2016 Exam 1 MW X Solutions_annotated
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Feb 20, 2024
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ISE 4204—Production Planning & Inventory Control Midterm 1 – Fall 2016, October 3 M/W Section Version X
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If questions arise, state your assumptions and continue to work the problem. •
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Use the pages provided to answer the questions unless otherwise given permission. Exam Hints: •
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1) Babak owns a candy shop that makes and sells ChocoPrez, chocolate covered pretzels. He forecasts the annual demand for ChocoPrez at 2500 units. To begin production the coating machine requires a cleaning and testing that takes one hour of labor. Production labor costs are $15/hour. The holding cost for a finished ChocoPrez is $0.25 per unit per year. Assuming a 250 day working year, answer the following questions: a) (5 points) What is the optimum number of units per production run? 547.7226 Solutions to all parts highlighted in the table below given lamda 2500 units annually Labor cost $15 per hour Set up time 1 hour h = $0.25 /part/year K = $15 per setup Q* = 547.7226 units/run runs/year = 4.564355 runs/year T* = 0.219089 years/run 2.629068 months/run Set up costs $ 68.47 holding costs $ 68.47 total $ 136.93 tau 2 weeks 0.038462 years R 96.15385 units For the remaining questions, answer under the assumption that the shop uses the optimum production run size found in part (a). b) (5 points) How many production runs will occur during the year? 547.7226
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c) (4 points) How often will a coating machine set-up occur? 0.219089 years/run 2.629068 months/run d) (4 points) What is the total annual average costs for set-up (ordering not purchasing)? Set up costs $ 68.47 e) (4 points) What is the total annual average costs for holding? holding costs $ 68.47 f) (6 points) The pretzels need to be ordered from a supplier before each production and it takes 2 days for the delivery. At what inventory level should the pretzel order be placed? R 96.15385 units
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2) Babak orders chocolate from a supplier in Belgium. Normally the cost for a case of chocolate is $50, but a quantity discount is provided by the manufacturer, and the cost for quantities over 200 cases or more is $40. Order cost is $25 per order, and the projected annual demand for chocolate is 500 cases of chocolate. Inventory carrying charge, as a percentage of cost, is 25%. a) (7 points) Assuming Babak wants to take advantage of the discount, what is the per unit cost, as a function of Q? 2000
𝑄𝑄
+ 40
b) (7 points) Again assuming he wants to take advantage of the discount, write out the cost equation he needs to minimize. (Include all appropriate values - The only variable should be Q). if Q>200 G(Q) = Setup + purchase + holding (25)(500)/Q (2000/Q+40)2500 (0.25)(2000/Q+40)
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3) (3 points) For the level aggregate plan, fluctuations in demand are absorbed by ______________________. Inventory (and backorders) 4) (3 points) What costs are considered in the finite production model in solving for Q*? a) annual ordering costs + annual holding costs b) annual purchasing costs + annual holding costs c) annual ordering costs + annual holding costs + annual shortage costs d) annual purchasing costs + annual ordering costs + annual holding costs e) ordering costs per order + annual holding costs 5) (3 points) What costs are considered in the quantity discount model to solve for Q*? a) annual ordering costs + annual holding costs b) annual purchasing costs + annual holding costs c) annual ordering costs + annual holding costs + annual shortage costs d) annual purchasing costs + annual ordering costs + annual holding costs e) ordering costs per order + annual holding costs 6) (3 points) In the Finite Production Model what is the expected time between the start of production runs? a) 𝐻𝐻
/
𝜆𝜆
b) 𝐻𝐻
/(
𝑃𝑃 − 𝜆𝜆
)
c) 𝐻𝐻
/
𝑃𝑃
d) 𝑄𝑄
/(
𝑃𝑃 − 𝜆𝜆
)
e) 𝑄𝑄
/
𝑃𝑃
f) 𝑄𝑄
/
𝜆𝜆
7) (3 points) In the Theory of Constraints five focusing steps, step 3 is to subordinate everything to the system’s bottleneck. Give one example of how Alex Rogo and his team performed this step in The Goal.
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8) Given the following sequence of dependent events below answer the questions: a. (3 points) If the bottleneck is Z, what problem is likely to occur if flow is not balanced? Build up of WIP before Z b. (3 points) State two ways you might balance and or improve the flow with the bottleneck at Z? Balance flow - Operate X, Y, and Z at same rate - X and Y at the bottleneck rate. Improve flow by balancing and improving the bottleneck through quality, efficiency, increase its capacity, etc. c. (3 points) If the bottleneck is X, what problem is likely to occur at Y and Z if flow is not balanced? Y and Z will be starved d. (4 points) Assume the following possible rates at each workcenter: X process 90 parts per hour, Y processes 75 parts per hour, Z processes 90 parts per hour, and Market Demand is 60 parts per hour. i. What should be the hourly output from the line? 60 parts ii. Assuming proper balance of line to flow, what percentage of the time should Z be operating? 60/90 = 67% X
Y
Z
Market Demand
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9) Consider a production facility with four resources, A,B,C, & D, manufacturing three products: P,Q, and R. Weekly market demand is noted at the top of the figure below. Assume that resources operate 5 days a week for 8-hour shifts; thus, all four resources are available for 2400 minutes a week. To ease your work on this problem, Table 1 is provided with the Minutes required on a resource for each product. Table 1: Resource Time per Product in Minutes Resource Product P Product Q Product R A 2 4 13 B 12 12 18 C 4 10 10 D 4 6 10 Raw Material Costs per Product $40 $40 $40 A) (15 points) Write the linear programming model that could determine the product mix to maximize profit. B) (15 points) Assuming Resource B is the bottleneck, what is the optimal product mix?
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Work page PROBLEM 1 2 3-7 8 9 TOTAL POINTS POSSIBLE 28 14 15 13 30 100 POINTS EARNED
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