MBA 6325 Decision Models for Supply Chain ManagersLinear Programming Case: A Production Problem at T

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MBA 6325 Decision Models for Supply Chain ManagersLinear Programming Case: A Production Problem at TS6 Fabricators Inc.Steven Coy, Ph.D.©2010-2015″I think that will do it. Thanks Mr. Bear. I will send the order in today. As always, it is a pleasuredoing business with you.” Helena Troya returned the phone to its cradle and leaned back in herchair smiling. In four years as Vice President of Marketing at TS6 Fabricators Inc., Helen hadnever had such a good month. She laughed and said to the empty room, “The economy must bemoving again. This is the fourth big order this month!” Helen mused for another moment andthen picked up the phone and punched in a familiar number.”Production scheduling. This is Francisco Pizaro.””Francisco! This is Helen. I just closed a deal with Bear industries for another big order.”Dead silence.”Francisco! Are you there?””Helen, you said big order?””Yes. Why?” Helen asked.”When is the deadline?” Francisco replied.Helen hesitated and then said, “Ninety days—just like the others. Francisco is somethingwrong?””No. Nothing is wrong, Helen. But, with the three orders that we already have, we are alreadynearly at capacity. We may have to outsource some of the order.”Helen thought for a moment and said, “That will be okay Francisco. I have enough margin builtinto the price to cover a substantial purchase.””Good. Then email me the order and I will see what I can do…And Helen…””Yes, Francisco?””Take it easy for the rest of the month. Okay?”Helen laughed and said, “No problem Francisco!”1TS6 Fabricators Inc.TS6 Fabricators, which is known in the business as TFab, is a large pipe manufacturer in the Houston,Texas metropolitan area. T-Fab is a publicly tradedcompany, which has been in the pipe fabricationbusiness for 75 years.T-Fab produces several types of steel pipe for theenergy and utility industries. All of their products aremade from rolled plate steel, which is then weldedinto 10 foot sections and assembled and welded intopipes up to 50 feet long. T-Fab’s products are shownin Table 1.The production process at T-Fab varies depending onthe product. Each product is produced from steelplate. Casings are manufactured from ½” plate, andRolled and welded (R&W) products are producedfrom 1″ or 1½” plate. Casings typically requirerolling, welding and visual inspection. R&W pipesrequire rolling, welding, visual inspection, x-rayinspection, sand blasting, and finishing. Longersections require additional assembly and welding.Radius casings are standard casings that are bent into10 or 20 foot radius arcs for curved assemblies.Mitered elbows are right angle assemblies of R&Wpipe that require cutting, straight and angle rolling,welding, visual inspection, x-ray inspection, sandblasting, and finishing.Part#106C206C206C10R206C20R1012C2012C2524RW5024RW5036RW5072RW5084RW24ME36ME72ME84MEDescription10′ x 6″ Casing20′ x 6″ Casing10′ Radius Casing20′ Radius Casing10′ x 12″ Casing20′ x 12″ Casing25′ x 24″ R&W Pipe50′ x 24″ R&W Pipe50′ x 36″ R&W Pipe50′ x 72″ R&W Pipe50′ x 84″ R&W Pipe24″ Mitered Elbow36″ Mitered Elbow72* Mitered Elbow84″ Mitered ElbowTable 1: TS6-Fabricators’ Product Line.The figures below illustrate how straight pipes are Figure 1: A 10′ capacity plate bending rolling machineassembled. The pipe labeled Cylinder 1 shows a pipe milling a steel plate. (http://www.bisewelding.com)up to 10 feet long. Plate steel is rolled in a large platebending rolling machine as shown in the picture in Figure 1. The two edges of the rolled plateare welded together to form a seam. The second figure illustrates how a longer pipe is assembledfrom smaller sections. The seams are staggered, which inhibits separation along the seam.Figure 2: Pipe assembly examples. Cylinder 1 is formed from a single steel plate. The pipe at right illustrateshow a longer pipe is formed. (Illustration from http://www.bisewelding.com)2Orders to be Completed 90 DaysHelena Troya has secured four orders for the next 90 days. The orders are shown in Table 2below.Product10′ x 6″ Casing20′ x 6″ Casing10′ Radius Casing20′ Radius Casing10′ X 12″ Casing20′ x 12″ Casing25′ x 24″ R&W Pipe50′ x 24″ R&W Pipe50′ x 36″ R&W Pipe50′ x 72″ R&W Pipe50′ x 84″ R&W Pipe24″ Mitered Elbow36″ Mitered Elbow72* Mitered Elbow84″ Mitered ElbowPart #106C206C206C10R206C20R1012C2012C2524RW5024RW5036RW5072RW5084RW24ME36ME72ME84METotal Sales RevenueBearIndustries???????????????HugoEnergy???????????????DR RileyDrilling???????????????BastibugWaterTreatment???????????????????Table 2: TS6-Fabricators Orders. All orders must