. Step 1: To calculate the penalty cost for each row and column, we look at the least cost cell and next least cell. For each row and column subtract the least cost cell from the next least cell. This gives the penalty cost of not allocating into the cell with cheapest cost. Write the penalty cost of each row on the righthand side of the concerned row and penalty cost of each column on the below of the concerned column. Step 2: We choose the row or column with the largest penalty cost and allocate as much as possible to the least cost cell in that row or column depending upon the quantity available. In this way, the highest penalty costs; are avoided as far as possible. In case of tie between the penalty cost, select the row or column having least cost cell however in case of tie even in the case of least cost cell; make allocation to that cell by which maximum requirement are exhausted. Step 3: Shade the row/column whose availability or requirement is exhausted so that it shall not be considered for further allocation. Step 4: Repeat the Step1 to Step3 till all requirements are exhausted i.e. entire demand and supply is exhausted. CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.3
4 Advance Management Accounting Optimality Test: It can be applied to a transportation table if it satisfies the following conditions: a) It contains exactly m+n1 allocations, where m & n represent the no. of rows & columns of the table. {Note: (i) In case degeneracy occurs (i.e. allocations are less than m+n1), infinitely small allocation(s) i.e. α is/are introduced in least cost & independent cell to nondegenerate the solution. If least cost cell(s) is/are not independent, then cell(s) with next lower cost(s) is/are chosen. (ii) Degeneracy can occur at initial basic feasible solution or at a later stage. It may be removed once the purpose is over.} b) These allocations are independent i.e. loop can not be performed by them. {Note: (i) Closed path or loop should have even no. of turns & is formed with an allocation on each corner, which in turn is a join of horizontal & vertical (not diagonal) lines. A loop may not involve all the allocations. (ii) Generally, IBFS obtained by Northwest Corner rule or VAM are always in independent positions though they may be m+n1 or less than m+n1 in no.} The SteppingStone Method 1. Start with an arbitrary empty cell (a cell without allocation a.k.a. nonbasic variables) and allocated +1 unit to this cell. 2. In order to maintain conditions of requirement & supply (a.k.a. rim constraints), 1 unit will be deducted/added to basic variables (i.e. cells having allocations). 3. Calculate Net change (a.k.a. opportunity cost or net evaluation) in transportation cost as a result of this perturbation. 4. Calculation Net evaluation for every empty cell. 5. If any cell evaluation is ve, the cost can be reduced so that the solution under consideration can be improved i.e. it is not optimal. On the other hand if all net evaluation are +ve, the given solution is optimal one. If any net evaluation is Zero, the given solution is optimal but there exist other optimal solutions as well. 6. If solution is not optimal, the cell with largest ve opportunity cost should be selected & allocate maximum units to this route (subject to rim constraints). 7. Iterate towards optimal solution, if further savings are possible. Modified Distribution Method (MODI) 1. For the current IBFS (Initial Basic Feasible Solution) with m+n1 occupied cell, calculate index numbers (dual variables) U i (i= 1,2,3, m) and V j (j= 1,2,3, n) for rows and columns, respectively. For calculating values of U i andv j, the following relationship (formula) for occupied cells is used. C ij = (U i +V j ) for all I,J. 2. Calculation Opportunity Cost for unoccupied cells by using the following formula: ij = C ij  (U i +V j ) 3. Examine unoccupied cells evaluation for all ij. (a) If ij >0; then the cost of transportation will increase. i.e. and optimal solution has been arrived at. (b) If ij =0; then the cost of transportation will remain unchanged. But there exists are alternative solution. (c) If ij <0; then an improved solution can be obtained by introducing cell (i,j) in the basis and go to next step. 4. Select an unoccupied cell with largest negative opportunity cost among all unoccupied cells. 1. Page 11.4
5 The Transportation Problems 5. Construct a closed path for the unoccupied cell determined in Step 7 and assign plus (+) and minus () sign alternatively beginning with plus sign for the selected unoccupied cell in clock wise or the direction. eg: ᶲ 7ᶲ ᶲmax i.e the maximum Qnty to be transferred from occupied cell to unoccupied cell = 10 ᶲ 5+ᶲ min of ᶲ cells i.e. min of 7, 10 i.e. 7 units 6. Assign as many units as possible to the unoccupied cells satisfying rim conditions. The smallest allocation in a cell with negative sign on the closed path indicated the number of units that can be transported to the unoccupied cells. This quantity is added to all the occupied cells on the path marked with plus sign and subtract from those cells on the path marked with minus sign. 7. Go to Step2 and repeat procedure until all ij >0 i.e. an optimal solution is reached. Calculate the associated total transportation cost. CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.5
6 Advance Management Accounting Theoretical Questions Q 1: Will the initial solution for a minimization problem obtained by Vogel s Approximation Method and the Least Cost Method be the same? Why? [M 11,4d, 4M] Q 2: What do you mean by Degeneracy in transportation problem? How this can be solved? [M 10, 6b, 4M] Q 3: In an unbalanced minimization transportation problem, with positive unit transport costs from 3 factories to 4 destinations, it is necessary to introduce a dummy destination to make it a balanced transportation problem. How will you find out if a given solution is optimal? [M10, 4b, 4M] [Ans.: No, Dummy destination won t be introduced if total units available at factories = total units required at destinations.] [Nov09 New] Q 4: How do you know whether an alternative solution exists for a transportation problem? [N 09, 2b, 4M] Q 5: Explain the term degeneracy in a transportation problem. [N 09*, 4c, 4M] Q 6: Q 7: State the methods in which initial feasible solution can be arrived at in a transportation problem [N 08 *, 4a, 4M] What are the common methods of obtaining initial feasible solution in a transportation problem? [N02, 2b, 3M] 1. Page 11.6
7 The Transportation Problems Practical Questions Q 1: [SA1] Find Initial basis feasible solution by (i) NorthWest Corner Method; (ii) Least Cost Method; (iii) Vogel s Approximation Method (VAM) for the following transportation problem in the following cases. (i) When Cell entries represent the unit transportation cost (ii) When Cell entries represent the Contribution Store W 1 W 2 W 3 W 4 Supplies Factory F F F F Demand Q 2: [SA2] Find Initial basis feasible solution by (i) NorthWest Corner Method; (ii) Least Cost Method; (iii) Vogel s Approximation Method (VAM) for the following transportation problem in the following cases. (i) When Cell entries represent the unit transportation cost (ii) When Cell entries represent the Contribution Store W 1 W 2 W 3 Supplies Factory F F F F Demand Q 3: [SA3] Find Initial basis feasible solution by (i) NorthWest Corner Method; (ii) Least Cost Method; (iii) Approximation Method (VAM) for the following transportation problem in the following cases. (i) When Cell entries represent the unit transportation cost (ii) When Cell entries represent the Contribution Store W 1 W 2 W 3 W 4 Supplies Factory F F F Demand Vogel s CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.7
