# Logistics (System) Management

Logistics (System) Management

Take Home Questions (Part I)

1. Farm Supplies, Inc. sells water pumps. The annual demand for pumps is 600 units. The ordering cost is \$200 per order and the carrying cost is 20% of the unit price. Its supplier, North Manufacturing, offers discounts as shown in the following table

Order Quantity             Unit Price

Up to 99          \$150

100 up to 199 \$145

200 and more \$140

QA1. If the lowest price (\$140) WERE available to all units, what would the optimal order quantity (EOQ) have been?

QA2. Consider the next lower price (\$145/unit) and its related Break Point requirement (100 units or more). What will be the BEST order quantity for this price range (not necessarily the same as EOQ)? [Please make sure it is feasible.]

QA3. Based on this discount schedule, please demonstrate your calculations how you determine the total costs under those appropriate order quantities and relevant prices. What would the optimal order quantity that leads to the lowest total relevant costs (inventory carrying, order setup, and purchase costs) be?

QA4. The logistics manager at Lonestar Packing Company is considering freight consolidation program for serving the Kansas market. The program would involve the small-volume customers located in 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. Currently all orders are shipped LTL directly from Forth Worth, Texas to their destinations in Kansas. Average biweekly orders (one period) from the Kansas territory are as follows

 Average biweekly orders (# of cases) Weight (cwt) biweekly Weight (cwt) if Holding 2 Periods Weight (cwt) if Holding 3 Periods Hays 300 Manhattan 250 Salina 300 Great Bend 150

The average case weights 40 pounds. Orders could be (i) shipped in the biweekly period that they are received, (ii) held-and-shipped after two biweekly order periods, or (iii) 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 as

 Truck AQ* >= 100 cwt >= 200 cwt >= 400 cwt Hays 12.78 5.19 4.26 3.06 Manhattan 12.78 5.19 4.26 2.22 Salina 10.26 4.08 3.42 2.46 Great Bend 12.27 4.98 4.08 2.94

*Any quantity less than 10000 lb

Here, the logistics manager establishes the following spreadsheet table(s) to calculate the total transportation cost, total lost sales cost, total costs for each approach (including any additional holding period), and the average cost per period – an Excel hint file is also provided in HW-Preview for your convenience. Please complete your calculations in the hint file, and use that to answer the following questions. You should also attach your Excel printout when turning the answers here.

QB1. Using the Current Approach (i), what would the total weight (cwt) for order shipment from Fort Worth to Great Bend be?

QB2. Based on the (i) Current Approach, (applying the Break-Weight concept) the order shipment from Fort Worth to Hays should be declared as what weight and applied with what transportation rate (\$/cwt)?

QB3. Based on the (i) Current Approach, the transportation costs for order shipments from Fort Worth to Salina and Great Bend are respectively

QB4. Based on the (i) Current Approach, the Total transportation cost and Total Lost Sales Cost (only for those orders that need to be held beyond the current biweekly period) are respectively equal to?

QB5. Based on the (ii) Proposal 1 to Consolidate 1st Period Orders with 2nd period Orders before Shipping, what would the total weight for order shipment from Fort Worth to Hays be about?

QB6. Based on the (ii) Proposal 1 to Consolidate 1st Period Orders with 2nd period Orders before Shipping, the order shipment from Fort Worth to Hays should be declared as what weight and applied with what transportation rate (\$/cwt)?

QB7. Based on the (ii) Proposal 1 to Consolidate 1st Period Orders with 2nd period Orders before Shipping, the Total transportation cost and Total Lost Sales Cost (only for those orders that need to be held beyond the current biweekly period) are respectively equal to?

QB8. Based on the (iii) Proposal 2 to Consolidate 1st, 2nd, and 3rd period Orders before Shipping, the order shipment from Fort Worth to Salina should be declared as what weight and applied with what transportation rate (\$/cwt)?

QB9. Based on the (iii) Proposal 2 to Consolidate 1st, 2nd, and 3rd period Orders before Shipping, the Total transportation cost and Total Lost Sales Cost (only for those orders that need to be held beyond the current biweekly period) are respectively equal to?

QB10.  After comparing the Average Costs per Period for (i) Current Approach, (ii) Proposal 1, and (iii) Proposal 2, what would be the best option?

1. Short Answer: It is commonly understood that typically the inventory level is increasing with the customer service to be achieved. However, recently there is an industry emphasis on increasing customer service while reducing inventory investment simultaneously. Please explain the tools or approaches that could make this paradox possible by giving appropriate examples.

