# IE 652 PRODUCTION PLANNING AND CONTROL Assignment #1 ...

IE 652 PRODUCTION PLANNING AND CONTROL Assignment #1 ...

IE 652 PRODUCTION PLANNING AND CONTROL Assignment #1 ...

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<strong>IE</strong> <strong>652</strong> <strong>PRODUCTION</strong> <strong>PLANNING</strong> <strong>AND</strong> <strong>CONTROL</strong><strong>Assignment</strong> <strong>#1</strong> (Due date: 04.08.2010)1. The Skatz company has forecast demand for in-line skates to be 56, 84, 108, and 59 casesfor the next four quarters. There is an initial inventory of 20 cases, and it costs $5 permonth to hold a case in inventory. Customers will backorder, but there is a loss-of-goodwillcost of $15 per case to delay demand for one quarter. Production costs are as follows:Quarter 1 2 3 4Internal capacity 60 70 60 55Subcontracting capacity 40 40 40 40Internal prod. Cost $/case 20 21 23 22Subcontracting costs $/case 22 28 30 28a) Find a feasible initial plan using transport model least cost approach.b) Develop a mathematical model.2. A manufacturer producing a single product having a seasonal demand is faced withdecisions about production levels, work force size, and overtime during a planning horizonof six weeks. His capacity is determined by his work force level, which presently is 100people, each working a 40-hour work week. Overtime, up to eight hours a week per man ispossible. Labour costs average $5 per hour, resulting in an overtime rate of $7.5 per hour. Ittakes 6.0 man hours to produce a unit of product. Product costs other than labour are $50per unit. The cost to carry a unit of inventory for one week is 40 cents. Shortages arebackordered at an estimated cost of $1 per unit per week: however, company policy is tofill all orders within a two week period. Costs to change work force are based on anestimated $240 to hire and train a worker and $180 to lay off a worker. Estimatedrequirements by week are 650,700,800,900,800, and 700 units. The current inventory levelis 50 units. Formulate this program as a linear programming model, assuming that newworkers are able to produce at 100 percent effectiveness in the period they are hired.3. Harriet is the purchasing manager for High-Tech Company. She is faced now with thefollowing decision situation. Her operation uses 10,000 units a year of copper cableconnectors. She knows that it can be manufactured internally at the rate of 100,000 unitsper year and at a cost of $40 per unit. However, associated with each production run thereis a set-up cost of $5000, and the annual inventory holding cost is i= 20 percent.Harriet decided to get a price from two external suppliers. Hardware Company offered aprice of $44 per unit and no fixed cost of ordering, provided that the minimum quantityshipped is 1000 units; they could supply 6000 units per year. Metstamp Company fixedthe price of $43.5 per unit, with a fixed cost of $200 per shipment, regardless of thequantity; they could supply up to 4000 units per year. Harriet must decide whetherpurchase required items from these two suppliers or manufacture them inside thecompany. What is the optimal policy Harriet should use to minimize the total annual cost?Assume that no shortages are allowed.4. Consider the case of finite replenishment rate in which backlog is not allowed. During td,the machine is idle. Suppose the cost of idle time is cd dollars per unit time (as themachine can be used to manufacture other products). Develop an equation for Q* thatyields minimum average total cost that includes idle time cost.

5. The time-phased net requirements for the base assembly in a table lamp over the next sixweeks areWeek 1 2 3 4 5 6Requirements 335 200 140 440 300 200The setup cost for the construction of the base assembly is $200, and the holding cost is$0.30 per assembly per week.a) Determine the lot sizes using the Silver-Meal Method.b) Determine the lot sizes using the Wagner-Whitin Method.6. For the given table below, solve the problem with Wagner-Whitin algorithm?Week 1 2 3 4 5 6Demand 75 150 20 25 100 120Order cost 80 80 80 100 100 100Cost per unit 4 4 5 5 6 6Hoolding cost 1 1 1 2 2 2