be filled during the planning period. Note: ask your professor for your team’sversion of this table.Given the vast quantity of steelrequired to fill these orders and thelead time to resupply, T-Fab mustrely on material on hand to fill theseorders. Table 3 lists the amount ofplate steel required to produce oneunit of each product and the totalamount of steel on hand. T-Faborders plate steel in 10′ widths. Forassemblies that require differentsizes of plate (i.e., 25 foot pipes andmitered elbows), the plates must becut before rolling.Part #106C206C206C10R206C20R1012C2012C2524RW5024RW5036RW5072RW5084RW24ME36ME72ME84METotal Available0.5″ Plate????????????????1″ Plate????????????????1.5″ Plate????????????????Table 3: Steel requirements for each product and total amount of each type ofplate steel on hand. All values are in square feet. Note: ask your professor foryour team’s version of this table.3As with raw materials, plant capacity is limited. Each department has a fixed amount of free timein the next 90 days. The total time available (in hours) and the processing time requirements ofeach product (in minutes) are shown in Table 4 below.Part #106C206C206C10R206C20R1012C2012C2524RW5024RW5036RW5072RW5084RW24ME36ME72ME84MEHoursAvailablePlateCutting???????????????Rolling???????????????Bending???????????????Assembly???????????????Welding???????????????Sandblasting???????????????Finishing???????????????VisualInspection???????????????X-rayInspection????????????????????????Table 4: Processing time (minutes) required in each department and total number of hours available during the planning period.Note: ask your professor for your team’s version of this table.Depending on the data, it is quite possible that plantproduction capacity and available plate steel will beinsufficient to meet demand. Therefore, Francisco contactedMidnight Manufacturing, which is a Houston-area pipefabricator, to produce product that T-Fab will be unable tomanufacture. Francisco is confident that Midnight has thecapacity to assume as much of the order as necessary. Withthe exception of radius casing and mitered elbows, Midnightis able to produce modest quantities of all of T-Fab’sproducts, they have similar standards of quality to T-Fab,and they have been very reliable in the past. Unfortunately,this reliability comes at a price. Product costs will beconsiderably higher than if T-Fab produced the productsthemselves. Table 5 contains the cost to manufacture andpurchase each product. Note: material and labor costs areincluded in the costs shown in the second column of thetable.Part #106C206C206C10R206C20R1012C2012C2524RW5024RW5036RW5072RW5084RW24ME36ME72ME84MEProduce$512$925$650$1,039$1,428$1,817$2,206$2,595$2,984$3,373$3,762$4,151$4,540$4,929$5,318PurchasefromMidnight$640$1,156$1,785$2,271$2,758$3,244$3,730$4,216$4,703Table 5: Product manufacturing and purchasecosts.4In the past, Francisco has relied on an in-house team of operations and supply chainprofessionals to develop a production schedule when some of the product must be outsourced.As he has done in the past, he has decided to call on your team to develop a plan. He sent thefollowing email to your team leader this morning.From: Francisco Pizaro [mailto:Francisco.Pizaro@TS6.com]Sent: Tue 9/7/2010 3:21 PMTo: MS Team Leader [mailto: MSTeam.Leader@TS6.com]Cc: Helen TroyaSubject: 90 Day PlanTeam,By now I am sure you know that T-Fab’s success in the sales office has resulted in a schedulingproblem for us. I am relying on you to determine what products we should make in house andwhat products we should outsource. Please refer to the tables in the attached document[Francisco is referring to Tables 1-5 above] when formulating your linear program.As before, I would like you to set up a model in Excel and use Solver to find the appropriatedivision of products between us and Midnight Pipe Manufacturing. Once you have set up themodel, please answer the questions below.Questions1. How much of each product should T-Fab produce in house, and how much should weoutsource to Midnight?2. What is the expected profit from this decision?3. What is the additional cost from outsourcing?4. Which of our resources (material and/or capacity) are constraining our ability to produceeverything in house?5. Think outside the box. Is there a better way to solve this problem? Am I missingsomething? [Note: this question asks you to consider the problem from a freshperspective. You should not change any of your preceding analysis. Instead, youranswer should be framed as advice for future order cycles.]Thanks!FranciscoFrancisco PizaroDirector of Production SchedulingTS6 Fabricators Inc.8512 Nonesuch DriveHouston, TX 770025