8 Advance Management Accounting Q4: [SM1] A company has factories at A, B and C which supply warehouse at D, E, F and G. Monthly factory capacities are 160, 150 and 190 units respectively. Monthly warehouse requirements are 80, 90, 110 and 160 units respectively. Units shipping costs (in Rs.) are as follows: To D E F G From A B C Q 5: [SM2] [Multiple solution case] Solve the following transportation problem To D1 D2 D3 D4 From Q Q Q Q 6: [SM3] [MAXIMIZATION TRANSPORTATION PROBLEMS] A company has 3 factories manufacturing the same product and 5 sole agencies in different parts of the country. Production costs differ from factory to factory, and the sales prices from agency to agency. The shipping cost per unit product from each factory to any agency is known. Given the following data, find the production and distribution schedules most profitable to the company Production Max Capacity Factory i Cost/Unit No. of Units Cost Agency j Demand Sales to be Met Price Shipping Q 7: [SM4] [N89] [Prohibited routes] Solve the following transportation problem Godown 1 Godown 2 Godown 3 Godown 4 Godown 5 Godown 6 Stock Availability Factory Factory * 5 20 Factory Factory Demand Note: It is not possible to transport any quantity from factory 2 to godown 5. State whether the solution derived by you is unique. 1. Page 11.8
9 [Ans.: Total Cost Rs. 1120] The Transportation Problems Q 8: [SM 5] The Link manufacturing company has several plants, three of which manufacture two principal products, standard card table and deluxe card table. A new deluxe card table will be introduced which must be considered in term of selling price & costs. The selling prices are: Standard Rs , Deluxe Rs , and new Deluxe Rs Requirements Variable costs Available plant capacity Model Quantity Plant A Plant B Plant C Plant Capacity Standard A 800 Deluxe B 600 New Deluxe C 700 Solve this problem by the transportation technique for the greatest contribution. Q 9: [SM6] [SA35] A company wishes to determine an investment strategy for each of the next four years. Five investment types have been selected, investment capital has been allocated for each of the coming four years, and maximum investment levels have been established for each investment type. An assumption is that amounts invested in any year will remain invested until the end of the planning horizon of four years. The following table summaries the data for this problem. The values in the body of the table represent net return on investment of one rupee up to the end of the planning horizon. For example, a rupee invested in investment type B at the beginning of year 1 will grow to Rs by the end of the fourth year, yielding a net return of Rs Investment made at the beginning of year Investment Type Amount available (Rs. In 000) A B C D E Maximum Rupee Investment (Rs. In 000) The objective is this problem is to determine the amount to be invested at the beginning of each year in an investment type so as to maximize the net rupee return for the fouryear period. Solve the above transportation problem and get an optimal solution. Also calculate the net return on investment for the planning horizon for fouryear period. [Ans: 1E 500; 2B 390; 3D 375; 4A 37.5; 4C 125; 4D 17.5; Total Return = 1445.] CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.9
10 Advance Management Accounting Q 10: [SM7] [N 96, 2b, 10M] [V2E9] [Investment decision] XYZ and co. has provided the following data seeking your advice on optimum investment strategy: Beginning of the year Net Return Data (in paise) of Selected Investments Amount available (Lacs) P Q R S Maximum Investment (lacs) The following additional information are also provided: P, Q, R, and S represent the selected investments. The company decided to have four years investment plan. The policy of the company is that amount invested in any year will remain so until the end of the fourth year. The values (paise) in the table represent net return on investment of one Rupee till the end of the planning horizon (for example, a Rupee invested in Investment P at the beginning of year 1 will grow to Rs by the end of the fourth year, yielding a return of 95 paise). Using the above, determine the optimum investment strategy. Q 11: [SM8] [N 97, 2b, 10M] [SA30] A particular product is manufactured in factories A, B, C and D; and is sold at centres 1, 2, and 3. The cost in Rs. of product per unit and capacity in kgs per unit time of each plant is given below: Factory Cost (Rs.) per unit Capacity (kgs) per unit A B C D The sale price in Rs. per unit and the demand in kgs per unit time are as follows: Sales Centre Sale Price (Rs.) per unit Demand (kgs) per unit Find the optimal sale distribution. [Ans.: From Factory To Sales Centre Quantity Total Profit A B C D D Dummy Page 11.10
11 The Transportation Problems Q 12: [SM9] [M 98, 5c, 10M] [V23] [SA24] Consider the following data for the transportation problem: Factory Destination Supply to be exhausted A B C Demand Since there is not enough supply, some of the demands at the three destinations may not be satisfied. For the unsatisfied demands, let the penalty costs be rupees 1,2 and 3 for destinations (1), (2) and (3) respectively. Find the optimal allocation that minimizes the transportation and penalty cost. Q 13: [SM10] [N 98, 4b, 10M] [SA34] ABC Enterprises is having three plants manufacturing drycells, located at different locations. Production cost differs from plant to plant. There are five sales offices of the company located in different regions of the country. The sales prices can differ from region to region. The shipping cost from each plant to each sales office and other data are given by following table: Production Data Table Production cost per unit Max Capacity in no. of units Plant no Shipping Cost and Demand & Sales Prices table Shipping Cost Sales Office 1 Sales Office 2 Sales Office 3 Sales Office 4 Sales Office 5 Plant Plant Plant Demand and Sales Price Sales Office 1 Sales Office 2 Sales Office 3 Sales Office 4 Sales Office 5 Demand Sales Price Find the production and distribution schedule most profitable to the company. [Ans.: Plant Sales Office Units Total Profit (Rs.) Dummy Total 3170 CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.11
12 Advance Management Accounting Q 14: [SA19] Find Initial basic feasible solution by Vogel s Approximation Method. Is the number of allocation equal to m+n 1 if no, how will you deal with this situation? Store W 1 W 2 W 3 W 4 Supplies Factory F F F Demand Note: Cell entries represent the unit transportation cost F F F Q 15: [SA20] [Number of allocation = m+n1] Test the following Initial basic solution for Optimality. Store Factory W 1 W 2 W 3 W F Demand Note: Cell entries represent the unit transportation cost Supplies F Q 16: [SA21] [Number of allocation < m+n1] Test the following Initial basic solution for Optimality. Store Factory W 1 W 2 W 3 W 4 F 1 e F Demand Note: Cell entries represent the unit transportation cost Supplies Page 11.12
13 The Transportation Problems Q 17: [SA22] Solve the following transportation problem with the restriction that nothing can be transported from F 2 to W 3. Store W 1 W 2 W 3 W 4 Supplies Factory F F Required Note: Cell entries represent the unit transportation cost 4 11 Q 18: [SA36] Solve the following transportation problem to maximize profit and give criteria for optimality: Store Profit ( )/Unit Destination Origin Supplies A B C Demand Q 19: [SA37] Solve the following transportation problem: Stock Available Demand Q 20: [SA27] Consider the following transportation cost table. The costs are given in Rupees, the supply and demand are in units. Determine the optimal solution: Destination Source Supply I II III Demand CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.13
14 Advance Management Accounting Q 21: [SA25] Solve the following transportation cost table for minimum cost: Origins Destinations A B C D Requirements I II III IV Availabilities Q 22: [SA23] Solve the following transportation cost table for minimum cost: Godowns Stock Factory Available I II III IV Demand Note: It is not possible to transport any quantity from factor 2 to Godown 5. Required: State whether the solution derived by you is unique. Q 23: [V2E2] [SA32] A Company has four factories F1, F2, F3 and F4, manufacturing the same product. Production and raw material costs differ from factory to factory and are given in the first two rows of the following table. The Transportation costs from the factories to sales depots S1, S2 and S3 are given in the next three rows of the table. The production capacity of each factory is given in the last row. The last two columns in the table given the sales price and the total requirement at each depot: Item Per unit Factory Sales price Per unit Requirement F1 F2 F3 F4 Production cost Raw material cost Transportation cost Production capacity Determine the most profitable production and distribution schedule and the corresponding profit. The surplus should be taken to yield zero profit. [Ans:Profit associated with the optimum Program is Rs. 480.] Q 24: [SA28] [N 90] Stronghold Construction Company is interested in taking loans from banks for some of its projects P, Q, R, S and T. The rates of interest and the lending capacity differ from bank to bank. All these projects are to be completed. The relevant details are provided in the following table. Assuming the role of a consultant, advise this company 1. Page 11.14
