The Job Shop GameWhat is a Job Shop?A Simple Job ShopSlide 4The Playing CardsThe Four Product typesThe PlaySlide 8Slide 9Calculating Flow DaysRecord KeeperTraditional Results for Scatter Plot and Histogram (first Game)Second Game. Play again juggling the release order using the best schedule you can find.Third Game DBR in the Job ShopWashington State University’s Engineering Management Program http://www.engrmgt.wsu.edu/© Washington State University-2010 1Engineering Management Tidbits! [email protected]://www.en grmgt.wsu. edu/James R. Holt, Ph.D., PEProfessorEngineering ManagementThe Job Shop GameSolving the NP Complete Scheduling Problem© Washington State University-2010 2What is a Job Shop?•Say you have a shop that makes machine parts. Many, many types of machine parts. You could have 50-100 machines and produces 2000 different parts. •Each part takes a different route through the machine shop using different machines in different order. Some are drilled first. Some are milled first. Some are cut, polished, ground. Others are not. Some are turned, taped, threaded. Some are not. •Big parts take longer than small parts. Simple parts take shorter paths than complex parts.•The algorithm to solve such a complex scheduling problems is called “NP complete.” That is, the number of computations needed to find the optimal schedule is estimated to be some number raised to the n power where n is the number of tasked to schedule. You could do the math or simulate the system to find an answer. But, it is faster to do the work than to calculate the optimal schedule.•Operations Researchers love to talk about Job Shop schedules, but never solve them. I know, I’m one. So, I invented a Job Shop Game.© Washington State University-2010 3A Simple Job Shop•Consider a simple shop with four operations: A, B, C, D and four products P1, P2, P3, P4.•Each product flows through four processes but not the same ones or in the same orderADBCIn OutP1P2P4P3P1 goes: A->B->C->D OutP3 goes: A->C->D->B OutP2 goes: B->C->B->D OutP4 goes: A->B->B->C Out© Washington State University-2010 4The Job Shop Game•Let’s use this simple Job Shop and develop our intuition about such processes.•Here are some world wide web links to detailed instructions about playing this game:Video InstructionInstructions Playing CardsBlank Recording Sheets (may look funny but prints fine)•I’ll explain a bit about the game in the next few slides.ADBCIn OutP1P2P4P3© Washington State University-2010 5The Playing Cards•Here is a typical order card. This one is for Product 4. •On the left is the Routing path (first to A, then to B, and then return to B for a second operation, then to C and out).•At the top is the Release Day line. On this line the Gate Keeper records the date the order was released to the shop floor.•Each operation has a box to write the date their process was completed.•Flow time is the last operation completion date minus release date.© Washington State University-2010 6The Four Product types•There are four on one page at Playing Cards•Print out 5+ copies of the Playing Card page for each game. Cut out the order cards. You should have at least 20 cards (equal numbers of P1, P2, P3, P4)•For the first game, shuffle the 20 cards.•We will be playing the game until all the order cards are processed (just short of 35 days for 20 cards).© Washington State University-2010 7The Play•You need these people: Assign a Gate Keeper, a person for each operation (A, B, C, D) and a Recorder.(Hard to do alone, but you could)•Each operation can perform a maximum of one operation per day. The operation is documented by writing the date in the appropriate Routing Box•The Gate Keeper holds the shuffled stack of Order Cards. Each day, the Gate Keeper writes the day on the Release Day line and calls out loud the day (so the operations will know which number to write).© Washington State University-2010 8The Play•After the operator writes a date in the Routing Box (or the Gate Keeper releases the Order Card) the order advances to the next operation where it waits for the next day (or longer) to be completed.• The routing must be followed and each Order only receives one operation per day. •Each operator can only write a number if they have an Order Card that needs their operation on that day.•Sounds complicated, but its not. I’ll show you a couple of days.ABCDStart FinishProduct #1ABCDStart FinishProduct #2ABCDStart FinishProduct #3ABCDStart FinishProduct #4© Washington State University-2010 9The PlayAssume the first card in the shuffled deck is Product 2. As the play starts, the Gate Keeper calls out loud, “Day 1” and writes a “1”. No one else has work.1Assume the second card in the deck is Product 3. As the play starts, the Gate Keeper calls out loud, “Day 2” and writes a “2” on the Product 3 Card.2On Day 2, Operation B can work and writes a “2”.2“Day 3,” the Gate Keeper calls out and writes on a Product 1 Order Card.3On Day 3, both Operation C and A have work.33The Gate Keeper releases one card per day until the Order Cards are gone.© Washington State University-2010 10Calculating Flow Days•On Day 5 (or maybe 6) the first job will finish and come to the recorder. •The recorder subtracts the Release Day from the Last Operation to calculate the total flow days for the Product.•Here, Product #4 was released on Day 4, finished A on day 5, finished first B on day 9, finished second B on day 10, finished C on day 12.•The flow days then are 12-4=8days•The flow days number is recorded on two charts45910128© Washington State University-2010 11Record KeeperOn the left are two charts (turned to be on this page--so tilt your head).The top chart (left most) is a scatter plot of the Day Released versus Flow days. There is one Order released each Day. Put an X for the flow days are for each completed order.xThe second chart (right most) is a histogram of the number of times a particular flow day occurred. I’ll but an ‘x’ for the first 8 flow days. There will probably be many orders with 8 flow daysx© Washington State University-2010 12Traditional Results for Scatter Plot and Histogram (first Game)21 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3617 18 19 201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3617 18 19