1. Alamo Automotive Company purchases two component parts from three different suppliers. No one suppler can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (FOB destination at Alamo, in price \$ per unit) are as follows:
 Component purchased from Supplier 1 from Supplier 2 from Supplier 3 1 \$12 \$13 \$14 2 \$10 \$11 \$10 Total capacity (units) 600 1000 800

Each supplier has limited capacity in total as demonstrated in the last row above, but as long as Alamo provides sufficient advance orders, each supplier can devote the limited total capacity to component 1, component 2, or any combination of the two components.

If Alamo’s production plan for the next period for the next period includes 1000 unites of component 1 and 800 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? What is total purchase cost for the components? You can address this Linear Programming problem in the following separate steps.

QD1. Please clearly define all decision variables.

D2. Using the variables defined, please give the objective function.

QD3. Please give the constraints for the problem.

QD4.  Please solve this linear programming problem using either Excel Solver or QM-for-Windows [by attaching your printout as well]. What would be the optimal purchasing plan, and the total purchase cost?

1. (Graduate Student only) The B&S Company manufactures small engines at three different plants. From the plants, the engines are transported to two different warehouse facilities before being distributed to three wholesale distributors. The per-unit manufacturing cost at each plant is shown in the following table in addition to the minimum required and maximum available daily production capacities, if each plant is ever used. It is NOT required to use all plants.

 Plant Mfg. Cost (\$/unit) Minimum Req’d Production (units) Maximum Production Capacity (units) 1 \$13 150 500 2 \$15 150 500 3 \$12 150 400

The unit cost of transporting engines from each plant to each warehouse is shown in the first three columns of following table, while the unit cost of shipping engines from each warehouse to each distributor is shown in the last four columns along with the daily demand for each distributor:

 From/to Warehouse1 Warehouse2 From/to Distrib.1 Distrib.2 Distrib.3 Plant 1 \$7 \$5 Warehouse1 \$8 \$5 \$7 2 \$3 \$4 Warehouse2 \$5 \$6 \$10 3 \$5 \$6 Demandà 300 units 600 units 100 units

Distributor 1 clearly states that they require “single-sourcing” – they would like to receive shipments from single warehouse only, not multiple warehouses. The transportation carrier serving the Plant1-Warehouse2 corridor requires that you ship either at least 150 units or nothing, due to the equipment utilization concern. The fixed (minimum) transport fee is \$800 for this corridor, on top of which the original \$/unit of transportation cost is levied. B&S would like to design a production and shipment plan to minimize the total manufacturing and shipment costs, while conforming to various capacity, demand, flow, and sourcing requirements above.

QE1. Please draw a network representation and clearly define all decision variables.

QE2. Using the variables defined, please give the objective function.

QE3. Please give the constraints for the problem.

QE4.  Please solve this integer linear programming problem using either Excel Solver or QM-for-Windows [by attaching your printout as well]. What would be the optimal production and shipment pattern, and the resulted total cost?

Hints for Questions D and E in Exam II – Part I (Linear and Integer Programming)

First, please take a look at the slides 4-17 of Chapter 6 lecture notes attached; and slides 23-27 of chapter 5.

You would see that the basic model set up of transportation problem in Chapter 6 could be applied to the purchasing problem (Question D) in the test.

Second, continuing from that to the transshipment model in Chapter 6, you would find the basic framework for Question E as well. Here you would need to define some continuous decision variables such as

Xij = units of product shipped from node i to node j.

However, to enforce single sourcing requirement, you would need to define one more TYPE of variables for whichever link involved, i.e.,

Yij = WHETHER to ship the product from node i to node j (1=yes, 0=no).

Third, following slides 23-27 of Chapter 5, you would need to implement the logical constraints to force Xij to satisfy the demand requirements at the destinations controlled by Yij, and use Yij to connect with each other, etc. For instance, if node j as a destination needs to be single-sourced from source nodes i=1,2,3, then:

Xij <= 1000000 * Yij   for i=1,2,3;  [I use 1000000 or any LARGE number, if that is a shipment quantity that Xij could never exceed]

Y1j + Y2j + Y3 j =1.

There might be a couple of other constraints that you need to include too.

Fourth, after you formulate the models for Questions D and E, please plug them into QM for Windows (the easiest), or Excel Solver (well, some Excel set up required). QM for Windows is available from
http://wps.prenhall.com/bp_taylor_introms_10/112/28870/7390752.cw/index.html
by clicking on QM-for-Windows.

You can click on Solve to get the optimal solutions.

Hope this helps.

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