15 The Transportation Problems as to how it should take the loans so that the total interest payable will be the least. Are there alternative optimum solutions? If so, indicate one such solution. Interest Rate in Percentage for Project Max. Credit Bank P Q R S T ( 000) Pvt. Bank Any Amount Nationalized CoOperative Amount Required ( 000) Q 25: [SA29] A Manufacturer of jeans is interested in developing an advertising campaign that will reach four different age groups. Advertising campaigns can be conducted through TV, Radio and Magazines. The following table gives the estimated cost in paise per exposure for each age group according to the medium employed. In addition, maximum exposure levels possible in each of the media, namely TV, Radio and Magazines are 40, 30 and 20 million respectively. Also the minimum desired exposures within each age group namely 1318, 1925, 2635, 36 and older are 30, 25, 15 and 10 million. The objective is to minimum exposure level in each age group. Required: (i) (ii) Media Age Group & Older TV Radio Magazines Formulate the above as a transportation problem, and find the optimal solution. Solve this problem if the policy is to provide at least 4 million exposures through TV in the age group and at least 8 million exposures through TV in the age group CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.15
16 Advance Management Accounting Practical Questions Previous Examinations Paper Q: [M 11, 1d, 5M] The following matrix is a minimization problem for transportation cost. The unit transportation costs are given at the right hand corners of the cells and the ij values are encircled. D 1 D 2 D 3 D 4 Supply F F 2 8 F Demand Find the optimum solution (s) and the minimum cost. [Ans: (i) F 1 D ; F 1 D ; F 1 D ; F 2 D ; F 3 D ; Total Cost = (ii) F 1 D ; F 1 D ; F 1 D ; F 2 D ; F 3 D ; Total Cost = 4500 Q: [N 10, 6a, 8M] A company has three plants located at A, B and C. The production of these plants is absorbed by four distribution centres located at X, Y, W and Z. the transportation cost per unit has been shown in small cells in the following table: Distribution Centre X Y W Z Supply Factories (Units) A B C Demand Find the optimum solution of the transportation problem by applying Vogel s Approximation Method. [Ans: Total Cost ] 1. Page 11.16
17 The Transportation Problems Q: [N 10*, 5a,10M] A company has 3 factories F1, F2 and F3 which supply the same product to 5 agencies, A1, A2, A3, A4 and A5. Unit production costs, shipping costs and selling prices differ among the different sources and destinations and are given below: F1 F2 F3 Production Cost (`/Unit) Production Capacity (No. of units) Agencies A1 A2 A3 A4 A5 Selling Price (`/Unit) Demand (No. of units) Shipping Costs/Unit A1 A2 A3 A4 A5 F F F (i) Set up the initial transportation matrix for minimization. (ii) After doing (i) above, you are given the following additional information: (a) 40 units must be transported from F2 to A2 as per an earlier agreement made by F2 with A2 s customer. This quantity is included in the figures given for total production and demand at these locations. (b) Not more than 30 units may be sent from F1 to A1, since the transporter s vehicle lacks space in this route. Incorporating conditions (a) and (b) above, obtain the initial solution by Vogel s Approximation Method. (Do not attempt to continue for the full and final solution.) Q: [M 09, 4a, 6M] [V210][ Minimizationbalanceddegeneracy] The cost per unit of transporting goods from factories X, Y, Z to destinations A, B and C, and the quantities demanded and supplied are tabulated below. As the company is working out the optimum logistics, the Govt. has announced a fall in oil prices. The revised unit costs are exactly half the costs given in the table. You are required to evaluate the minimum transportation cost. Factories\Destinations A B C Supply X Y Z Demand [Ans.: Min. transportation cost is. 105] Q: [M 08, 6a, 10M] [V28] [SA27] Goods manufactured at 3 plants, A, B and C are required to be transported to sales outlets X, Y and Z. The unit costs of transporting the goods from the plants to the outlets are given below: Sales outlets\plants A B C Total Demand X Y Z Total supply CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.17
18 Advance Management Accounting You are required to: i. Compute the initial allocation by NorthWest Corner Rule. ii. Compute the initial allocation by Vogel s approximation method and check whether it is optional. iii. State your analysis on the optionality of allocation under NorthWest corner Rule and Vogel s Approximation method. [Ans: (i) AX20 60; AY20 80; BY20 80; BZ30 90; CZ ; Total Cost = 460 (ii) AX20 60; AY20 80; BZ50 80; CY ; CZ ; Total Cost = 460 (iii)the solution under VAM is optimal with a zero in R2C2 which means that the cell C2R2 which means that the cell C2R2 can come into solution, which will be another optimal solution. Under NWC rule the initial allocation had C2R2 and the total cost was the same Rs. 460 as the total cost under optimal VAM solution. Thus, in this problem, both methods have yielded the optimal solution under the 1st allocation. If we do an optimality test for the solution, we will get a zero for ij in C3R2 indicating the other optimal solution which was obtained under VAM.] Q: [M 07, 1b, 6M] [V27] The initial allocation of a transportation problem, along with the unit cost of transportation from each origin to destination is given below. You are required to arrive at the minimum transportation cost by the Vogel s Approximation method and check for optimality. (Hint: Candidates may consider u1 = 0 at Row 1 for initial cell evaluation) Requirement Availability [Ans: Minimum Transportation Cost 204] Q: [M03, 5c, 10M][ Maximizationunbalanced] A company has three factories and four customers. The company furnishes the following schedule of profit per unit on transportation of its goods to the customers in rupees: Customers Factory A B C D Supply P Q R Demand Page 11.18
19 The Transportation Problems You are required to solve the transportation problem to maximize the profit and determine the resultant of optimal profit. [Ans.: Maximum Profit. 5130] Q: [M02, 3b, 10M] [V21][ MinimizationUnbalanced] A product is manufactured by four factories A, B, C & D. The unit production costs are Rs. 2, Rs. 3, Re. 1 and Rs. 5 respectively. Their daily production capacities are 50, 70, 30 and 50 units respectively. These factories supply the product to four stores P, Q, R, S. The demand made by these stores are 25, 35, 105 and 20 units respectively. Unit transportation cost in rupees from each factory to each store is given in the following table: Stores Factories P Q R S A B C D Determine the extent of deliveries from each of the factories to each of the stores so that the total cost (production and transportation together) is minimum. [Ans.: Total Cost 1465] Q: [N 01, 3c, 10] [V22] Multiple Optimal Solutions A Compressed Natural Gas (CNG) company has three plants producing gas and four outlets. The cost of transporting gas from different production plants to the outlets, production capacity of each plant & requirement at different outlet is shown in the following costmatrix table. Outlets Plants A B C D Capacity of Production X Y Z Requirement Determine a transportation schedule so that the cost is minimized. The cost in the costmatrix is given in thousand of rupees. [Ans.: Minimum costs 7350 thousands] Q: [M 01, 3c, 10M] A company has 3 plants and 3 warehouses. The Cost of sending a unit from different plants to the warehouses, production at different plants and demand at different warehouses are shown in the following cost matrix table: Warehouses Plants A B C Production X Y Z Demand Determine a transportation schedule, so that the cost is minimized. Assume that the cost in the cost matrix is given in thousand of rupees. [Ans.: XB ; YB ; YC ; Ydummy40 0; ZA ; ZB ; Total Cost = 9696] CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.19
