The Ohio Truck Company produces two models of trucks at its factory…

Question Answered step-by-step The Ohio Truck Company produces two models of trucks at its factory… The Ohio Truck Company produces two models of trucks at its factory in Columbus, Ohio: larger trucks (the Warrior model) and small trucks (the Chomper model). The factory can produce only one type of truck every month, and so the production-planning department needs to determine which model and how many of that model to produce each month. If the plan switches from producing one model one month to the other model the next month, they incur a switchover cost of $15 million. Historically, the demand for both models has fluctuated significantly over the calendar year. It is now December, and the end-of-December inventory of trucks is expected to be 50 thousand Warrior models and 50 thousand Chomper models. The forecasted demand for the Warrior and the Chomper models for the next twelve months is given here:MonthWarrior Demand (in 1,000s)Chomper Demand (in 1,000s)January (i=1)3442February (i=2)3945March (i=3)4046April (i=4)3138May (i=5)3036June (i=6)3343July (i=7)3242August (i=8)4141September (i=9)4044October (i=10)3847November (i=11)4148December (i=12)4046 The variable unit production cost for the first six months of next year is expected to be $7,000 for the Warrior Model and $6,000 for the Chomper Model. It is expected that these costs will increase by 10% after the first six months of next year due to anticipated higher labor costs under a new union contract. The factory can produce up to 100 thousand Warrior models each month, or up to 110 thousand  Chomper models each month. The unit storage cost per month is $700 per truck for the Warrior and $600 per truck for the Chomper. Let Wi denote the integer number of Warrior trucks (in thousands) to produce in month i=1,…,12 and let Ci denote the integer number of Chomper trucks (in thousands) to produce in month i=1,…,12. Let Xi be a binary variable that is 1 if Warrior trucks are produced in month i, and 0 if Warrior Trucks are not produced. Let Yi be a binary variable that is 1 if Chomper trucks are produced in month i, and 0 if Chomper Trucks are not produced. Let IWi denote the inventory of Warrior trucks at the end of month i, and let ICi denote the inventory of Chomper trucks at the end of month i.  a) Write the linear inventory balance constraints for both the Warrior and Chomper trucks for the end of March and April (i=3,4). b) Write linear constraints that ensure that at most one model type is produced during June (i=6). Hint: It is easiest to write three constraints. c) Let Si denote a binary variable that equals 1 if the type of truck produced in month i is different than the truck produced in the previous month i-1; Si equals 0 if the truck produced in month i is the same as that produced in the previous month i-1. Write linear constraints that enforce the definition of the Si variable for September (i=9). Hint: It is easiest to write two constraints. d) Write a linear expression for the cost incurred during July (i=7).  Engineering & Technology Industrial Engineering Supply Chain Management QMETH 450 Share QuestionEmailCopy link Comments (0)