20 Advance Management Accounting Q: [N 00, 3b, 10M] [V2E4] Following is the profit matrix based on four factories and three sales depots of the company: S1 S2 S3 Availability F Factories F F F Requirement Determine the most profitable distribution schedule and the corresponding profit, assuming no profit in case of surplus production. [Ans: Total Profit = 480] Q: [M 00, 4b, 10M] [V2E5] A company produces a small component for all industrial products and distributes it to five wholesalers at a fixed prices of Rs.2.50 per unit. Sales forecasts indicate that monthly deliveries will be 3,000, 3,000, 10,000, 5,000 and 4,000 units to wholesalers 1,2,3,4 and 5 respectively. The monthly production capabilities are 5,000, 10,000, 12,500 at plants 1, 2 and 3 respectively. The direct costs of production of each unit are Rs.1.00 and Rs.0.80 at plants 1, 2 and 3 respectively. The transportation costs of shipping a unit from a plant to a wholesaler are given below: Wholesaler Plant Find how many components each plant supplies to each wholesaler in order to maximize profit. [ Ans: Profit 32520] Q: [N 99, 2c, 10M] [V2E6] The following table shows all the necessary information on the available supply to each warehouse, the requirement of each market and the unit transportation cost from each warehouse to each market: Market I II III IV Supply A Warehouse B C Requirement The shipping clerk has worked out the following schedule from his experience: 12 Units from A to II 1 Unit from A to III 9 Units from A to IV 15 Units from B to III 7 Units from C to I and 1 Unit from C to III You are required to answer the following: (i) Check and see if the clerk has the optimal schedule; (ii) Find the optimal schedule and minimum total shipping cost; and 1. Page 11.20
21 The Transportation Problems (iii) If the clerk is approached by a carrier of route C to II, who offers to reduce his rate in the hope of getting some business, by how much should the rate be reduced before the clerk should consider giving him an order? [Ans: (i) Clerk has not worked out the optimal schedule; (ii) Minimum total shipping cost 104; (iii) Total Shipping Cost = Rs.103] Q: [M 99, 3b, 10M] [V2E7] A company has three warehouses W1, W2 and W3. It is required to deliver a product from these warehouses to three customers A, B and C. There warehouses have the following units in stock. Warehouse: W1 W2 W3 No. of units: and customer requirements are: Customer: A B C No. of units: The table below shows the costs of transporting one unit from warehouse to the customer: Warehouse W1 W2 W3 A Customer B C Find the optimal transportation route. Answer Total Cost = Rs. 830 [Ans.: W 1 A ; W 2 A5 35; W 2 B ; W 2 C7 49; W 3 C ; Total Cost = 680] Q: [N 98, 4b, 10M] [SM10] [SA34] ABC Enterprises is having three plants manufacturing drycells, located at different locations. Production cost differs from plant to plant. There are five sales offices of the company located in different regions of the country. The sales prices can differ from region to region. The shipping cost from each plant to each sales office and other data are given by following table: Production Data Table Production cost per unit Max Capacity in no. of units Plant no Shipping Cost and Demand & Sales Prices table Shipping Cost Sales Office 1 Sales Office 2 Sales Office 3 Sales Office 4 Sales Office 5 Plant Plant Plant Demand and Sales Price Sales Office 1 Sales Office 2 Sales Office 3 Sales Office 4 Sales Office 5 Demand Sales Price Find the production and distribution schedule most profitable to the company. [Ans.: ; ; ; ; 2dummy50 0; ; ; ; Total Profit = 3170] CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.21
22 Advance Management Accounting Q: [M 98, 5c, 10M] [SM9] [V23] [SA24] Consider the following data for the transportation problem: Factory Destination Supply to be exhausted A B C Demand Since there is not enough supply, some of the demands at the three destinations may not be satisfied. For the unsatisfied demands, let the penalty costs be rupees 1,2 and 3 for destinations (1), (2) and (3) respectively. Find the optimal allocation that minimizes the transportation and penalty cost. [Ans.: A ; B ; B ; B ; C ; Dummy ; Total Cost = 555] Q: [N 97, 2b, 10M] [SM8] [SA30] A particular product is manufactured in factories A, B, C and D; and is sold at centres 1, 2, and 3. The cost in Rs. of product per unit and capacity in kgs per unit time of each plant is given below: Factory Cost (Rs.) per unit Capacity (kgs) per unit A B C D The sale price in Rs. per unit and the demand in kgs per unit time are as follows: Sales Centre Sale Price (Rs.) per unit Demand (kgs) per unit Find the optimal sale distribution. [Ans.: A ; B ; C ; D ; D ; Dummy ;Total Profit = 680] Q: [M 97,4b, 10M] [V2E10][ Minimizationbalanceddegeneracy] A company has four terminals U, V, W, and X. At the start of a particular day 10, 4, 6, and 5 trailers respectively are available at these terminals. During the previous night 13, 10, 6, and 6 trailers respectively were loaded at plants A, B, C, and D. The company dispatcher has come up with the costs between the terminals and plants as follows: Plants Terminals A B C D U V W X Find the allocation of loaded trailers from plants to terminals in order to minimize transportation cost. [Ans: UA 80; U C 60; VB 60; VD 20; WB 210; XD 125;Terminal Plant Cost = 555] 1. Page 11.22
23 The Transportation Problems Q: [N 96, 2b, 10M] [SM7] [V2E9] [Investment decision] XYZ and co. has provided the following data seeking your advice on optimum investment strategy: Beginning of the year Net Return Data (in paise) of Selected Investments Amount Available (Lacs) P Q R S Maximum Investment (lacs) The following additional information are also provided: P, Q, R, and S represent the selected investments. The company decided to have four years investment plan. The policy of the company is that amount invested in any year will remain so until the end of the fourth year. The values (paise) in the table represent net return on investment of one Rupee till the end of the planning horizon (for example, a Rupee invested in Investment P at the beginning of year 1 will grow to Rs by the end of the fourth year, yielding a return of 95 paise). Using the above, determine the optimum investment strategy. [Ans: Net Return lacs] Q: [M 96, 2b, 10M] [V2 E8] [SA33] A company has four factories situated in four different locations in the country and four sales agencies located in four other locations in the country. The cost of production (Rs. Per unit), the sales price (Rs. per unit), and shipping cost (Rs. Per unit) in the case of matrix, monthly capacities and monthly requirements are given below: Factory Sales Agency Monthly Cost of Capacity Production (Units) A B C D Monthly Requirement Sale Price Find the monthly production and distribution schedule which will maximize profit. [Total Profit = 155] CA. B L Chakravarti (FCA, CPA, CAIIB) Page 11.23
24 Advance Management Accounting Q: [May95] [SA31] A leading firm has three auditors. Each auditor can work up to 160 hours during the next month, during which time three projects must be completed. Project 1 will 130 hours, project 2 will take 140 hours, and project 3 will take 160 hours. The amount per hour that can be billed for assigning each auditor to each project is given in Table 1: Table1 Project Auditor Rs. Rs. Rs Formulate this as a transportation problem and find the optimal solution. Also find out the maximum total billings during the next month. [Ans: ; ; ; ; Total Billing= ] Important Notes 1. Page 11.24
The Transportation Problem
The Transportation Problem Stages in solving transportation problems Steps for Stage 1 (IBFS) 1) If problem is not balanced, introduce dummy row/column to balance it. [Note: Balancing means ensuring that
More information3. Transportation Problem (Part 1)
3 Transportation Problem (Part 1) 31 Introduction to Transportation Problem 32 Mathematical Formulation and Tabular Representation 33 Some Basic Definitions 34 Transportation Algorithm 35 Methods for Initial
More informationTRANSPORTATION PROBLEM AND VARIANTS
TRANSPORTATION PROBLEM AND VARIANTS Introduction to Lecture T: Welcome to the next exercise. I hope you enjoyed the previous exercise. S: Sure I did. It is good to learn new concepts. I am beginning to
More informationISE 204 OR II. Chapter 8 The Transportation and Assignment Problems. Asst. Prof. Dr. Deniz TÜRSEL ELİİYİ
ISE 204 OR II Chapter 8 The Transportation and Assignment Problems Asst. Prof. Dr. Deniz TÜRSEL ELİİYİ 1 The Transportation and Assignment Problems Transportation Problems: A special class of Linear Programming
More informationAssignment Technique for solving Transportation Problem A Case Study
Assignment Technique for solving Transportation Problem A Case Study N. Santosh Ranganath Faculty Member, Department of Commerce and Management Studies Dr. B. R. Ambedkar University, Srikakulam, Andhra
More informationApplication of Transportation Linear Programming Algorithms to Cost Reduction in Nigeria Soft Drinks Industry
Application of Transportation Linear Programming Algorithms to Cost Reduction in Nigeria Soft Drinks Industry A. O. Salami Abstract The transportation problems are primarily concerned with the optimal
More informationA comparative study of ASM and NWCR method in transportation problem
Malaya J. Mat. 5(2)(2017) 321 327 A comparative study of ASM and NWCR method in transportation problem B. Satheesh Kumar a, *, R. Nandhini b and T. Nanthini c a,b,c Department of Mathematics, Dr. N. G.
More informationTransportation Logistics Part I and II
Transportation Logistics Part I and II Exercise Let G = (V,E) denote a graph consisting of vertices V = {,2,3,4,5,6,,8} and arcs A = {(,2),(,3),(2,4),(3,2),(4,3),(4,5),(4,6),(5,3),(5,),(6,8),(,4),(,6),(,8)}.
More informationInternational Journal of Mathematics Trends and Technology (IJMTT) Volume 44 Number 4 April 2017
Solving Transportation Problem by Various Methods and Their Comaprison Dr. Shraddha Mishra Professor and Head Lakhmi Naraian College of Technology, Indore, RGPV BHOPAL Abstract: The most important and
More informationThe Transportation and Assignment Problems. Chapter 9: Hillier and Lieberman Chapter 7: Decision Tools for Agribusiness Dr. Hurley s AGB 328 Course
The Transportation and Assignment Problems Chapter 9: Hillier and Lieberman Chapter 7: Decision Tools for Agribusiness Dr. Hurley s AGB 328 Course Terms to Know Sources Destinations Supply Demand The Requirements
More informationTRANSPORTATION MODEL IN DELIVERY GOODS USING RAILWAY SYSTEMS
TRANSPORTATION MODEL IN DELIVERY GOODS USING RAILWAY SYSTEMS Fauziah Ab Rahman Malaysian Institute of Marine Engineering Technology Universiti Kuala Lumpur Lumut, Perak, Malaysia fauziahabra@unikl.edu.my
More informationAn Alternative Method to Find Initial Basic Feasible Solution of a Transportation Problem
Annals of Pure and Applied Mathematics Vol., No. 2, 2, 39 ISSN: 2279087X (P), 22790888(online) Published on 6 November 2 www.researchmathsci.org Annals of An Alternative Method to Find Initial Basic
More informationUnderstanding the meaning of Learning Curve. Understanding the meaning of Learning Curve Effect. Feature and Limitations of Learning Curve Theory.
C H A P T E R 15 Learning Curve Learning Objectives: Understanding the meaning of Learning Curve. Understanding the meaning of Learning Curve Effect. Feature and Limitations of Learning Curve Theory. Past
More informationSYLLABUS Class:  B.B.A. IV Semester. Subject:  Operations Research
SYLLABUS Class:  B.B.A. IV Semester Subject:  Operations Research UNIT I Definition of operations research, models of operations research, scientific methodology of operations research, scope of operations
More informationTechniques of Operations Research
Techniques of Operations Research C HAPTER 2 2.1 INTRODUCTION The term, Operations Research was first coined in 1940 by McClosky and Trefthen in a small town called Bowdsey of the United Kingdom. This
More informationDIS 300. Quantitative Analysis in Operations Management. Instructions for DIS 300Transportation
Instructions for Transportation 1. Set up the column and row headings for the transportation table: Before we can use Excel Solver to find a solution to C&A s location decision problem, we need to set
More informationLECTURE 41: SCHEDULING
LECTURE 41: SCHEDULING Learning Objectives After completing the introductory discussion on Scheduling, the students would be able to understand what scheduling is and how important it is to high volume
More informationSolving Transportation Logistics Problems Using Advanced Evolutionary Optimization
Solving Transportation Logistics Problems Using Advanced Evolutionary Optimization Transportation logistics problems and many analogous problems are usually too complicated and difficult for standard Linear
More informationPRODUCTION PLANNING MODULE
Anar Pharmaceuticals Limited ERP Project In Sales & Distribution Module I had recommended: PRODUCTION PLANNING MODULE 1. Monthly Corporate Sales Budget Process (Refer Sales Budget  page 32) & 2. Macro
More informationThe Efficient Allocation of Individuals to Positions
The Efficient Allocation of Individuals to Positions by Aanund Hylland and Richard Zeckhauser Presented by Debreu Team: Justina Adamanti, Liz Malm, Yuqing Hu, Krish Ray Hylland and Zeckhauser consider
More informationMARGINAL COSTING CATEGORY A CHAPTER HIGH MARKS COVERAGE IN EXAM
1 MARGINAL COSTING CATEGORY A CHAPTER HIGH MARKS COVERAGE IN EXAM Question 1 Arnav Ltd. manufacture and sales its product R9. The following figures have been collected from cost records of last year for
More informationCUSTOMER PROFITABILITY DOCUMENTATION UPDATES
DOCUMENTATION UPDATES Date Description Where Changed 3/5/08 You can create an expense class basis for sales, direct ship lines of billing, and warehouse lines of billing to better define expense reporting
More informationMGSC 1205 Quantitative Methods I
MGSC 1205 Quantitative Methods I Class Seven Sensitivity Analysis Ammar Sarhan 1 How can we handle changes? We have solved LP problems under deterministic assumptions. find an optimum solution given certain
More informationTopics in Supply Chain Management. Session 3. Fouad El Ouardighi BARILAN UNIVERSITY. Department of Operations Management
BARILAN UNIVERSITY Department of Operations Management Topics in Supply Chain Management Session Fouad El Ouardighi «Cette photocopie (d articles ou de livre), fournie dans le cadre d un accord avec le
More informationTHE "OPERATIONS RESEARCH METHOD" Orientation. Problem Definition. Data Collection. Model Construction. Solution. Validation and Analysis
THE "OPERATIONS RESEARCH METHOD" Orientation Problem Definition F E E D B A C K Data Collection Model Construction Solution Validation and Analysis Implementation & Monitoring An OR Problem  A Simple
More informationProcess Costing Joint and By Product CA Past Years Exam Question
CA R. K. Mehta Process Costing Joint and By Product CA Past Years Exam Question Question : 1 May, 2012 A product passes through two processes A and B. During the year, the input to Process A of Basic raw
More information6 Managing freight transport
6 Managing freight transport 6.1 Introduction 6.2 Freight traffic assignment problems 6.3 Service network design problems 6.4 Vehicle allocation problems 6.5 A dynamic driver assignment problem 6.6 Fleet
More informationSupply Chain Location Decisions Chapter 11
Supply Chain Location Decisions Chapter 11 1101 What is a Facility Location? Facility Location The process of determining geographic sites for a firm s operations. Distribution center (DC) A warehouse
More informationA Particle Swarm Optimization Algorithm for Multidepot Vehicle Routing problem with Pickup and Delivery Requests
A Particle Swarm Optimization Algorithm for Multidepot Vehicle Routing problem with Pickup and Delivery Requests Pandhapon Sombuntham and Voratas Kachitvichayanukul Abstract A particle swarm optimization
More informationModeling of competition in revenue management Petr Fiala 1
Modeling of competition in revenue management Petr Fiala 1 Abstract. Revenue management (RM) is the art and science of predicting consumer behavior and optimizing price and product availability to maximize
More informationWork Orders Quick Reference
Work Orders Quick Reference Header tab Ordering location the distributor location ordering the item that is being built on this work order. Locations are set up in Location Master Maintenance. You can
More informationBalancing a transportation problem: Is it really that simple?
Original Article Balancing a transportation problem: Is it really that simple? Francis J. Vasko a, * and Nelya Storozhyshina b a Mathematics Department, Kutztown University, Kutztown, Pennsylvania 19530,
More informationDesigning and Managing Integrated Marketing Channels
Designing and Managing Integrated Marketing Channels OVER THE PAST THREE DECADES, THE OVERWHELMING EMPHASIS IN THE MARKETING MIX HAS BEEN ON: PRODUCT STRATEGY WITH PRICING STRATEGY AND PROMOTIONAL STRATEGY
More informationA Heuristic on Risk Management System in Goods Transportation Model Using MultiOptimality by MODI Method
Open Journal of Applied Sciences, 16, 6, 1 Published Online August 16 in SciRes. http://www.scirp.org/journal/ojapps http://dx.doi.org/.26/ojapps.16.6 A Heuristic on Risk Management System in Goods Transportation
More informationLecture Series: Consumer Electronics Supply Chain Management
Lecture Series: Consumer Electronics Supply Chain Management Mohit Juneja i2 Technologies Divakar Rajamani, Ph.D. University of Texas at Dallas Center for Intelligent Supply Networks () 2003 Mohit Juneja
More informationCHAPTER 6 PROCESS COST ACCOUNTING ADDITIONAL PROCEDURES
CHAPTER 6 PROCESS COST ACCOUNTING ADDITIONAL PROCEDURES Review Summary 1. In many industries where a process cost system is used, the materials may be put into production in irregular quantities and at
More informationOPERATIONS RESEARCH TWO MARKS QUESTIONS AND ANSWERS
OPERATIONS RESEARCH TWO MARKS QUESTIONS AND ANSWERS 1.when does degenaracy happen in transportation problem? In transportation problem with m orgins and n destinations, if a IBFS has less than m+n1 allocations,
More informationDepartment of Information and Public Relations, Government of Andhra Pradesh invites applications from reputed advertising agencies for empanelment.
GOVERNMENT OF ANDHRA PRADESH DEPARTMENT OF INFORMATION AND PUBLIC RELATIONS: Vijayawada. **** Tender Schedule Terms and conditions for Empanelment of Print Media Advertising Agencies2017 Department of
More informationShortRun Costs and Output Decisions
SemesterI Course: 01 (Introductory Microeconomics) Unit IV  The Firm and Perfect Market Structure Lesson: ShortRun Costs and Output Decisions Lesson Developer: Jasmin Jawaharlal Nehru University Institute
More informationModeling Using Linear Programming
Chapter Outline Developing Linear Optimization Models Decision Variables Objective Function Constraints Softwater Optimization Model OM Applications of Linear Optimization OM Spotlight: Land Management
More informationSAP Supply Chain Management
Estimated Students Paula Ibanez Kelvin Thompson IDM 3330 70 MANAGEMENT INFORMATION SYSTEMS SAP Supply Chain Management The Best Solution for Supply Chain Managers in the Manufacturing Field SAP Supply
More informationACCOUNTING FOR CONSIGNMENT
ACCOUNTING FOR CONSIGNMENT A shipment of goods by a manufacturer or wholesale dealer to an agent in home country or abroad on commission basis and on the risk and accounts of the former is known as consignment.
More informationSupplier Policies & Procedures
20.0 PERFORMANCE REQUIREMENTS Supplier Policies & Procedures True Value is committed to providing its Retailers with products that consistently meet or exceed their expectations for value and merchandise
More informationgo vertical. for Microsoft Dynamics AX About MBS Dev Professional Microsoft Dynamics AX Partner Wholesale Distribution Suite
WDS Professional Microsoft Dynamics AX Partner Improve Quality Increase Competitive Edge Enhance Service Deliver Fast Reliable Solutions Wholesale Distribution Suite High Volume Distribution (HVD) Executive
More informationPredictive Planning for Supply Chain Management
Predictive Planning for Supply Chain Management David Pardoe and Peter Stone Department of Computer Sciences The University of Texas at Austin {dpardoe, pstone}@cs.utexas.edu Abstract Supply chains are
More informationIntegrated Accounting, CRM and ERP System for Mac OS X, Windows, Linux, ios, Android and AIX
Integrated Accounting, CRM and ERP System for Mac OS X, Windows, Linux, ios, Android and AIX Purchase Ledger Reports Program version: 7.1 131231 2014 HansaWorld Ireland Limited, Dublin, Ireland Preface
More informationBusiness Plan. (Not required if you have already prepared a formal business plan using another format)
(Not required if you have already prepared a formal business plan using another format) IF SPACE PROVIDED IS INSUFFICIENT PLEASE ATTACH A SEPARATE SHEET. 1. Business Profile Company Name Company Telephone
More informationProgramming Technique 1 Assignment 2
Programming Technique 1 Assignment 2 Question 1: Write a program that implement the day of the week in a program. The program should be able to perform the following operations: Set the day. Print the
More informationCROSSDOCKING: SCHEDULING OF INCOMING AND OUTGOING SEMI TRAILERS
CROSSDOCKING: SCHEDULING OF INCOMING AND OUTGOING SEMI TRAILERS 1 th International Conference on Production Research P.Baptiste, M.Y.Maknoon Département de mathématiques et génie industriel, Ecole polytechnique
More informationChapter 7 Condensed (Day 1)
Chapter 7 Condensed (Day 1) I. Valuing and Cost of Goods Sold (COGS) II. Costing Methods: Specific Identification, FIFO, LIFO, and Average Cost III. When managers use FIFO, LIFO, and Average Cost IV. LowerofCostorMarket
More informationAdvertising 133. Nontaxable advertising services
www.revenue.state.mn.us Advertising 133 Sales Tax Fact Sheet 133 Fact Sheet Nontaxable advertising services Minnesota Rule 8130.9250, Advertising, is the basis for this fact sheet. The guidelines in the
More informationLinear Programming. 1 Goals and Agenda. Management 560: Management Science. Tuesday, March 17, 2009
Linear Programming Management 560: Management Science Tuesday, March 17, 2009 1 Goals and Agenda Learning Objective Learn how to formulate optimization problems with constraints (linear programming problems).
More informationABC Company Recommended Course of Action
ABC Company Recommended Course of Action ABC Company has been utilizing Vantage by Epicor for several months. During the monthly close for November 1999, it was discovered that the G/L accounts for inventory,
More informationAUTOMATE AND ACCELERATE YOUR ENTIRE FUEL SUPPLY CHAIN MANAGEMENT PROCESS
AUTOMATE AND ACCELERATE YOUR ENTIRE FUEL SUPPLY CHAIN MANAGEMENT PROCESS Adjust to market changes in real time, maximize margins, save time and increase customer satisfaction with Axxis fuel management
More informationBusiness Plan Template (For a Startup Business)
Business Plan Template (For a Startup Business) Your Business Name ABN Number Address Line 1 Address Line 2 City, State Postcode Telephone Fax EMail 1/15 Table of Contents Table of Contents... 2 Executive
More informationWe consider a distribution problem in which a set of products has to be shipped from
in an Inventory Routing Problem Luca Bertazzi Giuseppe Paletta M. Grazia Speranza Dip. di Metodi Quantitativi, Università di Brescia, Italy Dip. di Economia Politica, Università della Calabria, Italy Dip.
More informationFinancial Transfer Guide DBA Software Inc.
Contents 3 Table of Contents 1 Introduction 4 2 Why You Need the Financial Transfer 6 3 Total Control Workflow 10 4 Financial Transfer Overview 12 5 Multiple Operating Entities Setup 15 6 General Ledger
More informationCEBU CPAR CENTER. M a n d a u e C I t y
Page 1 of 9 CEBU CPAR CENTER M a n d a u e C I t y AUDITING PROBLEMS AUDIT OF INVENTORIES PROBLEM NO. 1 The Pasay Company is a wholesale distributor of automobile replacement parts. Initial amounts taken
More informationBioPharma A Global Supply Chain Network
BioPharma A Global Supply Chain Network Executive Summary We have analyzed the supply chain of BioPharma with respect to the costs incurred to meet the global demand. The report finds that the current
More informationVector Pipeline L.P. Original Sheet No. 30 FERC Gas Tariff First Revised Volume No. 1 v0.0.0 RATE SCHEDULE FT1 FIRM TRANSPORTATION SERVICE
Vector Pipeline L.P. Original Sheet No. 30 1. AVAILABILITY RATE SCHEDULE FT1 FIRM TRANSPORTATION SERVICE This FT1 Rate Schedule is available to any party (hereinafter called "Shipper"), for firm transportation
More informationPlanning Optimized. Building a Sustainable Competitive Advantage WHITE PAPER
Planning Optimized Building a Sustainable Competitive Advantage WHITE PAPER Planning Optimized Building a Sustainable Competitive Advantage Executive Summary Achieving an optimal planning state is a journey
More informationSelling Price 60 Direct material 28 Direct Rs. 3 p. hr. 12 Variable overheads 6 Fixed cost (Total) 1,05,500
Question 1 (a) PAPER 5 : ADVANCED MANAGEMENT ACCOUNTING Answer all questions. Working notes should form part of the answer. E Ltd. is engaged in the manufacturing of three products in its factory. The
More informationChapter 12 Textbook Summary Notes Marketing Channels Delivering Customer Value
Chapter 12 Textbook Summary Notes Marketing Channels Delivering Customer Value The supply chain consists of upstream and downstream partners Upstream from the company is the set of firms that supply the
More informationChapter 4. Models for Known Demand
Chapter 4 Models for Known Demand Introduction EOQ analysis is based on a number of assumptions. In the next two chapters we describe some models where these assumptions are removed. This chapter keeps
More informationUse an Excel spreadsheet to solve optimization problems
Math 19 Project 4 (Work in groups of two to four.) Linear Programming Names Use an Excel spreadsheet to solve optimization problems Example 1: The Solar Technology Company manufactures three different
More informationa) Measures are unambiguous quantities, whereas indicators are devised from common sense understandings
Chapter1: QUANTITATIVE TECHNIQUES Self Assessment Questions 1. An operational definition is: a) One that bears no relation to the underlying concept b) An abstract, theoretical definition of a concept
More informationSEQUENCING & SCHEDULING
SEQUENCING & SCHEDULING November 14, 2010 1 Introduction Sequencing is the process of scheduling jobs on machines in such a way so as to minimize the overall time, cost and resource usage thereby maximizing
More information56:171 Homework Exercises  Fall 1993 Dennis Bricker Dept. of Industrial Engineering The University of Iowa
56:7 Homework Exercises  Fall 99 Dennis Bricker Dept. of Industrial Engineering The University of Iowa Homework # Matrix Algebra Review: The following problems are to be found in Chapter 2 of the text,
More informationPricing Decisions & Profitability Analysis
Pricing Decisions & Profitability Analysis Economic theory The optimum selling price is the price at which marginal revenue equals marginal cost. 1 Problems with applying economic theory 1. Difficult and
More informationCredit Card Marketing Classification Trees
Credit Card Marketing Classification Trees From Building Better Models With JMP Pro, Chapter 6, SAS Press (2015). Grayson, Gardner and Stephens. Used with permission. For additional information, see community.jmp.com/docs/doc7562.
More informationSage ERP X3 Distribution x2500
Distribution www.blytheco.com 1.800.425.9843 x2500 solutions@blytheco.com Distribution Sage ERP X3 distribution functionality is comprised of Sales, Purchasing, and Inventory. Sage ERP X3 Sales enables
More informationParwadi Moengin, Member IAENG
International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:16 No:5 23 Mathematical Model and Algorithm of Integrated ProductionInventoryDistribution System for Billet Steel Manufacturing
More informationA Bayesian Approach to Operational Decisions in Transportation Businesses
From: FLAIRS02 Proceedings Copyright 2002, AAAI (wwwaaaiorg) All rights reserved A Bayesian Approach to Operational Decisions in Transportation Businesses NilsPeter Andersson, Love Ekenberg and Aron
More information1). Fixed cost per unit decreases when:
1). Fixed cost per unit decreases when: a. Production volume increases. b. Production volume decreases. c. Variable cost per unit decreases. d. Variable cost per unit increases. 2). Prime cost + Factory
More informationSome network flow problems in urban road networks. Michael Zhang Civil and Environmental Engineering University of California Davis
Some network flow problems in urban road networks Michael Zhang Civil and Environmental Engineering University of California Davis Outline of Lecture Transportation modes, and some basic statistics Characteristics
More informationThe Product Lifecycle and the Marketing Strategy
The Product Lifecycle and the Marketing Strategy Enterprise & Project Management Please note that these slides are not intended as a substitute to reading the recommended text for this course. Objectives
More informationMOVING TERMINOLOGY VON PARIS MOVING TERMINOLOGY 1
MOVING TERMINOLOGY Movers have their own language. Learn how to speak that language with the Von Paris northamerican Moving Services Glossary of Moving Terms. Accessorial (additional) services services
More informationChapter 7. Process Analysis and Diagramming
Chapter 7 Process Analysis and Diagramming Chapter 5 introduced the concept of business process composition as an aspect of process design. But how can you recognize a process in a description of some
More informationService Level Agreement For Interconnect Paths
Service Level Agreement For Interconnect Paths 21/06/17 Version 3.0  Final 1 Version Control Version Status Update Effective Date 2.7 Document rebranded to open eir 16 th September 2015 V3.0 Final This
More informationeircom Service Level Agreement for Interconnect Paths
eircom Service Level Agreement for Interconnect Paths Document Control Document name Document Owner Document Type eircom Service Level Agreement for Interconnect Paths eircom ltd. Microsoft Word Last updated
More informationExcel Solver Tutorial: Wilmington Wood Products (Originally developed by Barry Wray)
Gebauer/Matthews: MIS 213 Handson Tutorials and Cases, Spring 2015 111 Excel Solver Tutorial: Wilmington Wood Products (Originally developed by Barry Wray) Purpose: Using Excel Solver as a Decision Support
More information1.224J/ESD.204J TRANSPORTATION OPERATIONS, PLANNING AND CONTROL: CARRIER SYSTEMS
1.224J/ESD.204J TRANSPORTATION OPERATIONS, PLANNING AND CONTROL: CARRIER SYSTEMS Professor Cynthia Barnhart Professor Nigel H.M. Wilson Fall 2003 1.224J/ ESD.204J Outline Signup Sheet Introductions Carrier
More informationEntrepreneurship. & the Economy. Section 2.1 Importance of. Entrepreneurship. in the Economy Section 2.2 Thinking Globally, Acting Locally CHAPTER
CHAPTER Entrepreneurship & the Economy Section 2.1 Importance of Entrepreneurship in the Economy Section 2.2 Thinking Globally, Acting Locally SECTION Importance of Entrepreneurship in the Economy OBJECTIVES
More informationAPPLIED A NEW METHOD FOR MULTIMODE PROJECT SCHEDULING
project, project scheduling, resourceconstrained project scheduling, projectdriven manufacturing, multimode, heuristic, branch and bound scheme, maketoorder Iwona PISZ Zbigniew BANASZAK APPLIED A
More informationAll NEMOs proposal for the price coupling algorithm and for the continuous trading matching algorithm, also incorporating TSO and NEMO proposals for
All NEMOs proposal for the price coupling algorithm and for the continuous trading matching algorithm, also incorporating TSO and NEMO proposals for a common set of requirements, in accordance with Article
More informationAdvanced Supply Chain Management (POM 625)  Lecture 1  Dr. Jinwook Lee
Advanced Supply Chain Management (POM 625)  Lecture 1  Dr. Jinwook Lee Topics of Lecture 1  Introduction  What is Supply Chain Management?  Issues of SCM  Goals, importance, and strategies of SCM
More informationLogistics Agreement CLAAS Group
CLAAS KGaA mbh Münsterstrasse 33 33428 Harsewinkel CLAAS Logistics The 6 Pillars of CLAAS Logistics Communication Supply Category Concept Transport Management Container Management Inventory Management
More informationWholesale Terms of Sale
Wholesale Terms of Sale Approval Process & First Order All orders are subject to corporate approval by The Thymes LLC, a Delaware limited liability company ( Thymes ). Opening Order Requirements Thymes
More informationBilling and Invoices. March 31, 2016 Version 2016 Release 1
March 31, 2016 Version 2016 Release 1 General Notices Sample Code NetSuite Inc. may provide sample code in SuiteAnswers, the Help Center, User Guides, or elsewhere through help links. All such sample code
More informationWHEN THE SMART GRID MEETS ENERGYEFFICIENT COMMUNICATIONS: GREEN WIRELESS CELLULAR NETWORKS POWERED BY THE SMART GRID
WHEN THE SMART GRID MEETS ENERGYEFFICIENT COMMUNICATIONS: GREEN WIRELESS CELLULAR NETWORKS POWERED BY THE SMART GRID Authors S. Bu, F. R. Yu, Y. Cai, and X. P. Liu IEEE Transactions on Wireless Communications,
More informationMaterial Requirements Planning (MRP) and ERP 14. Outline
Material Requirements Planning (MRP) and ERP 14 1 Outline Global Company Profile: Wheeled Coach Dependent Demand Dependent Inventory Model Requirements MRP Structure MRP Management 2 1 Outline  Continued
More informationACCOUNTING FOR PERPETUAL AND PERIODIC INVENTORY METHODS
ACCOUNTING FOR PERPETUAL AND PERIODIC INVENTORY METHODS Key Terms and Concepts to Know Merchandise Inventory: Merchandise Inventory (Inventory or MI) refers to the goods the company has purchased and intends
More informationINTEGRATING VEHICLE ROUTING WITH CROSS DOCK IN SUPPLY CHAIN
INTEGRATING VEHICLE ROUTING WITH CROSS DOCK IN SUPPLY CHAIN Farshad Farshchi Department of Industrial Engineering, Parand Branch, Islamic Azad University, Parand, Iran Davood Jafari Department of Industrial
More informationQuestion 2: How do we make decisions about inventory?
uestion : How do we make decisions about inventory? Most businesses keep a stock of goods on hand, called inventory, which they intend to sell or use to produce other goods. Companies with a predictable
More informationComedy Hour Inc. (Recommended Time: 90 minutes)
Comedy Hour Inc. (Recommended Time: 90 minutes) Shirley and Adam Whalen are the stars of the hit online podcast Comedy Hour. The show provides a weekly dose of topical satire that manages to be both thought
More informationMarketing Channels: Delivering Customer Value Chapter 12 BUS 101 WEEK 7
Marketing Channels: Delivering Customer Value Chapter 12 BUS 101 WEEK 7 1 Marketing Channels: Delivering Customer Value Topic Outline Supply Chains and the Value Delivery Network The Nature and Importance
More informationAnalysis of Electricity Markets. Lennart Söder
Analysis of Electricity Markets Lennart Söder Electric Power Systems Royal Institute of Technology March 2011 ii Contents 1 Basic electricity market modelling 1 1.1 Demand model...............................
More informationPAPER 5 : COST MANAGEMENT QUESTIONS
Decision Making  Profit Maximization PAPER 5 : COST MANAGEMENT QUESTIONS 1. ABC Co Ltd which produces household electronic gadget HIFY had 90% capacity utilization (4.5 lakh units) current year of Department
More informationWhy Businesses Love Payables Lockbox
Why Businesses Love Payables Lockbox (And Yours Should, Too!) A whitepaper examining how businesses can streamline accounts payable processing, reduce payment processing time, and lower accounts payable
More informationManage Your Own Company Business Game LIUC Cattaneo University
Manage Your Own Company Business Game LIUC Cattaneo University Player s Guide Initiative promoted by the University Carlo Cattaneo  LIUC in collaboration with the Regional School Office for Lombardy Versione
More information